An Introduction to Text Analysis

DDD: Elements of Statistical Machine Learning & Politics of Data

Ayush Patel

At Azim Premji University

08 Mar, 2026

Hello

I am Ayush.

I am a researcher working at the intersection of data, development and economics.

I am a RStudio (Posit) certified tidyverse Instructor.

I am a Researcher at Oxford Poverty and Human development Initiative (OPHI), at the University of Oxford.

Hello (Eh bonjour– donc–.) by Charles Motte

Did you come prepared?

You have installed R. If not see this link.
You have installed RStudio/Positron/VScode or any other IDE. It is recommended that you work through an IDE
You have the libraries {tidytext} {sentimentr} {quanteda} {magrittr} {topicmodels} {ldatuning} {keras} {recipes} {textrecipes} installed

Armor (Gusoku) Helmet signed by Bamen Tomotsugu

Before NLP and Text Analysis

One needs to know how to mine, warngle, and manipulate text data.

tidy priciples can make this task easy (relatively)

“Treating text as data frames of individual words allows us to manipulate, summarize, and visualize the characteristics of text easily and integrate natural language processing into effective workflows…”

We do this using the {tidytext} along with other know methods

Tidy Data

As described in Wickham 2014

Each variable is a column.
Each observation is a row.
Each type of observational unit is a table.

Tidy Text

As described by Silge and Robinson 2017

A table with one-token-per-row
token: A meaningful unit of text. (word,sentence,etc)
There are other forms of text data structures: string, corpus, document-term matric. (more on this later)

Tokens

“A token is a meaningful unit of text, most often a word, that we are interested in using for further analysis, and tokenization is the process of splitting text into tokens.”

Unnesting Tokens

We need to get the text in one-token-per-row to acheive the Tidy Text format. This can be dome by the unnest_tokens() function from {tidytext}

text <- c("Because I could not stop for Death -",
          "He kindly stopped for me -",
          "The Carriage held but just Ourselves -",
          "and Immortality")

text

[1] "Because I could not stop for Death -"  
[2] "He kindly stopped for me -"            
[3] "The Carriage held but just Ourselves -"
[4] "and Immortality"

Unnesting Tokens

Notice any punctuations?

# A tibble: 20 × 2
     row word       
   <int> <chr>      
 1     1 because    
 2     1 i          
 3     1 could      
 4     1 not        
 5     1 stop       
 6     1 for        
 7     1 death      
 8     2 he         
 9     2 kindly     
10     2 stopped    
11     2 for        
12     2 me         
13     3 the        
14     3 carriage   
15     3 held       
16     3 but        
17     3 just       
18     3 ourselves  
19     4 and        
20     4 immortality

Unnesting Tokens

Tokens can be sentences, characters, lines, paragraphs, or a regex pattern

Not all words are useful. We can remove stop words

The RBI MPC minutes

See a sample here

identifier	lines
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	2. The meeting was chaired by Shri Sanjay Malhotra, Governor and was attended
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	by all the members – Dr. Nagesh Kumar, Director and Chief Executive, Institute for
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Studies in Industrial Development, New Delhi; Shri Saugata Bhattacharya, Economist,
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Mumbai; Professor Ram Singh, Director, Delhi School of Economics, Delhi; Dr.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Poonam Gupta, Deputy Governor in charge of monetary policy and Shri Indranil
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Bhattacharyya, Executive Director (the officer of the Reserve Bank nominated by the
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Central Board under Section 45ZB(2)(c) of the Reserve Bank of India Act, 1934).
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	3. According to Section 45ZL of the Reserve Bank of India Act, 1934, the Reserve
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Bank shall publish, on the fourteenth day after every meeting of the Monetary Policy
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Committee, the minutes of the proceedings of the meeting which shall include the
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	following, namely:
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	(a) the resolution adopted at the meeting of the Monetary Policy Committee;
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	(b) the vote of each member of the Monetary Policy Committee, ascribed to such
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	member, on the resolution adopted in the said meeting; and
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	(c) the statement of each member of the Monetary Policy Committee under sub-
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	section (11) of section 45ZI on the resolution adopted in the said meeting.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	4. The MPC reviewed in detail the staff’s macroeconomic projections, and
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	alternative scenarios around various risks to the outlook. The MPC also reviewed the
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	surveys conducted by the Reserve Bank to gauge consumer confidence, households’
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	inflation expectations, corporate sector performance, credit conditions, the outlook for
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	the industrial, services and infrastructure sectors, and the projections of professional
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	forecasters. Drawing on the above and after extensive discussions on the stance of
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	monetary policy, the MPC adopted the resolution that is set out below.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Resolution
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	5. The Monetary Policy Committee (MPC) held its 59th meeting from February 4
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	to 6, 2026, under the chairmanship of Shri Sanjay Malhotra, Governor, Reserve Bank
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	of India. The MPC members Dr. Nagesh Kumar, Shri Saugata Bhattacharya, Prof.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Ram Singh, Dr. Poonam Gupta and Shri Indranil Bhattacharyya attended the meeting.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	6. After a detailed assessment of the evolving macroeconomic and financial
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	developments and the outlook, the MPC voted unanimously to keep the policy repo
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	rate under the liquidity adjustment facility (LAF) unchanged at 5.25 per cent.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Consequently, the standing deposit facility (SDF) rate remains at 5.00 per cent and
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	the marginal standing facility (MSF) rate and the Bank Rate remains at 5.50 per cent.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	The MPC also decided to continue with the neutral stance.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Growth and Inflation Outlook
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	7. The global economy showed remarkable resilience in 2025, aided and
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	supported by trade front-loading, a milder-than-anticipated impact of tariffs, broad
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	fiscal stimulus and accommodative monetary policy. Inflation is on a path of gradual
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	decline, although it remains above target in several advanced economies. US yields
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	are trading with an upward bias amidst receding expectations of imminent rate cuts
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	underpinned by firm economic data. Equities, supported by sustained investment in
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	tech stocks, have advanced, even as fiscal strains, geopolitical uncertainty and
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	monetary policy divergence continue to impart volatility to financial markets.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	8. On the domestic front, real gross domestic product (GDP), as per the First
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Advance Estimates (FAE), is estimated to grow at 7.4 per cent (y-o-y) in 2025-26.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Private consumption and fixed investment contributed significantly to overall growth.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Net external demand, however, continued to be a drag, with imports outpacing
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	exports. On the supply side, real GVA growth of 7.3 per cent is driven by buoyant
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	services sector, resilient agricultural sector and revival in manufacturing activity.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	9. Looking ahead, sustained buoyancy in services sector, GST rationalisation,
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	healthy rabi prospects, monetary easing and benign inflation environment should
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	support private consumption. Investment activity, supported by high capacity
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	utilisation, conducive financial conditions, healthy balance sheets of financial
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	institutions and corporates, robust credit growth and Government’s continued thrust
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	on capital expenditure, is expected to maintain its momentum. Moreover, robust
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	domestic demand is likely to attract fresh investments by the private sector. While
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	services exports are expected to remain strong, merchandise exports will get a boost
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	from the prospective trade deal with the US. The landmark comprehensive trade pact
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	with the European Union coupled with trade deals with New Zealand and Oman
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	should help diversify exports and strengthen the external sector. On the other hand,
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	headwinds from geopolitical tensions, uncertain global trade environment, volatility in
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	global financial markets and international commodity prices continue to pose downside
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	risks to the outlook. Taking all these factors into consideration, real GDP growth
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	projections for Q1:2026-27 and Q2 are revised upwards to 6.9 per cent and 7.0 per
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	cent, respectively (Chart 1). 1 The risks are evenly balanced.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	10. Headline CPI inflation remained low at 0.7 per cent in November and 1.3 per
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	cent in December, 2025. While food group continued to be in deflation, inflation within
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	the fuel group remained moderate in November and December. Core inflation (CPI
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	excluding food and fuel) too remained benign, despite the pick-up in prices of precious
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	metals. Excluding gold, core inflation remained stable at 2.6 per cent in December.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Projections for full year 2026-27 will be set out in the Monetary Policy Resolution to be announced in April 2026 after
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	incorporating the new GDP and CPI series (base 2024=100) to be released on February 27 and February 12, 2026, respectively.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	11. Near-term outlook suggests that food supply prospects remain bright on the
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	back of healthy kharif production, adequate buffer stocks of foodgrains and favourable
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	rabi sowing. Core inflation, barring potential volatility induced by prices of precious
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	metals, is expected to be range-bound. Geopolitical uncertainty coupled with volatility
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	in energy prices and adverse weather events are other possible upside risks to
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	inflation. In terms of headline inflation trajectory, unfavourable base effects stemming
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	from large decline in prices observed in Q4:2024-25 would lead to an uptick in y-o-y
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	inflation in Q4:2025-26, despite the anticipated momentum being muted. Considering
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	all these factors, CPI inflation for 2025-26 is now projected at 2.1 per cent with Q4 at
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	3.2 per cent. CPI inflation for Q1:2026-27 and Q2 are projected at 4.0 per cent and
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	4.2 per cent, respectively (Chart 2). Excluding precious metals, the underlying inflation
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	pressures remain muted. The risks are evenly balanced.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Rationale for Monetary Policy Decisions
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	12. The MPC noted that since the last policy meeting, external headwinds have
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	intensified though the successful completion of trade deals augurs well for the
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	economic outlook. Overall, the near-term domestic inflation and growth outlook remain
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	positive.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	13. Headline inflation during November-December remained below the tolerance
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	band of the inflation target. The outlook for CPI inflation in Q1:2026-27 and Q2
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	continues to be benign and near the inflation target. The slight upward revision in the
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	inflation outlook is primarily due to increase in prices of precious metals, which
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	contribute about 60-70 basis points. The underlying inflation continue to be low.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	14. On the growth front, economic activity remains resilient. The First Advance
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Estimates suggest continuing growth momentum, driven by domestic factors amidst a
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	challenging external environment. The growth outlook remains favourable.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	15. Based on a comprehensive review of the domestic macroeconomic conditions
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	and the outlook, the MPC is of the view that the current policy rate is appropriate.
Minutes of the Monetary Policy Committee Meeting, February 4 to 6, 2026	Accordingly, the MPC voted to continue with the existing policy rate. The MPC also

The RBI MPC minutes

Unnest tokens to get tidytext format

mpc_minutes |>
  mutate(
    identifier = str_remove(identifier,".{1,}ting|.{1,}ting,")
  ) |>
  unnest_tokens(output = word,input = lines)  -> mpc_minutes_unnested

mpc_minutes_unnested

# A tibble: 417,226 × 2
   identifier              word    
   <chr>                   <chr>   
 1 , February 4 to 6, 2026 2       
 2 , February 4 to 6, 2026 the     
 3 , February 4 to 6, 2026 meeting 
 4 , February 4 to 6, 2026 was     
 5 , February 4 to 6, 2026 chaired 
 6 , February 4 to 6, 2026 by      
 7 , February 4 to 6, 2026 shri    
 8 , February 4 to 6, 2026 sanjay  
 9 , February 4 to 6, 2026 malhotra
10 , February 4 to 6, 2026 governor
# ℹ 417,216 more rows

The RBI MPC minutes - removing stop words

You can choose which stop words to remove

mpc_minutes_unnested |>
  anti_join(stop_words |>
  filter(!word %in% c("yes","no"))) -> mpc_minutes_unnested

The RBI MPC Minutes - Word freq

Notice any problems?

mpc_minutes_unnested |>
  count(word, sort = T)

# A tibble: 9,402 × 2
   word          n
   <chr>     <int>
 1 inflation  5757
 2 growth     3630
 3 cent       3363
 4 policy     3101
 5 rate       2340
 6 prices     1793
 7 monetary   1636
 8 food       1402
 9 demand     1327
10 global     1114
# ℹ 9,392 more rows

The RBI MPC Minutes - Word freq

Can do other stuff

Is the MPC always attended by all the members

mpc_minutes |>
  group_by(identifier) |>
  summarise(
    attend_all = ifelse(sum(str_detect(lines,"was attended by all the members")) ==1,"Yes","No")
  ) |>
    ggplot(aes(x=""))+
    geom_bar(aes(fill = attend_all),
    position = "fill",
    width = 0.25)+
    scale_fill_manual(values = c("#b35a54ff","#6c8562ff"))+
    theme_minimal() +
    theme(
      legend.position = "none",
      plot.title.position = "plot",
      panel.grid.major.y = element_blank(),
      aspect.ratio = 0.25
    )+
    scale_y_continuous(expand = expansion(mult = c(0, 0)),limits = c(0,1))+
    scale_x_discrete(expand =  expansion(mult = c(0, 0)))+
    labs(
      x = NULL,
      y = NULL,
      title = "Proportion of MPC meetings that do not have all members present.",
      subtitle = "Green rpresents meetings with all members present. Red represents one or more absent members. n=58"
    ) +
    coord_flip()

Can do other stuff

Can do other stuff

Is the decision making in the MPC usually unanimous? doc doc1

mpc_minutes |>
  filter(str_detect(lines, "[:alpha:]{1,}\\s{1,}Yes$") | str_detect(lines, "[:alpha:]{1,}\\s{1,}No$") | 
  str_detect(lines, "[:alpha:]{1,}\\s{1,}Yes\\s{1,}[:digit:]{2}$") | str_detect(lines, "[:alpha:]{1,}\\s{1,}No\\s{1,}[:digit:]{2}$")) |>
  mutate(
    identifier = str_remove(identifier,"Minutes of the Monetary Policy Committee Meeting"),
    identifier = paste0(str_extract(identifier,"[:alpha:]{1,} "),str_extract(identifier," [:digit:]{4}")),
    individual = str_squish(str_extract(lines,"^.{1,}(?=Yes|No)")),
    identifier = lubridate::my(identifier),
    decision = str_squish(str_extract(lines," Yes| No| Yes | No "))
  ) |> 
  select(-lines) |>
  ggplot(aes(identifier)) +
  geom_bar(aes(fill = decision)) +
  scale_fill_manual(values = c("#b35a54ff","#6c8562ff"))+
    labs(
      title = "MPC decisions across time.",
      x = NULL,
      y = "Number of Members",
      subtitle = "Green represents members in favour of resolution. Red represents members not in favour. n=58. 19/58 are not unanimous."
    ) +
    scale_y_continuous(expand = expansion(mult = c(0, 0)),limits = c(0,6))+
    scale_x_date(expand =  expansion(mult = c(0, 0)),
    breaks = scales::breaks_width("2 months"),
    labels = scales::label_date("%m-%y")
     )+
    theme_minimal() +
    theme(
      panel.grid.minor.x = element_blank(),
      axis.text.x = element_text(angle = 90),
      plot.title.position = "plot",
      legend.position = "none"
    )

Can do other stuff

Can AI do this

Yes, be careful with what you want.

See this

Can do other stuff

who say no?

mpc_minutes |>
  filter(str_detect(lines, "[:alpha:]{1,}\\s{1,}Yes$") | str_detect(lines, "[:alpha:]{1,}\\s{1,}No$") | 
  str_detect(lines, "[:alpha:]{1,}\\s{1,}Yes\\s{1,}[:digit:]{2}$") | str_detect(lines, "[:alpha:]{1,}\\s{1,}No\\s{1,}[:digit:]{2}$")) |>
  mutate(
    identifier = str_remove(identifier,"Minutes of the Monetary Policy Committee Meeting"),
    identifier = paste0(str_extract(identifier,"[:alpha:]{1,} "),str_extract(identifier," [:digit:]{4}")),
    individual = str_squish(str_extract(lines,"^.{1,}(?=Yes|No)")),
    identifier = lubridate::my(identifier),
    decision = str_squish(str_extract(lines," Yes| No| Yes | No "))
  ) |> 
  select(-lines) |>
  mutate(
    individual = ifelse(str_detect(individual,"Dr.[:alpha:]"),
    str_replace(individual,pattern = "Dr.","Dr. "),
    individual)
    ) |>
  group_by(individual) |>
  summarise(
    n = n(),
    in_favour = sum(decision == "Yes"),
    not_in_favour = n - in_favour
  ) |>
    arrange(desc(n)) |>
    kableExtra::kable() |>
    kableExtra::kable_styling() |>
    kableExtra::scroll_box(width = '100%', height = '500px')

Can do other stuff

individual	n	in_favour	not_in_favour
Dr. Michael Debabrata Patra	51	48	3
Shri Shaktikanta Das	37	37	0
Dr. Ashima Goyal	25	21	4
Dr. Shashanka Bhide	25	25	0
Prof. Jayanth R. Varma	25	19	6
Dr. Chetan Ghate	24	21	3
Dr. Pami Dua	24	24	0
Dr. Ravindra H. Dholakia	24	19	5
Dr. Rajiv Ranjan	21	21	0
Dr. Viral V. Acharya	15	13	2
Dr. Urjit R. Patel	14	14	0
Dr. Mridul K. Saggar	11	11	0
Dr. Nagesh Kumar	9	7	2
Prof. Ram Singh	9	8	1
Shri Saugata Bhattacharya	9	9	0
Shri Sanjay Malhotra	7	7	0
Dr. Poonam Gupta	5	5	0
Dr. Janak Raj	3	3	0
Shri Bibhu Prasad Kanungo	3	3	0
Shri Indranil Bhattacharyya	3	3	0
Shri M. Rajeshwar Rao	2	2	0
Shri R. Gandhi	2	2	0

All this is fine. Where is the cool stuff?

Sentiment Analysis

With word frequencies we can compare what is relatively more or less important across a selection of documents. (With some caution)

But it would be better to get an understanding of the opinion or sentiment behid the text.

What is the text trying to convey? Doom, Acche din (good times), Caution, negativity, etc.

Text mining can help us to programmatically find the emotional content of a text.

Sentiment Analysis

We will consider the sentiment of an entire text as the sum of sentiment content of thee individual words of the text.

This is one of the approaches

Sentiment Analysis - Lexicons

For the tidytext format, unigram based lexicons are suited.
Three general purpose lexicons are AFINN, bing, and nrc.
These are available through the {tidytext}.
These do not contain all possible english words. Many words are neutral.
Developed through croudsourcing or by authors, are validate by some combination of approaches.
What care should be taken while choosing a lexicon?

Sentiment Analysis - AFINN

Words are assigned a score between [-5,5]. Negative scores indicate negative sentiments and positve scores indicate positive sentiments

# A tibble: 2,477 × 2
   word       value
   <chr>      <dbl>
 1 abandon       -2
 2 abandoned     -2
 3 abandons      -2
 4 abducted      -2
 5 abduction     -2
 6 abductions    -2
 7 abhor         -3
 8 abhorred      -3
 9 abhorrent     -3
10 abhors        -3
# ℹ 2,467 more rows

Sentiment Analysis - bing

Classifies words in to a binary: positive or negative

# A tibble: 6,786 × 2
   word        sentiment
   <chr>       <chr>    
 1 2-faces     negative 
 2 abnormal    negative 
 3 abolish     negative 
 4 abominable  negative 
 5 abominably  negative 
 6 abominate   negative 
 7 abomination negative 
 8 abort       negative 
 9 aborted     negative 
10 aborts      negative 
# ℹ 6,776 more rows

Sentiment Analysis - nrc

“categorizes words in a binary fashion (“yes”/“no”) into categories of positive, negative, anger, anticipation, disgust, fear, joy, sadness, surprise, and trust”

# A tibble: 13,872 × 2
   word        sentiment
   <chr>       <chr>    
 1 abacus      trust    
 2 abandon     fear     
 3 abandon     negative 
 4 abandon     sadness  
 5 abandoned   anger    
 6 abandoned   fear     
 7 abandoned   negative 
 8 abandoned   sadness  
 9 abandonment anger    
10 abandonment fear     
# ℹ 13,862 more rows

Sentiment Analysis - Use with Care

Unigram based approaches have issues with qualifier words

There is a decline in growth.

This is not good.

Subjectivity in Sentiment Analysis

Ref: Sentiment Analysis and Subjectivity

“(1) I bought an iPhone a few days ago. (2) It was such a nice phone. (3) The touch screen was really cool. (4) The voice quality was clear too. (5) Although the battery life was not long, that is ok for me. (6) However, my mother was mad with me as I did not tell her before I bought it. (7) She also thought the phone was too expensive, and wanted me to return it to the shop. …”

Who/What are these opinions about? Who is making/providing these opinions?

Looking for Sentiments in the RBI MPC Minutes

Once again, lets look at the doc.

Looking for Sentiments in the RBI MPC Minutes

The real stuff is in para 6 and later. (Assessments, Outlook, Rationale, and Statements)

MPC Sentiments - Set up

While we use words as unit of analyses, we aggregate at Para level

  mpc_minutes |> 
  # Mark Para number for each line from the MPC
  filter(str_length(str_squish(lines))>2)|> 
  mutate(
    lines = str_squish(lines),
    para_num = str_extract(lines,pattern = "^[:digit:]{1,2}\\. ")
  ) |> 
  fill(para_num , .direction = "down") |>
  mutate(
    para_num = str_remove_all(para_num, "[:punct:]") |> str_squish() |> as.integer()
  ) |> 
  # Keep only relevant para of the MPC
  filter(para_num >= 6) |>
  # Get in one-word-per-row shape
  unnest_tokens(word, lines) -> mpc_sentiments_setup

  mpc_sentiments_setup

MPC Sentiments - Set up

# A tibble: 393,501 × 3
   identifier                                                     para_num word 
   <chr>                                                             <int> <chr>
 1 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 6    
 2 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 after
 3 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 a    
 4 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 deta…
 5 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 asse…
 6 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 of   
 7 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 the  
 8 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 evol…
 9 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 macr…
10 Minutes of the Monetary Policy Committee Meeting, February 4 …        6 and  
# ℹ 393,491 more rows

MPC Sentiments - augment with lexicon

mpc_sentiments_setup |>
  # rermove stop words |>
  anti_join(stop_words) |> 
  # join with sentiments lexicon
  inner_join(get_sentiments("bing")) -> mpc_sentiments_augmented

  mpc_sentiments_augmented

# A tibble: 18,312 × 4
   identifier                                           para_num word  sentiment
   <chr>                                                   <int> <chr> <chr>    
 1 Minutes of the Monetary Policy Committee Meeting, F…        6 marg… negative 
 2 Minutes of the Monetary Policy Committee Meeting, F…        7 rema… positive 
 3 Minutes of the Monetary Policy Committee Meeting, F…        7 supp… positive 
 4 Minutes of the Monetary Policy Committee Meeting, F…        7 acco… positive 
 5 Minutes of the Monetary Policy Committee Meeting, F…        7 decl… negative 
 6 Minutes of the Monetary Policy Committee Meeting, F…        7 adva… positive 
 7 Minutes of the Monetary Policy Committee Meeting, F…        7 bias  negative 
 8 Minutes of the Monetary Policy Committee Meeting, F…        7 supp… positive 
 9 Minutes of the Monetary Policy Committee Meeting, F…        7 adva… positive 
10 Minutes of the Monetary Policy Committee Meeting, F…        7 vola… negative 
# ℹ 18,302 more rows

MPC Sentiments - Aggregate at Para level

 mpc_sentiments_augmented |>
  # get MPC para level sentiment
  group_by(identifier, para_num) |>
    summarise(
      pos = sum(sentiment == "positive")/n(),
      neg = sum(sentiment == "negative")/n(),
      tot = pos + neg
    ) |>
  ungroup() -> mpc_sentiments_bing

mpc_sentiments_bing

# A tibble: 3,163 × 5
   identifier                                         para_num   pos   neg   tot
   <chr>                                                 <int> <dbl> <dbl> <dbl>
 1 Minutes of the Monetary Policy Committee Meeting …        6 0.333 0.667     1
 2 Minutes of the Monetary Policy Committee Meeting …        7 0     1         1
 3 Minutes of the Monetary Policy Committee Meeting …        8 0.5   0.5       1
 4 Minutes of the Monetary Policy Committee Meeting …        9 0.308 0.692     1
 5 Minutes of the Monetary Policy Committee Meeting …       10 0.4   0.6       1
 6 Minutes of the Monetary Policy Committee Meeting …       11 0     1         1
 7 Minutes of the Monetary Policy Committee Meeting …       13 0.571 0.429     1
 8 Minutes of the Monetary Policy Committee Meeting …       14 1     0         1
 9 Minutes of the Monetary Policy Committee Meeting …       15 0     1         1
10 Minutes of the Monetary Policy Committee Meeting …       17 0     1         1
# ℹ 3,153 more rows

MPC Sentiments - Bing

mpc_sentiments_bing |>
   # Get the MPC identifier as date
  mutate(
    identifier = str_remove(identifier,".{1,} Meeting|.{1,} Meeting,"),
    identifier = str_remove(identifier,"^,"),
    identifier = str_remove(identifier,"[.{1,}]"),
    mpc_date = lubridate::my(paste0(str_extract(str_squish(identifier),"^[:alpha:]{1,}"), str_extract(identifier," [:digit:]{4}")))
  ) |>
  select(mpc_date, para_num, pos, neg, tot) -> mpc_sentiments_bing

mpc_sentiments_bing

# A tibble: 3,163 × 5
   mpc_date   para_num   pos   neg   tot
   <date>        <int> <dbl> <dbl> <dbl>
 1 2019-04-01        6 0.333 0.667     1
 2 2019-04-01        7 0     1         1
 3 2019-04-01        8 0.5   0.5       1
 4 2019-04-01        9 0.308 0.692     1
 5 2019-04-01       10 0.4   0.6       1
 6 2019-04-01       11 0     1         1
 7 2019-04-01       13 0.571 0.429     1
 8 2019-04-01       14 1     0         1
 9 2019-04-01       15 0     1         1
10 2019-04-01       17 0     1         1
# ℹ 3,153 more rows

MPC Positive Sentiments - Bing

mpc_sentiments_bing |>
  ggplot(aes(para_num,as.character(mpc_date))) +
  geom_tile(aes(fill = pos),colour = "#ffffff") +
  scale_fill_gradient(low = "#ccece6",high = "#006d2c")+
  scale_x_continuous(breaks = seq(6,125,2),expand = expansion(mult = c(0,0)))+
  guides(fill = guide_colourbar(barwidth = 15))+
  labs(
    y = NULL,
    x = "Paragrapha Number",
    title = "Proportion of Positive words in a Para using bing lexicon"
  ) +
  theme_minimal()+
  theme(
    plot.title.position = "plot",
    legend.position = "top",
    legend.direction = "horizontal",
    legend.title = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank() 
  )

MPC Positive Sentiments - Bing

MPC Negative Sentiments - Bing

mpc_sentiments_bing |>
  ggplot(aes(para_num,as.character(mpc_date))) +
  geom_tile(aes(fill = neg),colour = "#ffffff") +
  scale_fill_gradient(low = "#fdd49e",high = "#b30000")+
  scale_x_continuous(breaks = seq(6,125,2),expand = expansion(mult = c(0,0)))+
  guides(fill = guide_colourbar(barwidth = 15))+
  labs(
    y = NULL,
    x = "Paragrapha Number",
    title = "Proportion of Negative words in a Para using bing lexicon"
  ) +
  theme_minimal()+
  theme(
    plot.title.position = "plot",
    legend.position = "top",
    legend.direction = "horizontal",
    legend.title = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank() 
  )

MPC Negative Sentiments - Bing

MPC Cumulative Sentiments - Bing

mpc_sentiments_bing |>
  mutate(
    cumilative = pos-neg
  ) |>
  ggplot(aes(para_num,as.character(mpc_date))) +
  geom_tile(aes(fill = cumilative),colour = "#ffffff") +
  scale_fill_gradient2(high = "#4575b4",low = "#d73027",mid = "#ffffbf")+
  scale_x_continuous(breaks = seq(6,125,2),expand = expansion(mult = c(0,0)))+
  guides(fill = guide_colourbar(barwidth = 15))+
  labs(
    y = NULL,
    x = "Paragrapha Number",
    title = "Cumulative prop of positive sentiment words in a Para using bing lexicon"
  ) +
  theme_minimal()+
  theme(
    plot.title.position = "plot",
    legend.position = "top",
    legend.direction = "horizontal",
    legend.title = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank() 
  )

MPC Cumulative Sentiments - Bing

Same stuff using Loughran-McDonald

Sentence as Token

Using {Sentimentr} see highlight file.

Code

mpc_minutes |>
  # Mark Para number for each line from the MPC
  filter(str_length(str_squish(lines))>2)|> 
  mutate(
    lines = str_squish(lines),
    para_num = str_extract(lines,pattern = "^[:digit:]{1,2}\\. ")
  ) |> 
  fill(para_num , .direction = "down") |>
  mutate(
    para_num = str_remove_all(para_num, "[:punct:]") |> str_squish() |> as.integer()
  ) |> 
  # Keep only relevant para of the MPC
  filter(para_num >= 6) |>
  # Clean identifier
   mutate(
    identifier = str_remove(identifier,".{1,} Meeting|.{1,} Meeting,"),
    identifier = str_remove(identifier,"^,"),
    identifier = str_remove(identifier,"[.{1,}]"),
    identifier = lubridate::my(paste0(str_extract(str_squish(identifier),"^[:alpha:]{1,}"), str_extract(identifier," [:digit:]{4}")))
  ) |>
  group_by(identifier,para_num) |>
  summarise(
    text = str_c(lines,collapse = " ")
  ) |>
  ungroup() |>
  mutate(
    split_para = get_sentences(text)
  ) %$%
  sentiment_by(split_para, list(identifier,para_num), polartity_dt = lexicon::hash_sentiment_loughran_mcdonald) -> snetence_para_sentiment_mpc

snetence_para_sentiment_mpc

Key: <identifier, para_num>
      identifier para_num word_count         sd ave_sentiment
          <Date>    <int>      <int>      <num>         <num>
   1: 2016-10-01        6         27 0.05443311   -0.04200695
   2: 2016-10-01        7         63 0.21373734    0.22938423
   3: 2016-10-01        8         99 0.15350212   -0.06731600
   4: 2016-10-01        9        136 0.10979967   -0.05223755
   5: 2016-10-01       10        320 0.24947362    0.13992667
  ---                                                        
3517: 2026-02-01       50         46 0.02665009    0.02447871
3518: 2026-02-01       51         82 0.33281343    0.02675166
3519: 2026-02-01       52        122 0.25366620    0.31469155
3520: 2026-02-01       53        123 0.19281831   -0.14059337
3521: 2026-02-01       54        110 0.19684037    0.23015059

Sentence as token

Beyond Descriptive

We have seen ways to perfrom some form of descriptive analysis on text data. Some of this can be extended in building features for modeling exercises.

Topic Modeling

We might need to divide documents in different groups to better understand what are these about.

We use Topic Modeling, a unsupervised classification methods, to “cluseter” documents in different natural groups

Topic Modeling

Latent Dirichlet allocation (LDA) used for topic modeling

Each doc is treated(modeled) as a (finite)mixture of topics

Each tpoic is treated as a mixture of words

Allows for overlap, complete discrete groups are not necessary

LDA

See paper for theory/Math.

Doc as mixture of topics: MPC1 can be about fuel inflation due to stressed middle east conditions. This can be 10% of MPC1. MPC14 can be about food grain inflation due to poor rain. This can be 20% of MPC14…

Topic as mixture of words: Let us say that MPCs can be about topics like agri production, fuel price shocks, fiscal space. Each of these topics can be realted to different words. Words can overlap across topics.

LDA

Simultaneously, LDA estimates:

mixture of words associated with each topic
mixture of topics associate with each document

Applying LDA

A collection of speeches given by Dr Manmohan Singh is available here.

These are speeches delivered in year 2006-07. On various topics at various occasions/locations.

My goal is to demonstrate how to apply LDA on these text to group them in a given number of topics.

Lets see what comes out.

Applying LDA

The data

speech_data

# A tibble: 133 × 2
   title                                                                   text 
   <chr>                                                                   <chr>
 1 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… "Str…
 2 TOWARDS ACHIEVING EXCELLENCE IN LEGAL SYSTEM Speech at Golden Jubilee … "Tow…
 3 INDIA - MARCHING STEADILY TOWARDS NEW FRONTIERS Independence Day Addre… "Ind…
 4 URGENT NEED TO DISMANTLE BARRIERS TO INTER-STATE TRADE Speech at the C… "Urg…
 5 TOWARDS UNLEASHING FULL POTENTIAL TO EXPAND NEW HORIZONS OF DEVELOPMEN… "Tow…
 6 RECOGNIZING THE NEED TO ROOT OUT CORRUPTION Keynote address to confere… "Rec…
 7 EMPOWERING PANCHAYATI RAJ FOR RURAL PROSPERITY Speech at the conferenc… "Emp…
 8 URGENT NEED FOR PARADIGM SHIFT IN DISASTER MANAGEMENT APPROACH Speech … "Urg…
 9 INCULCATING NEW VISION IN PUBLIC SERVICE Speech at the Golden Jubilee … "Inc…
10 ENSURING EQUAL PARTICIPATION OF ALL IN NATION BUILDING Address at the … "Ens…
# ℹ 123 more rows

Applying LDA

Convert data to tidytext format

speech_data|>
  unnest_tokens(word,text) -> speech_data_tidy

speech_data_tidy

Applying LDA

# A tibble: 193,308 × 2
   title                                                                   word 
   <chr>                                                                   <chr>
 1 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… stri…
 2 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… for  
 3 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… effe…
 4 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… gove…
 5 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… i    
 6 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… am   
 7 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… happy
 8 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… to   
 9 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… be   
10 STRIVING FOR EFFECTIVE GOVERNANCE Speech at the meeting with Chief Sec… in   
# ℹ 193,298 more rows

Applying LDA

get word counts by doc

speech_data_tidy |>
  anti_join(stop_words)|>
  count(title,word,sort = T) -> words_count_speech_data

words_count_speech_data

# A tibble: 51,228 × 3
   title                                                             word      n
   <chr>                                                             <chr> <int>
 1 STATEMENT ON THE INDIA-US NUCLEAR AGREEMENT Statement in Rajya S… nucl…   121
 2 STATEMENT ON THE INDIA-US NUCLEAR AGREEMENT Statement in Rajya S… india    86
 3 INTEGRATED ENERGY POLICY : TURNING ENERGY SECURITY TO REALITY Sp… ener…    49
 4 IN QUEST OF EXCELLENCE IN SCIENCE EDUCATION Speech at laying fou… scie…    46
 5 EFFECTIVE WATER MANAGEMENT : OPTIMISING THE USE Speech at the in… water    44
 6 TOWARDS EXPLORING NEW POTENTIAL OF RICE CULTIVATION Speech at th… rice     41
 7 KERALA : EXCELLENT RECORD IN HUMAN DEVELOPMENT Address at the 50… kera…    39
 8 PROMOTING SCIENCE RESEARCH AND SCIENTIFIC TEMPER ON A LARGER SCA… scie…    39
 9 RECOGNIZING THE NEED TO ROOT OUT CORRUPTION Keynote address to c… corr…    36
10 EMBARKING ON A NEW AMBITIOUS EXPANSION PLAN FOR STEEL SECTOR Spe… steel    35
# ℹ 51,218 more rows

Applying LDA

Convert tidy data to dopcument term Matrix
Each row is a doc, each column is a term, values are freq of appearance

words_count_speech_data |>
  cast_dtm(title,word,n) -> speech_dtm

speech_dtm

Applying LDA

<<DocumentTermMatrix (documents: 133, terms: 10079)>>
Non-/sparse entries: 51228/1289279
Sparsity           : 96%
Maximal term length: 19
Weighting          : term frequency (tf)

Applying LDA

I believe MPC minutes can have around 4 topics

speech_lda <- LDA(speech_dtm,k = 4)

Infering from LDA

How are the topics and speeches grouped?

tibble(
  title = speech_lda |> get_topics() |> names(),
  topic = speech_lda |> get_topics()
 ) |>
  arrange(topic)

# A tibble: 133 × 2
   title                                                                   topic
   <chr>                                                                   <int>
 1 INTEGRATED ENERGY POLICY : TURNING ENERGY SECURITY TO REALITY Speech a…     1
 2 IN QUEST OF EXCELLENCE IN SCIENCE EDUCATION Speech at laying foundatio…     1
 3 PROMOTING SCIENCE RESEARCH AND SCIENTIFIC TEMPER ON A LARGER SCALE Add…     1
 4 ENSURING EQUITABLE ACCESS TO ECONOMIC OPPORTUNITIES TO THE DEPRIVED SE…     1
 5 CANARA BANK : EQUIPPED TO DEAL WITH EMERGING CHALLENGES EFFECTIVELY Sp…     1
 6 FOCUS ON FINDING PRACTICAL SOLUTIONS TO THE PROBLEMS OF POWER SECTOR C…     1
 7 PERFORMANCE OF POWER SECTOR : CRUCIAL FOR THE GROWTH OF OUR ECONOMY Sp…     1
 8 PROMOTING GROWTH OF SCIENCE AND TECHNOLOGY INSTITUTIONS Speech on the …     1
 9 BLUEPRINT FOR PROSPEROUS AND EQUITABLE INDIA Address at the Meeting of…     1
10 TOWARDS TRANSFORMING POWER TO A SELF SUSTAINING SECTOR OF ECONOMY Spee…     1
# ℹ 123 more rows

Infering from LDA

Per-topic-per-word probablities

tidy(speech_lda, matric = "beta") -> speech_beta

speech_beta

# A tibble: 40,316 × 3
   topic term        beta
   <int> <chr>      <dbl>
 1     1 nuclear 0.000354
 2     2 nuclear 0.000201
 3     3 nuclear 0.00675 
 4     4 nuclear 0.000280
 5     1 india   0.00584 
 6     2 india   0.0129  
 7     3 india   0.0179  
 8     4 india   0.00590 
 9     1 energy  0.00405 
10     2 energy  0.00223 
# ℹ 40,306 more rows

Infering from LDA

Per-topic-per-word probablities

speech_beta |>
  group_by(topic) |>
  slice_max(beta, n=10) |>
  ungroup() |>
  arrange(topic,-beta)|>
  mutate(
    term = reorder_within(term,beta,topic)
  ) |>
    ggplot(aes(beta,term)) +
    geom_col(aes(fill = factor(topic))) +
    facet_wrap(~topic, scales = "free") +
    scale_y_reordered() +
    theme_minimal() +
    theme(legend.position = "none")

Infering from LDA

Infering from LDA

You can also show term probablities as distance across two topics
The distance between the probability of a term k in topic A and topic B, for all K terms.

in our case this can be done for K terms across pairs of topics 1-2,1-3,1-4,2-3,2-4,3-4

Since some probablities are very small, best show the distance as \(log_2(\frac{\beta_2}{\beta_1})\)

Inferring from LDA

per-document-per-topic probabilities

speech_lda |>
  tidy(matrix = "gamma") |>
  arrange(document)

# A tibble: 532 × 3
   document                                                       topic    gamma
   <chr>                                                          <int>    <dbl>
 1 AGENDA FOR SOCIO-ECONOMIC TRANSFORMATION Speech at the meetin…     1 1.000e+0
 2 AGENDA FOR SOCIO-ECONOMIC TRANSFORMATION Speech at the meetin…     2 4.61 e-5
 3 AGENDA FOR SOCIO-ECONOMIC TRANSFORMATION Speech at the meetin…     3 4.61 e-5
 4 AGENDA FOR SOCIO-ECONOMIC TRANSFORMATION Speech at the meetin…     4 4.61 e-5
 5 AT THE THRESHOLD OF INCREASED ECONOMIC COOPERATION WITH AFGHA…     1 6.73 e-5
 6 AT THE THRESHOLD OF INCREASED ECONOMIC COOPERATION WITH AFGHA…     2 1.000e+0
 7 AT THE THRESHOLD OF INCREASED ECONOMIC COOPERATION WITH AFGHA…     3 6.73 e-5
 8 AT THE THRESHOLD OF INCREASED ECONOMIC COOPERATION WITH AFGHA…     4 6.73 e-5
 9 BACKWARD REGIONS GRANT FUND : TOWARDS CAPACITY BUILDING OF PA…     1 5.90 e-5
10 BACKWARD REGIONS GRANT FUND : TOWARDS CAPACITY BUILDING OF PA…     2 5.90 e-5
# ℹ 522 more rows

Finding the right `k`

FindTopicsNumber(
  speech_dtm,
  topics = c(2:60),
  metrics = c("Griffiths2004", "CaoJuan2009", "Arun2010", "Deveaud2014"),
  method = "Gibbs",
  mc.cores = 3L,
  verbose = TRUE) -> results_lda_speech

Finding the right `k`

fit models... done.
calculate metrics:
  Griffiths2004... done.
  CaoJuan2009... done.
  Arun2010... done.
  Deveaud2014... done.

Finding the right `k`

FindTopicsNumber_plot(results_lda_speech)

Finding the right `k`

Supervised models for text analysis

Deep learning examples

Dense Neural Netowrks

Densely-connected neural network (feed-forward)

from smltar

Dense Neural Network

Input is provided all at once

Inputs are fully connected to the first hidden layer (densely)

“Neurons” of a given layer are only connected to the next layer

The number of layers and the number of neurons in a layer are variable and are hyperparameter of the model

What is not accurate in the previous image?

Dense Neural Network

Our goal is to build a binary classification model.

We use data from Reuters on news description. We try to classify news based on description.

Dense Neural Network

Data

Rows: 120,000
Columns: 2
$ class_index   <fct> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,…
$ combined_text <chr> "Wall St. Bears Claw Back Into the Black (Reuters). Reut…

Dense Neural Network

Traing and Test sets

news |>
  rsample::initial_split() -> news_split

news_train <- rsample::training(news_split)

news_test <- rsample::testing(news_split)

Dense Neural Network

Pre-processing
Sequences are modeled. Need to choose a max length of sequence.

Observations(docs/articles/chapters) longer than the chosen sequence are truncated

Observations shorter than the chosen sequence are cushioned by non-informative value

Sequence lenght is a hyperparamenter.

Best sequence lenght is something that does not waste too much information and doesnt add too many non-informative values

Dense Neural Networks

Pre-processing

Dense Neural Networks

Pre-processing

max_words <- 3e4

max_length <- 80

Dense Neural Networks

Feature Engineeing

news_recipe <- recipe(
  ~ combined_text,
  data = news_train
  ) |>
    step_tokenize(combined_text) |>
    step_tokenfilter(combined_text, max_tokens = max_words) |>
    step_sequence_onehot(combined_text, sequence_length = max_length,
    truncating = "post")

Dense Neural Networks

Feature Engineeing

one-hot sequence embedding transforms tokens to a numeric class so that we can perform modelling.
Also, one-hot sequence embedding considers the order of the tokens as well, unlike tf and tf-idf

Dense Neural Network

Tiny example of what features* look like

small_data <- tibble(
  text = c("Adventure Dice Game",
           "Spooky Dice Game",
           "Illustrated Book of Monsters",
           "Monsters, Ghosts, Goblins, Me, Myself and I")
)

small_spec <- recipe(~ text, data = small_data) %>%
  step_tokenize(text) %>%
  step_sequence_onehot(text, sequence_length = 6, prefix = "")

prep(small_spec)

Dense Neural Network

Tiny example of what features* look like

prep(small_spec) %>%
  tidy(2)

# A tibble: 14 × 4
   terms vocabulary token       id                   
   <chr>      <int> <chr>       <chr>                
 1 text           1 adventure   sequence_onehot_E7Zwe
 2 text           2 and         sequence_onehot_E7Zwe
 3 text           3 book        sequence_onehot_E7Zwe
 4 text           4 dice        sequence_onehot_E7Zwe
 5 text           5 game        sequence_onehot_E7Zwe
 6 text           6 ghosts      sequence_onehot_E7Zwe
 7 text           7 goblins     sequence_onehot_E7Zwe
 8 text           8 i           sequence_onehot_E7Zwe
 9 text           9 illustrated sequence_onehot_E7Zwe
10 text          10 me          sequence_onehot_E7Zwe
11 text          11 monsters    sequence_onehot_E7Zwe
12 text          12 myself      sequence_onehot_E7Zwe
13 text          13 of          sequence_onehot_E7Zwe
14 text          14 spooky      sequence_onehot_E7Zwe

Dense Neural Network

Tiny example of what features* look like (where are the monsters in the matrix ?)

prep(small_spec) %>%
  bake(new_data = NULL, composition = "matrix")

     _text_1 _text_2 _text_3 _text_4 _text_5 _text_6
[1,]       0       0       0       1       4       5
[2,]       0       0       0      14       4       5
[3,]       0       0       9       3      13      11
[4,]       6       7      10      12       2       8

Dense Neural Network

news_prep <- prep(news_recipe)

news_train_prepped <- bake(news_prep,
      new_data = NULL, 
      composition = "matrix")

dim(news_train_prepped)

[1] 90000    80

Dense Neural Network

A simple flattened dense network

dense_news <- keras_model_sequential(input_shape = c(80)) |> # a linear stack of layers
  layer_embedding(
    input_dim = max_words + 1,
    output_dim = 12,
    input_length = max_length
  ) |>
    layer_flatten() |>
    layer_dense(units = 32, activation = "relu") |>
    layer_dense(unit = 4, activation = "softmax")

  dense_news

Dense Neural Network

Model: "sequential"
┌───────────────────────────────────┬──────────────────────────┬───────────────
│ Layer (type)                      │ Output Shape             │       Param # 
├───────────────────────────────────┼──────────────────────────┼───────────────
│ embedding (Embedding)             │ (None, 80, 12)           │       360,012 
├───────────────────────────────────┼──────────────────────────┼───────────────
│ flatten (Flatten)                 │ (None, 960)              │             0 
├───────────────────────────────────┼──────────────────────────┼───────────────
│ dense (Dense)                     │ (None, 32)               │        30,752 
├───────────────────────────────────┼──────────────────────────┼───────────────
│ dense_1 (Dense)                   │ (None, 4)                │           132 
└───────────────────────────────────┴──────────────────────────┴───────────────
 Total params: 390,896 (1.49 MB)
 Trainable params: 390,896 (1.49 MB)
 Non-trainable params: 0 (0.00 B)

Dense Neural Network

A simple flattened dense network

keras_model_sequential(): compose a stack of layers with no feedback, skips or loops, i.e. linear stack of layers

layer_embedding(): Data is converted to a tensor of \(n_{obs} * S_{max} * OutDim\), in our case (90,000 * 80* 12)

layer_flatten(): the 12 * 80 matrix is converted into a vector with 960 features. So each news description is 960 numbers.

Dense Neural Network

Optimization alogrithm and loss function

dense_news |>
  compile(
    optimizer = optimizer_adam(), #"adam"
    loss = loss_sparse_categorical_crossentropy(), #"sparse_categorical_crossentropy"
    metrics = metric_sparse_categorical_accuracy() #c("accuracy")
  )

Dense Neural Network

Fitting the model

dense_fit_news <- dense_news |>
  fit(
    x = news_train_prepped,
    y = as.integer(news_train$class_index)-1, # carefull
    batch_size = 250,
    epochs = 20,
    validation_split = 0.25
  )

Epoch 1/20
270/270 - 1s - 5ms/step - loss: 0.6767 - sparse_categorical_accuracy: 0.7400 - val_loss: 0.2859 - val_sparse_categorical_accuracy: 0.9048
Epoch 2/20
270/270 - 1s - 3ms/step - loss: 0.2208 - sparse_categorical_accuracy: 0.9268 - val_loss: 0.2485 - val_sparse_categorical_accuracy: 0.9168
Epoch 3/20
270/270 - 1s - 3ms/step - loss: 0.1489 - sparse_categorical_accuracy: 0.9512 - val_loss: 0.2521 - val_sparse_categorical_accuracy: 0.9148
Epoch 4/20
270/270 - 1s - 3ms/step - loss: 0.1000 - sparse_categorical_accuracy: 0.9693 - val_loss: 0.2796 - val_sparse_categorical_accuracy: 0.9110
Epoch 5/20
270/270 - 1s - 3ms/step - loss: 0.0621 - sparse_categorical_accuracy: 0.9827 - val_loss: 0.3001 - val_sparse_categorical_accuracy: 0.9120
Epoch 6/20
270/270 - 1s - 5ms/step - loss: 0.0354 - sparse_categorical_accuracy: 0.9912 - val_loss: 0.3404 - val_sparse_categorical_accuracy: 0.9093
Epoch 7/20
270/270 - 1s - 3ms/step - loss: 0.0198 - sparse_categorical_accuracy: 0.9954 - val_loss: 0.3737 - val_sparse_categorical_accuracy: 0.9066
Epoch 8/20
270/270 - 1s - 3ms/step - loss: 0.0130 - sparse_categorical_accuracy: 0.9969 - val_loss: 0.4050 - val_sparse_categorical_accuracy: 0.9054
Epoch 9/20
270/270 - 1s - 3ms/step - loss: 0.0089 - sparse_categorical_accuracy: 0.9979 - val_loss: 0.4291 - val_sparse_categorical_accuracy: 0.9058
Epoch 10/20
270/270 - 1s - 4ms/step - loss: 0.0066 - sparse_categorical_accuracy: 0.9984 - val_loss: 0.4487 - val_sparse_categorical_accuracy: 0.9051
Epoch 11/20
270/270 - 1s - 3ms/step - loss: 0.0061 - sparse_categorical_accuracy: 0.9985 - val_loss: 0.4616 - val_sparse_categorical_accuracy: 0.9041
Epoch 12/20
270/270 - 1s - 3ms/step - loss: 0.0046 - sparse_categorical_accuracy: 0.9989 - val_loss: 0.4888 - val_sparse_categorical_accuracy: 0.9049
Epoch 13/20
270/270 - 1s - 3ms/step - loss: 0.0041 - sparse_categorical_accuracy: 0.9990 - val_loss: 0.5125 - val_sparse_categorical_accuracy: 0.9043
Epoch 14/20
270/270 - 1s - 4ms/step - loss: 0.0036 - sparse_categorical_accuracy: 0.9990 - val_loss: 0.5236 - val_sparse_categorical_accuracy: 0.9030
Epoch 15/20
270/270 - 1s - 4ms/step - loss: 0.0031 - sparse_categorical_accuracy: 0.9992 - val_loss: 0.5365 - val_sparse_categorical_accuracy: 0.9030
Epoch 16/20
270/270 - 1s - 4ms/step - loss: 0.0030 - sparse_categorical_accuracy: 0.9992 - val_loss: 0.5538 - val_sparse_categorical_accuracy: 0.9019
Epoch 17/20
270/270 - 1s - 4ms/step - loss: 0.0030 - sparse_categorical_accuracy: 0.9992 - val_loss: 0.6205 - val_sparse_categorical_accuracy: 0.8979
Epoch 18/20
270/270 - 1s - 4ms/step - loss: 0.0031 - sparse_categorical_accuracy: 0.9992 - val_loss: 0.5694 - val_sparse_categorical_accuracy: 0.9011
Epoch 19/20
270/270 - 1s - 4ms/step - loss: 0.0026 - sparse_categorical_accuracy: 0.9993 - val_loss: 0.5904 - val_sparse_categorical_accuracy: 0.9007
Epoch 20/20
270/270 - 1s - 4ms/step - loss: 0.0018 - sparse_categorical_accuracy: 0.9996 - val_loss: 0.5987 - val_sparse_categorical_accuracy: 0.9012

dense_fit_news


Final epoch (plot to see history):
                           loss: 0.001826
    sparse_categorical_accuracy: 0.9996
                       val_loss: 0.5987
val_sparse_categorical_accuracy: 0.9012

Dense Neural Network

plot(dense_fit_news) +
  theme_minimal()

Dense Neural Network

Dense Neural Network

Evaluate on test

news_baked <- bake(news_prep, new_data = news_test, composition = "matrix")

dim(news_baked)

[1] 30000    80

Dense Neural Network

news_baked_response <- as.integer(news_test$class_index)-1

dense_fit_test <- dense_news |>
  fit(
    x = news_train_prepped,
    y = as.integer(news_train$class_index)-1, # carefull
    batch_size = 250,
    epochs = 3,
    validation_data = list(news_baked, news_baked_response)
  )

Epoch 1/3
360/360 - 1s - 4ms/step - loss: 0.1086 - sparse_categorical_accuracy: 0.9722 - val_loss: 0.3309 - val_sparse_categorical_accuracy: 0.9033
Epoch 2/3
360/360 - 1s - 3ms/step - loss: 0.0291 - sparse_categorical_accuracy: 0.9924 - val_loss: 0.4459 - val_sparse_categorical_accuracy: 0.8990
Epoch 3/3
360/360 - 1s - 3ms/step - loss: 0.0098 - sparse_categorical_accuracy: 0.9978 - val_loss: 0.5097 - val_sparse_categorical_accuracy: 0.8975

dense_fit_test


Final epoch (plot to see history):
                           loss: 0.009771
    sparse_categorical_accuracy: 0.9978
                       val_loss: 0.5097
val_sparse_categorical_accuracy: 0.8975

Dense Neural Network

plot(dense_fit_test) +
  theme_minimal()

Dense Neural Network

Dense Neural Network

dense_news |> 
  evaluate(news_baked, news_baked_response)

938/938 - 1s - 907us/step - loss: 0.5097 - sparse_categorical_accuracy: 0.8975

$loss
[1] 0.509653

$sparse_categorical_accuracy
[1] 0.8974667

Dense Neural Network

dense_news |> 
  predict(news_baked)

938/938 - 1s - 678us/step

                 [,1]         [,2]         [,3]         [,4]
    [1,] 2.092844e-05 9.830788e-07 2.209612e-02 9.778820e-01
    [2,] 6.820588e-05 5.416569e-07 9.999254e-01 5.869203e-06
    [3,] 8.850472e-06 2.166265e-09 9.999911e-01 1.101618e-07
    [4,] 2.589705e-05 1.530331e-08 9.999741e-01 1.964474e-09
    [5,] 4.365947e-06 8.022069e-08 9.999955e-01 8.850623e-08
    [6,] 2.955020e-08 8.627967e-10 9.999999e-01 8.865090e-08
    [7,] 9.851475e-01 3.654067e-07 1.248095e-02 2.371144e-03
    [8,] 7.628147e-02 3.326405e-06 1.315234e-02 9.105628e-01
    [9,] 2.909523e-03 3.843081e-06 9.962565e-01 8.300786e-04
   [10,] 2.461071e-05 4.851034e-07 1.016049e-01 8.983699e-01
   [11,] 3.528783e-03 2.191695e-01 7.772402e-01 6.154994e-05
   [12,] 2.518635e-03 6.234992e-04 8.308645e-01 1.659933e-01
   [13,] 4.692692e-04 1.623996e-10 9.986613e-01 8.693680e-04
   [14,] 9.566027e-05 8.827445e-08 8.558697e-05 9.998186e-01
   [15,] 8.602273e-03 8.709900e-07 9.913657e-01 3.112659e-05
   [16,] 8.054715e-01 4.352085e-05 1.901721e-01 4.312873e-03
   [17,] 9.999707e-01 8.980423e-07 2.441089e-05 3.966170e-06
   [18,] 4.133265e-04 1.005792e-08 2.306684e-02 9.765198e-01
   [19,] 9.585871e-09 4.657180e-13 1.197458e-06 9.999988e-01
   [20,] 5.815561e-09 1.140211e-09 3.452010e-04 9.996548e-01
   [21,] 7.501199e-05 1.211830e-08 9.615248e-01 3.840018e-02
   [22,] 2.230997e-03 6.829258e-10 1.036694e-02 9.874021e-01
   [23,] 1.054603e-05 6.533984e-07 6.240113e-03 9.937487e-01
   [24,] 1.737982e-04 9.084902e-10 3.337184e-04 9.994924e-01
   [25,] 3.798825e-06 1.648472e-08 1.087483e-04 9.998875e-01
   [26,] 1.843220e-07 2.788309e-07 1.514168e-03 9.984854e-01
   [27,] 6.899152e-01 5.304153e-02 1.481024e-06 2.570418e-01
   [28,] 1.405890e-10 5.747970e-10 8.514629e-09 1.000000e+00
   [29,] 4.631703e-03 3.110647e-07 5.122894e-09 9.953680e-01
   [30,] 2.844535e-04 3.637209e-07 9.607958e-11 9.997151e-01
   [31,] 1.202035e-01 2.807673e-06 1.580940e-09 8.797937e-01
   [32,] 2.271255e-08 1.881227e-07 4.055575e-07 9.999993e-01
   [33,] 1.192296e-04 2.725664e-07 9.901652e-07 9.998795e-01
   [34,] 1.048625e-03 1.067377e-08 8.708143e-08 9.989513e-01
   [35,] 7.425316e-13 4.231139e-14 2.398784e-11 1.000000e+00
   [36,] 6.426445e-04 7.031291e-08 2.422305e-12 9.993573e-01
   [37,] 5.045579e-03 6.260586e-04 5.355005e-08 9.943283e-01
   [38,] 2.671628e-09 1.743058e-08 1.061888e-12 1.000000e+00
   [39,] 2.237306e-04 2.874358e-08 5.556045e-09 9.997763e-01
   [40,] 2.140121e-05 2.822776e-08 1.793717e-09 9.999785e-01
   [41,] 4.984596e-08 1.024224e-06 4.007862e-09 9.999989e-01
   [42,] 5.835179e-04 5.635310e-06 8.332196e-04 9.985777e-01
   [43,] 9.977452e-07 9.281933e-07 3.691707e-05 9.999611e-01
   [44,] 2.541616e-04 2.445492e-05 1.332853e-04 9.995882e-01
   [45,] 2.228863e-06 1.483091e-07 3.180983e-06 9.999945e-01
   [46,] 2.676041e-06 6.268289e-08 1.225622e-07 9.999971e-01
   [47,] 2.629940e-01 3.128307e-02 3.486974e-01 3.570254e-01
   [48,] 1.364001e-03 8.901675e-07 3.367465e-03 9.952676e-01
   [49,] 8.467872e-02 1.393649e-01 1.145510e-05 7.759449e-01
   [50,] 5.213178e-02 3.353224e-07 8.021117e-08 9.478678e-01
   [51,] 6.162989e-01 1.817093e-01 6.441962e-05 2.019274e-01
   [52,] 3.436476e-02 5.030913e-03 1.186270e-05 9.605924e-01
   [53,] 1.026719e-03 7.615147e-08 6.970685e-06 9.989662e-01
   [54,] 1.878221e-03 8.563624e-08 1.813165e-01 8.168052e-01
   [55,] 7.943548e-04 1.075231e-06 2.983939e-02 9.693652e-01
   [56,] 1.049798e-03 2.497678e-08 8.815631e-02 9.107938e-01
   [57,] 5.524168e-08 6.352844e-09 1.970343e-03 9.980295e-01
   [58,] 1.985981e-06 2.054489e-09 3.832309e-04 9.996147e-01
   [59,] 2.143387e-03 9.805257e-02 5.048916e-01 3.949125e-01
   [60,] 2.350927e-01 4.722371e-07 7.529441e-01 1.196272e-02
   [61,] 2.462231e-01 1.061440e-04 7.534047e-01 2.660569e-04
   [62,] 7.809519e-02 2.801248e-01 8.913173e-03 6.328669e-01
   [63,] 1.414801e-01 6.942028e-06 1.117234e-02 8.473406e-01
   [64,] 3.285790e-08 2.616818e-09 9.836275e-08 9.999999e-01
   [65,] 2.328949e-06 2.271032e-08 1.372436e-06 9.999963e-01
   [66,] 2.470215e-02 1.715898e-05 2.473971e-02 9.505410e-01
   [67,] 7.361994e-06 9.549830e-01 4.031431e-05 4.496934e-02
   [68,] 2.533023e-06 9.652592e-05 1.470937e-04 9.997539e-01
   [69,] 1.202906e-06 1.077330e-08 2.844135e-06 9.999959e-01
   [70,] 1.660841e-08 2.995129e-10 5.514978e-08 9.999999e-01
   [71,] 2.470122e-09 1.379776e-10 7.806180e-09 1.000000e+00
   [72,] 1.172874e-05 3.172812e-01 5.075181e-07 6.827066e-01
   [73,] 9.100257e-04 3.576586e-07 5.623600e-02 9.428536e-01
   [74,] 9.999932e-01 6.139555e-06 4.366726e-07 1.898737e-07
   [75,] 8.239882e-03 2.156251e-03 9.245006e-04 9.886793e-01
   [76,] 5.232909e-03 1.949532e-04 2.754748e-04 9.942966e-01
   [77,] 8.209553e-03 4.757306e-02 8.707952e-01 7.342219e-02
   [78,] 8.138227e-01 3.796470e-05 5.437361e-09 1.861393e-01
   [79,] 6.229242e-07 2.711900e-09 9.996169e-01 3.825135e-04
   [80,] 1.687308e-07 2.278939e-07 3.235735e-06 9.999963e-01
   [81,] 3.355019e-03 3.067060e-07 9.937219e-01 2.922775e-03
   [82,] 3.415280e-03 2.061942e-07 2.170206e-04 9.963675e-01
   [83,] 3.022056e-01 6.210637e-05 1.631022e-08 6.977322e-01
   [84,] 5.312874e-05 6.732946e-08 8.750904e-08 9.999467e-01
   [85,] 4.966951e-03 3.703808e-05 8.568099e-01 1.381860e-01
   [86,] 2.555234e-04 8.920483e-02 8.295473e-05 9.104567e-01
   [87,] 1.908033e-02 1.512709e-03 8.958828e-01 8.352406e-02
   [88,] 8.260085e-05 4.177759e-07 8.272624e-03 9.916443e-01
   [89,] 8.633903e-03 8.163680e-02 8.736414e-01 3.608782e-02
   [90,] 2.092213e-06 6.382332e-09 7.508606e-08 9.999979e-01
   [91,] 5.945141e-03 1.861053e-01 2.420583e-02 7.837437e-01
   [92,] 3.804808e-03 2.195326e-07 5.080473e-06 9.961898e-01
   [93,] 1.263221e-04 1.093999e-03 2.699759e-05 9.987526e-01
   [94,] 5.589380e-08 2.539404e-07 2.030939e-06 9.999976e-01
   [95,] 2.860264e-07 2.970477e-07 4.582157e-04 9.995413e-01
   [96,] 4.134065e-03 5.167405e-06 5.109775e-04 9.953498e-01
   [97,] 2.707187e-09 1.097261e-12 3.170444e-11 1.000000e+00
   [98,] 4.405250e-04 4.011330e-03 2.170455e-05 9.955264e-01
   [99,] 7.868147e-11 2.715835e-12 2.341410e-09 1.000000e+00
  [100,] 2.873482e-04 2.541374e-11 2.991367e-02 9.697990e-01
  [101,] 8.510425e-01 1.260845e-01 3.898348e-03 1.897469e-02
  [102,] 1.805382e-03 9.073345e-09 3.009553e-02 9.680991e-01
  [103,] 2.082249e-07 1.015681e-07 3.760951e-03 9.962387e-01
  [104,] 3.818837e-03 3.586194e-09 1.617177e-03 9.945639e-01
  [105,] 4.363089e-07 3.385113e-09 4.379535e-03 9.956200e-01
  [106,] 6.557713e-07 1.196240e-09 2.074059e-05 9.999787e-01
  [107,] 8.006208e-07 2.592163e-09 9.035277e-01 9.647150e-02
  [108,] 3.171470e-07 2.528473e-09 2.590957e-04 9.997405e-01
  [109,] 1.521676e-05 1.612504e-06 5.765273e-04 9.994066e-01
  [110,] 4.374427e-04 7.681435e-08 4.783026e-03 9.947795e-01
  [111,] 4.716345e-09 6.915139e-09 1.465576e-07 9.999999e-01
  [112,] 9.895994e-03 2.618337e-01 2.032445e-01 5.250258e-01
  [113,] 2.352531e-07 9.999998e-01 1.064307e-15 1.639096e-10
  [114,] 6.797328e-05 9.999321e-01 2.135150e-14 5.774305e-09
  [115,] 3.183821e-05 9.999596e-01 8.629348e-06 5.086588e-08
  [116,] 8.538963e-06 9.894615e-01 3.806092e-06 1.052609e-02
  [117,] 8.414382e-06 9.331688e-01 3.566682e-08 6.682272e-02
  [118,] 4.361007e-05 9.999206e-01 1.379234e-05 2.189995e-05
  [119,] 1.488006e-02 9.851102e-01 6.857198e-06 2.991697e-06
  [120,] 6.411212e-08 9.999897e-01 9.848464e-06 4.102865e-07
  [121,] 9.865002e-02 9.012341e-01 2.803301e-05 8.780997e-05
  [122,] 1.368539e-06 9.999267e-01 6.693410e-05 4.986557e-06
  [123,] 9.999989e-01 5.650939e-08 5.428558e-09 1.003868e-06
  [124,] 9.975064e-01 4.432488e-10 8.729888e-10 2.493561e-03
  [125,] 1.000000e+00 1.485120e-13 9.963513e-14 1.203594e-08
  [126,] 9.999099e-01 5.270875e-08 1.541937e-12 9.002988e-05
  [127,] 9.999963e-01 3.214761e-12 2.509424e-08 3.653560e-06
  [128,] 7.284285e-01 1.593943e-05 1.679751e-06 2.715538e-01
  [129,] 9.999999e-01 1.185868e-07 2.132901e-10 2.538369e-09
  [130,] 9.964323e-01 2.669167e-03 6.440002e-06 8.920634e-04
  [131,] 6.321971e-01 3.666242e-01 3.843946e-04 7.942545e-04
  [132,] 9.988741e-01 6.000731e-06 1.034047e-03 8.581499e-05
  [133,] 9.999999e-01 5.581283e-09 1.701570e-07 4.364763e-08
  [134,] 9.999828e-01 3.751212e-07 1.410417e-05 2.677162e-06
  [135,] 9.291722e-01 7.082509e-02 2.327051e-06 3.861426e-07
  [136,] 9.291722e-01 7.082509e-02 2.327051e-06 3.861426e-07
  [137,] 9.845873e-01 1.515130e-04 3.472348e-05 1.522642e-02
  [138,] 1.947000e-04 7.042234e-10 9.997992e-01 6.105453e-06
  [139,] 1.662934e-03 3.174470e-05 8.836391e-07 9.983044e-01
  [140,] 6.837654e-04 9.993122e-01 4.484345e-10 4.074653e-06
  [141,] 2.944375e-06 9.999970e-01 2.481101e-10 1.089939e-08
  [142,] 9.994703e-01 4.112866e-11 8.633831e-10 5.297589e-04
  [143,] 9.995547e-01 3.071504e-04 1.378165e-04 2.488498e-07
  [144,] 8.764783e-01 7.883058e-02 8.436765e-04 4.384740e-02
  [145,] 9.999914e-01 3.073315e-06 4.779011e-06 6.847325e-07
  [146,] 8.316992e-01 3.760122e-07 1.682860e-01 1.442833e-05
  [147,] 9.406488e-02 9.051569e-01 2.038371e-08 7.782268e-04
  [148,] 5.850510e-02 9.162070e-01 2.528788e-02 2.905872e-09
  [149,] 1.631426e-01 8.368567e-01 6.132724e-07 5.860718e-08
  [150,] 1.039298e-01 8.959023e-01 1.678699e-04 2.261203e-09
  [151,] 8.018935e-05 9.999198e-01 2.531231e-10 5.470943e-08
  [152,] 4.187455e-05 9.999582e-01 3.432395e-10 3.002531e-10
  [153,] 9.375312e-01 2.897198e-09 6.238834e-02 8.045348e-05
  [154,] 1.000000e+00 2.252060e-12 1.965467e-11 6.456360e-09
  [155,] 5.055079e-04 9.994944e-01 5.901494e-11 1.333588e-09
  [156,] 1.354257e-06 1.091893e-06 9.999975e-01 8.931122e-08
  [157,] 9.999955e-01 1.255063e-06 1.996510e-06 1.215979e-06
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 [1899,] 9.999924e-01 6.796128e-06 6.715583e-07 1.007386e-07
 [1900,] 1.000000e+00 9.688522e-13 1.513746e-11 8.785821e-12
 [1901,] 4.544532e-13 2.026177e-14 1.000000e+00 8.238708e-14
 [1902,] 3.765677e-07 1.167126e-07 9.999995e-01 2.622811e-10
 [1903,] 2.322185e-03 3.750554e-08 2.130496e-01 7.846282e-01
 [1904,] 2.896045e-01 4.017736e-03 4.986974e-01 2.076804e-01
 [1905,] 9.998734e-01 1.884534e-09 1.266155e-04 7.367264e-12
 [1906,] 7.118796e-07 1.319508e-08 9.999993e-01 1.089733e-08
 [1907,] 1.117085e-05 1.131568e-01 8.844781e-01 2.353995e-03
 [1908,] 3.010591e-08 7.277894e-09 1.000000e+00 3.013237e-10
 [1909,] 9.998719e-01 2.835825e-08 1.144109e-04 1.364084e-05
 [1910,] 1.036277e-05 9.999454e-01 1.066056e-08 4.422432e-05
 [1911,] 1.636223e-06 6.301949e-11 9.999983e-01 2.177274e-09
 [1912,] 3.652039e-02 6.641222e-01 5.358256e-06 2.993520e-01
 [1913,] 7.077363e-07 9.451883e-08 1.594059e-05 9.999832e-01
 [1914,] 2.255097e-05 9.999610e-01 1.659777e-06 1.482920e-05
 [1915,] 1.298991e-02 2.613894e-04 1.882566e-06 9.867468e-01
 [1916,] 2.492602e-07 9.997355e-01 5.373396e-07 2.636334e-04
 [1917,] 9.999880e-01 8.741793e-11 1.065737e-05 1.404692e-06
 [1918,] 9.967192e-01 2.925372e-03 3.550763e-04 4.226262e-07
 [1919,] 2.981411e-09 9.999999e-01 8.919437e-14 1.597923e-07
 [1920,] 1.554513e-03 2.322995e-04 9.962553e-01 1.957921e-03
 [1921,] 5.651640e-07 1.077423e-07 9.999986e-01 7.750186e-07
 [1922,] 6.643745e-07 6.116365e-10 9.999988e-01 4.418393e-07
 [1923,] 2.813318e-08 1.000000e+00 8.086193e-12 1.327258e-12
 [1924,] 1.658492e-06 9.999981e-01 2.912356e-07 8.871918e-09
 [1925,] 6.697627e-02 9.328942e-01 1.295222e-04 6.310098e-09
 [1926,] 9.999849e-01 1.299188e-08 1.487251e-05 2.646539e-07
 [1927,] 2.450149e-06 1.244037e-08 9.999975e-01 2.357564e-08
 [1928,] 1.339985e-02 3.237145e-08 9.790379e-01 7.562165e-03
 [1929,] 6.499926e-06 2.613605e-12 9.999934e-01 1.059698e-09
 [1930,] 2.877954e-11 6.891869e-14 3.777715e-10 1.000000e+00
 [1931,] 3.296456e-08 1.799570e-07 9.774587e-03 9.902251e-01
 [1932,] 1.723580e-06 1.465269e-11 4.075741e-04 9.995907e-01
 [1933,] 5.580548e-06 9.999944e-01 1.943417e-08 1.869989e-08
 [1934,] 1.327778e-07 9.999999e-01 4.039878e-09 2.742358e-10
 [1935,] 3.511136e-05 1.280116e-07 9.999645e-01 2.252667e-07
 [1936,] 1.067334e-05 2.019499e-04 5.785688e-02 9.419304e-01
 [1937,] 9.839787e-01 3.619486e-05 1.598496e-02 1.376846e-07
 [1938,] 3.314208e-06 1.591581e-08 5.740889e-04 9.994227e-01
 [1939,] 9.940079e-01 5.837687e-03 5.840496e-05 9.600401e-05
 [1940,] 5.412920e-09 7.625610e-09 8.246514e-08 9.999999e-01
 [1941,] 1.569380e-07 9.999393e-01 6.040452e-05 7.082685e-08
 [1942,] 3.131638e-03 9.968682e-01 1.309287e-07 1.017814e-08
 [1943,] 5.116053e-11 9.999999e-01 9.650187e-11 1.182598e-07
 [1944,] 3.635001e-06 1.102783e-07 9.999917e-01 4.633921e-06
 [1945,] 2.174397e-03 9.978254e-01 2.248112e-07 2.285165e-08
 [1946,] 9.856932e-04 2.846947e-07 9.990120e-01 1.997497e-06
 [1947,] 2.427664e-03 9.334677e-02 9.104487e-02 8.131807e-01
 [1948,] 3.500431e-01 6.498142e-01 5.757652e-08 1.426323e-04
 [1949,] 9.999996e-01 2.622773e-09 3.001716e-07 5.214227e-09
 [1950,] 1.799313e-10 3.029884e-15 1.000000e+00 3.676743e-10
 [1951,] 3.569822e-05 2.581015e-09 9.999640e-01 3.152371e-07
 [1952,] 9.962978e-01 3.222333e-03 1.707736e-04 3.091614e-04
 [1953,] 1.768506e-07 9.999998e-01 5.449837e-10 7.046986e-08
 [1954,] 1.090147e-07 3.719913e-08 3.213753e-04 9.996785e-01
 [1955,] 5.552128e-06 9.998259e-01 1.684903e-04 1.401647e-07
 [1956,] 5.611894e-04 3.323653e-09 1.656295e-03 9.977825e-01
 [1957,] 1.166163e-05 2.562935e-10 2.556351e-04 9.997327e-01
 [1958,] 2.066855e-07 9.999996e-01 4.870085e-13 7.377250e-08
 [1959,] 1.240756e-05 9.999869e-01 7.562801e-07 1.199913e-08
 [1960,] 1.851110e-07 5.285763e-13 9.999998e-01 9.200490e-12
 [1961,] 1.702570e-03 2.804176e-05 9.982693e-01 4.214799e-08
 [1962,] 6.322315e-07 1.921622e-10 9.999994e-01 2.364801e-08
 [1963,] 1.290218e-07 9.999999e-01 1.070822e-10 3.317947e-08
 [1964,] 7.454579e-04 9.992536e-01 9.326466e-07 1.906774e-09
 [1965,] 7.596904e-01 9.661415e-04 1.312875e-11 2.393434e-01
 [1966,] 9.998902e-01 5.155241e-07 1.045993e-05 9.875985e-05
 [1967,] 3.204612e-11 4.021230e-12 1.000000e+00 4.069013e-15
 [1968,] 1.587217e-04 2.804903e-07 9.998401e-01 8.508813e-07
 [1969,] 2.078121e-05 5.492409e-05 1.216587e-01 8.782656e-01
 [1970,] 4.042158e-02 5.900380e-07 9.595777e-01 5.027404e-08
 [1971,] 2.361916e-04 3.425404e-07 9.997634e-01 6.251369e-10
 [1972,] 8.848733e-08 6.597314e-08 5.266232e-04 9.994732e-01
 [1973,] 3.991888e-05 4.771862e-07 2.430988e-02 9.756497e-01
 [1974,] 7.442150e-07 8.813985e-11 9.999993e-01 2.416363e-13
 [1975,] 8.412016e-04 3.379081e-09 8.721735e-02 9.119414e-01
 [1976,] 9.999993e-01 1.941382e-11 6.832147e-07 5.233338e-08
 [1977,] 4.095014e-09 1.000000e+00 1.088771e-09 2.302048e-08
 [1978,] 5.630983e-01 4.368936e-01 2.473529e-06 5.721456e-06
 [1979,] 2.899618e-07 1.416695e-09 9.999998e-01 1.884189e-10
 [1980,] 9.993424e-01 4.819216e-07 6.570476e-04 7.139146e-08
 [1981,] 1.000000e+00 3.648968e-16 3.398269e-16 4.059042e-16
 [1982,] 2.194101e-05 5.994575e-08 1.230214e-06 9.999768e-01
 [1983,] 7.744834e-04 5.088126e-08 1.261356e-01 8.730898e-01
 [1984,] 1.010642e-01 6.618532e-07 3.140386e-04 8.986211e-01
 [1985,] 6.603955e-08 9.999965e-01 1.720657e-07 3.249144e-06
 [1986,] 6.173062e-07 4.801507e-12 8.609671e-07 9.999986e-01
 [1987,] 1.045326e-11 7.844552e-13 1.000000e+00 1.054871e-13
 [1988,] 1.555419e-03 8.699803e-08 9.237726e-01 7.467198e-02
 [1989,] 2.469943e-05 1.058198e-05 9.997160e-01 2.487157e-04
 [1990,] 1.379661e-03 1.057555e-06 9.986148e-01 4.583755e-06
 [1991,] 4.242346e-10 8.146053e-12 2.117928e-06 9.999979e-01
 [1992,] 9.999980e-01 1.141739e-08 2.041979e-06 1.246132e-09
 [1993,] 9.999996e-01 3.962440e-10 2.040521e-07 6.183341e-08
 [1994,] 1.024641e-06 1.250089e-06 9.999976e-01 1.680561e-08
 [1995,] 9.950571e-03 2.723517e-06 9.724817e-01 1.756500e-02
 [1996,] 1.061734e-06 3.805583e-08 1.267137e-05 9.999863e-01
 [1997,] 6.525968e-04 3.758594e-02 9.613891e-01 3.724085e-04
 [1998,] 1.566388e-03 9.980606e-01 3.729617e-04 5.209430e-09
 [1999,] 2.872167e-09 1.766549e-10 1.553507e-06 9.999985e-01
 [2000,] 3.251047e-07 1.422048e-08 5.358743e-03 9.946409e-01
 [2001,] 3.624033e-03 2.183872e-09 9.963759e-01 1.606925e-07
 [2002,] 3.057713e-09 3.947695e-13 1.000000e+00 4.092556e-12
 [2003,] 2.968489e-11 1.537401e-13 1.000000e+00 9.286866e-12
 [2004,] 9.885411e-09 3.312172e-08 7.828979e-07 9.999992e-01
 [2005,] 5.366883e-01 2.452010e-06 4.633046e-01 4.603301e-06
 [2006,] 3.848446e-03 1.407915e-06 2.990858e-04 9.958510e-01
 [2007,] 1.022334e-03 2.444601e-06 9.988182e-01 1.570133e-04
 [2008,] 9.015240e-09 6.548980e-10 1.091473e-07 9.999999e-01
 [2009,] 2.475681e-01 5.752599e-07 7.520463e-01 3.848905e-04
 [2010,] 9.971771e-01 1.754937e-11 2.565627e-09 2.822867e-03
 [2011,] 8.323385e-05 9.996390e-01 5.521701e-08 2.776086e-04
 [2012,] 5.829601e-05 9.999373e-01 3.642285e-06 7.607331e-07
 [2013,] 9.999993e-01 9.756503e-08 2.242332e-09 6.080052e-07
 [2014,] 1.724710e-06 1.881730e-08 9.999934e-01 4.837176e-06
 [2015,] 2.106276e-10 1.702690e-12 7.295625e-10 1.000000e+00
 [2016,] 9.999242e-01 4.151284e-09 1.428159e-09 7.579879e-05
 [2017,] 9.999993e-01 2.011603e-08 4.014662e-07 3.776400e-07
 [2018,] 1.253227e-04 2.404664e-10 9.998747e-01 7.919319e-09
 [2019,] 3.183520e-05 3.273650e-08 4.667733e-03 9.953004e-01
 [2020,] 9.866912e-01 9.761225e-05 6.157720e-07 1.321060e-02
 [2021,] 1.126187e-04 3.671170e-10 9.998869e-01 4.248764e-07
 [2022,] 5.389860e-10 3.270764e-09 2.459845e-08 1.000000e+00
 [2023,] 1.938018e-05 7.246558e-05 4.037258e-03 9.958709e-01
 [2024,] 9.244183e-03 9.907476e-01 8.259099e-06 1.650767e-09
 [2025,] 9.147959e-09 1.046294e-10 1.789547e-08 1.000000e+00
 [2026,] 9.941747e-07 1.135398e-05 2.358872e-08 9.999876e-01
 [2027,] 9.878560e-12 2.501918e-10 2.488033e-05 9.999751e-01
 [2028,] 4.787582e-08 2.817195e-07 7.823827e-07 9.999989e-01
 [2029,] 4.051007e-02 9.559900e-01 3.498624e-03 1.202657e-06
 [2030,] 9.046992e-08 1.340442e-10 1.991928e-06 9.999980e-01
 [2031,] 2.052451e-10 1.896785e-13 1.848923e-07 9.999998e-01
 [2032,] 2.270007e-10 2.160469e-11 9.367422e-06 9.999906e-01
 [2033,] 3.035640e-08 1.845807e-09 2.551489e-04 9.997448e-01
 [2034,] 9.413888e-01 5.860398e-02 4.262117e-06 2.992389e-06
 [2035,] 1.334968e-03 2.098465e-08 9.986629e-01 1.992964e-06
 [2036,] 2.343401e-02 9.302572e-01 4.613503e-02 1.737961e-04
 [2037,] 1.688153e-04 2.516236e-09 4.418314e-03 9.954129e-01
 [2038,] 1.832690e-06 8.946529e-10 4.427003e-03 9.955712e-01
 [2039,] 6.300730e-07 9.999993e-01 1.201172e-07 1.991566e-09
 [2040,] 1.319130e-02 3.847653e-06 9.868041e-01 8.258031e-07
 [2041,] 4.955118e-01 5.044572e-01 3.028699e-05 6.543027e-07
 [2042,] 4.347979e-05 2.693807e-14 9.999558e-01 7.628365e-07
 [2043,] 1.800349e-06 1.043133e-07 5.556368e-03 9.944417e-01
 [2044,] 7.943775e-09 4.573839e-08 9.962475e-01 3.752475e-03
 [2045,] 2.783123e-03 9.969109e-01 3.285648e-07 3.056852e-04
 [2046,] 7.124687e-01 2.873857e-01 9.793897e-08 1.455246e-04
 [2047,] 9.999995e-01 3.391713e-07 1.340915e-07 2.873260e-09
 [2048,] 2.751954e-04 3.625133e-05 3.024343e-03 9.966642e-01
 [2049,] 1.199228e-06 1.240574e-08 8.250134e-03 9.917487e-01
 [2050,] 1.000000e+00 3.893152e-10 4.680287e-08 3.489621e-09
 [2051,] 2.298891e-09 2.648560e-10 5.924794e-07 9.999994e-01
 [2052,] 1.290224e-08 5.434991e-11 1.000000e+00 1.711141e-09
 [2053,] 5.271566e-09 1.335431e-12 3.482848e-05 9.999652e-01
 [2054,] 5.614853e-05 9.999408e-01 4.828029e-07 2.608094e-06
 [2055,] 5.029041e-07 9.999995e-01 4.830685e-09 1.281375e-12
 [2056,] 9.987098e-01 2.560616e-04 2.089170e-08 1.034096e-03
 [2057,] 8.677021e-08 1.527670e-08 5.952802e-05 9.999404e-01
 [2058,] 1.949476e-03 9.036631e-01 9.438740e-02 3.050056e-09
 [2059,] 9.999813e-01 1.137553e-05 2.538688e-06 4.820075e-06
 [2060,] 9.999295e-01 3.422150e-07 1.616288e-06 6.846509e-05
 [2061,] 9.913374e-04 6.974154e-10 4.565429e-03 9.944432e-01
 [2062,] 7.887857e-01 3.466264e-06 1.216843e-05 2.111987e-01
 [2063,] 2.252759e-05 9.999775e-01 1.697280e-10 1.259175e-10
 [2064,] 9.999982e-01 9.548456e-07 1.520789e-08 8.529390e-07
 [2065,] 1.185572e-03 9.988142e-01 8.295057e-11 2.964265e-07
 [2066,] 1.482683e-04 9.998517e-01 3.368759e-12 1.009531e-10
 [2067,] 1.536112e-06 3.604901e-10 9.999982e-01 2.361433e-07
 [2068,] 1.947652e-04 2.487292e-04 7.236474e-12 9.995565e-01
 [2069,] 9.999985e-01 2.175179e-12 3.720176e-11 1.504665e-06
 [2070,] 2.036411e-08 1.000000e+00 3.465708e-10 1.424163e-12
 [2071,] 3.132376e-06 5.628658e-09 9.999969e-01 3.419019e-11
 [2072,] 7.370008e-07 2.619200e-08 6.684060e-01 3.315932e-01
 [2073,] 1.161546e-01 1.099238e-09 8.815750e-01 2.270453e-03
 [2074,] 9.995099e-01 1.090141e-08 4.866957e-04 3.375418e-06
 [2075,] 8.923687e-01 1.076211e-01 9.764922e-06 4.015077e-07
 [2076,] 2.370728e-03 1.393298e-03 1.827391e-03 9.944085e-01
 [2077,] 1.697589e-08 6.903898e-09 1.000000e+00 2.949440e-08
 [2078,] 9.081546e-06 8.306197e-07 9.999753e-01 1.484342e-05
 [2079,] 3.012364e-08 5.362903e-08 2.463537e-06 9.999975e-01
 [2080,] 9.999599e-01 6.688186e-06 3.327497e-05 6.999833e-08
 [2081,] 2.012381e-06 1.676649e-09 9.999826e-01 1.534253e-05
 [2082,] 3.271994e-03 5.640372e-07 9.967265e-01 8.627954e-07
 [2083,] 8.953941e-05 2.463967e-12 9.999099e-01 5.483882e-07
 [2084,] 9.999943e-01 4.341946e-08 5.661038e-06 1.031191e-07
 [2085,] 3.013067e-08 8.914999e-14 1.000000e+00 3.148264e-10
 [2086,] 9.999784e-01 7.399437e-10 2.281702e-08 2.160030e-05
 [2087,] 1.151585e-03 9.978448e-01 1.003635e-03 3.039849e-09
 [2088,] 1.183151e-03 9.988168e-01 7.520391e-09 6.065668e-09
 [2089,] 4.422342e-08 1.067609e-09 1.000000e+00 3.942062e-08
 [2090,] 3.518489e-06 1.344704e-07 9.952515e-01 4.744772e-03
 [2091,] 2.023298e-05 2.874610e-06 8.707914e-04 9.991061e-01
 [2092,] 1.710765e-06 9.999982e-01 3.512287e-08 9.057093e-12
 [2093,] 2.355308e-03 1.606723e-07 3.842363e-07 9.976441e-01
 [2094,] 9.997013e-01 1.217875e-08 1.142700e-09 2.986421e-04
 [2095,] 8.005027e-01 1.994973e-01 3.787970e-08 6.367150e-08
 [2096,] 4.112488e-01 1.245715e-01 1.039887e-01 3.601910e-01
 [2097,] 9.999987e-01 2.974949e-09 1.828531e-07 1.116392e-06
 [2098,] 1.976812e-02 2.019741e-07 9.800866e-01 1.451607e-04
 [2099,] 9.990584e-01 1.949489e-06 9.259817e-04 1.364760e-05
 [2100,] 3.994714e-05 7.824127e-07 9.999590e-01 2.563763e-07
 [2101,] 3.800652e-06 9.995369e-01 4.517437e-04 7.576521e-06
 [2102,] 1.000000e+00 1.458066e-13 4.822580e-11 3.351660e-11
 [2103,] 1.470560e-07 1.443822e-08 9.999999e-01 8.619939e-10
 [2104,] 2.704984e-05 8.816674e-08 4.442771e-09 9.999728e-01
 [2105,] 1.984343e-05 1.755572e-07 9.999799e-01 2.045188e-07
 [2106,] 9.999998e-01 2.991087e-10 2.160802e-11 1.843400e-07
 [2107,] 1.399191e-01 8.599974e-01 8.334338e-05 7.261381e-08
 [2108,] 2.312379e-07 9.999996e-01 1.181788e-07 1.778621e-10
 [2109,] 9.650234e-06 6.141655e-09 2.737524e-05 9.999629e-01
 [2110,] 1.000000e+00 7.477851e-12 5.384728e-08 5.397242e-08
 [2111,] 3.326751e-05 3.212524e-09 9.999665e-01 1.912490e-07
 [2112,] 2.236908e-06 3.459432e-11 9.999201e-01 7.759067e-05
 [2113,] 1.304106e-06 6.545883e-11 5.167255e-01 4.832731e-01
 [2114,] 8.029438e-07 1.086011e-07 9.775432e-02 9.022447e-01
 [2115,] 4.819346e-06 8.781098e-10 9.999952e-01 2.212566e-10
 [2116,] 1.320585e-02 2.623053e-06 9.397120e-01 4.707947e-02
 [2117,] 1.883511e-05 1.355052e-10 3.906066e-04 9.995906e-01
 [2118,] 3.219411e-05 1.385982e-10 9.999677e-01 8.968615e-08
 [2119,] 9.748663e-05 9.999025e-01 4.194381e-08 1.160743e-09
 [2120,] 2.600465e-07 9.999998e-01 5.824630e-13 1.062677e-14
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[10007,] 6.565144e-08 9.999999e-01 1.013679e-08 4.836180e-13
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[10009,] 6.250953e-04 9.993746e-01 3.178098e-07 1.079110e-09
[10010,] 1.054748e-05 9.999894e-01 4.917303e-09 2.338668e-11
[10011,] 6.204879e-02 3.208557e-04 9.332836e-01 4.346644e-03
[10012,] 2.990475e-04 9.946206e-01 5.080330e-03 1.170471e-11
[10013,] 3.246686e-02 9.674619e-01 2.913020e-05 4.207112e-05
[10014,] 9.987625e-01 4.660785e-08 1.237142e-03 3.123869e-07
[10015,] 9.999645e-01 1.412949e-08 3.551602e-05 1.547184e-08
[10016,] 7.118540e-04 3.131414e-07 9.992782e-01 9.621000e-06
[10017,] 2.926845e-04 9.989698e-01 7.327200e-04 4.707941e-06
[10018,] 4.324083e-06 9.999955e-01 1.788621e-11 2.491482e-07
[10019,] 6.180362e-01 1.999043e-02 3.614841e-01 4.893257e-04
[10020,] 2.277246e-04 4.059645e-08 4.059055e-03 9.957132e-01
[10021,] 5.080720e-08 5.750798e-07 1.252256e-07 9.999993e-01
[10022,] 4.049622e-06 7.261503e-10 1.318126e-02 9.868147e-01
[10023,] 4.768371e-04 9.995035e-01 1.971364e-05 2.077002e-08
[10024,] 9.799257e-01 8.098817e-06 2.006554e-02 7.047734e-07
[10025,] 1.967259e-07 6.480321e-08 9.999996e-01 2.492774e-08
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[10027,] 6.124224e-05 1.993677e-09 1.392648e-04 9.997995e-01
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[10030,] 5.622176e-03 1.677440e-05 1.771333e-10 9.943610e-01
[10031,] 2.413286e-06 6.067859e-09 9.999975e-01 8.110256e-08
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[10033,] 5.659172e-09 1.000000e+00 3.838800e-11 6.626813e-09
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[10035,] 9.999996e-01 2.129277e-12 1.054154e-10 3.006615e-07
[10036,] 3.173676e-03 5.099880e-06 9.154480e-01 8.137313e-02
[10037,] 1.197919e-05 1.137316e-04 9.998699e-01 4.319422e-06
[10038,] 8.801412e-05 6.191163e-02 8.663870e-01 7.161336e-02
[10039,] 1.666286e-06 9.999841e-01 4.776516e-06 9.360887e-06
[10040,] 9.999989e-01 9.994620e-07 7.809675e-08 1.448457e-09
[10041,] 9.999999e-01 6.683619e-08 3.718846e-08 8.226296e-08
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[10043,] 7.661597e-06 5.765783e-09 9.999924e-01 3.264989e-11
[10044,] 3.237160e-06 9.999968e-01 9.357113e-10 3.026775e-10
[10045,] 3.186126e-07 9.999996e-01 2.845085e-11 8.310300e-12
[10046,] 1.267266e-03 9.923137e-01 1.526659e-03 4.892313e-03
[10047,] 3.219534e-04 9.996780e-01 1.298762e-09 2.858427e-09
[10048,] 8.725420e-08 1.939936e-08 5.645844e-06 9.999943e-01
[10049,] 1.000000e+00 6.080067e-11 1.167422e-12 4.097501e-08
[10050,] 1.000000e+00 7.057210e-12 2.168978e-11 1.428104e-09
[10051,] 7.449624e-05 9.999225e-01 2.886368e-06 1.439363e-07
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[10053,] 1.029434e-05 9.999753e-01 1.401790e-05 3.367713e-07
[10054,] 9.999933e-01 5.784071e-06 7.112119e-08 7.320420e-07
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[10056,] 3.774896e-08 1.000000e+00 3.666199e-09 1.890790e-09
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[10059,] 8.460163e-06 9.999803e-01 2.237030e-06 8.943694e-06
[10060,] 9.991412e-01 3.653784e-05 8.221983e-04 5.957448e-08
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[10080,] 2.345486e-06 3.290304e-12 3.416011e-03 9.965816e-01
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[10111,] 4.241386e-06 7.989244e-05 9.988927e-01 1.023061e-03
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[10629,] 7.909941e-07 9.999992e-01 4.102041e-08 6.504207e-11
[10630,] 1.596375e-06 1.206241e-09 9.999985e-01 7.589527e-09
[10631,] 9.999998e-01 6.235673e-10 1.890234e-09 2.882717e-07
[10632,] 9.999706e-01 2.883691e-05 1.786121e-12 5.635991e-07
[10633,] 1.558851e-08 8.000947e-11 9.999985e-01 1.498138e-06
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[10635,] 7.427476e-03 2.290040e-08 9.210588e-01 7.151382e-02
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[10640,] 1.449490e-06 9.999986e-01 1.845336e-08 1.905277e-10
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[10642,] 9.999640e-01 2.266959e-05 1.331194e-05 1.859886e-09
[10643,] 9.999909e-01 2.455925e-06 4.803193e-08 6.554832e-06
[10644,] 1.000000e+00 4.136831e-10 2.144560e-10 2.983379e-10
[10645,] 4.565663e-09 9.999831e-01 2.473839e-08 1.687605e-05
[10646,] 1.027124e-06 1.480452e-13 9.999989e-01 4.866499e-09
[10647,] 2.230060e-08 5.363627e-10 1.000000e+00 2.368239e-11
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[10662,] 1.318922e-04 1.758900e-03 9.980943e-01 1.491353e-05
[10663,] 3.644414e-07 9.144453e-08 2.246273e-08 9.999995e-01
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[10668,] 1.125398e-07 2.455406e-11 4.135220e-06 9.999957e-01
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[10670,] 9.999794e-01 2.032341e-07 8.791952e-10 2.038432e-05
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[10675,] 1.664726e-05 1.131977e-06 9.324692e-01 6.751295e-02
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[10677,] 9.349323e-05 1.098028e-03 4.334846e-04 9.983749e-01
[10678,] 2.775025e-03 9.997824e-09 9.972248e-01 1.956267e-07
[10679,] 2.040409e-05 2.510918e-07 9.999777e-01 1.629574e-06
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[10682,] 9.154347e-04 7.091986e-06 1.608130e-04 9.989166e-01
[10683,] 3.928916e-03 1.188168e-06 1.316209e-01 8.644489e-01
[10684,] 1.053883e-10 1.000000e+00 3.271587e-13 1.393319e-13
[10685,] 9.999880e-01 1.142662e-09 2.036226e-06 9.975975e-06
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[10687,] 3.383407e-05 2.487966e-10 2.505201e-05 9.999411e-01
[10688,] 9.403636e-06 1.480438e-09 9.860253e-01 1.396537e-02
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[10690,] 1.371531e-05 9.054364e-10 1.058691e-02 9.893994e-01
[10691,] 4.285907e-02 2.150005e-08 9.571302e-01 1.069122e-05
[10692,] 3.073384e-04 1.703992e-11 9.996926e-01 8.665477e-08
[10693,] 2.528404e-05 9.255367e-10 2.565986e-04 9.997181e-01
[10694,] 7.431487e-06 4.522121e-09 3.164744e-10 9.999926e-01
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[10696,] 3.034814e-04 2.180254e-02 3.871907e-04 9.775069e-01
[10697,] 3.701579e-06 2.318339e-07 1.344867e-04 9.998616e-01
[10698,] 1.208929e-09 1.000000e+00 1.470858e-10 2.012861e-10
[10699,] 9.999993e-01 4.651417e-07 1.227094e-07 9.120814e-08
[10700,] 6.251133e-04 2.110273e-06 5.146215e-08 9.993727e-01
[10701,] 2.388654e-02 8.964652e-01 6.506320e-06 7.964172e-02
[10702,] 5.512139e-08 1.000000e+00 4.495276e-11 2.411965e-11
[10703,] 9.999778e-01 6.059618e-10 6.093928e-09 2.219351e-05
[10704,] 8.915407e-04 1.531940e-09 9.988974e-01 2.109463e-04
[10705,] 9.988230e-01 7.448162e-07 1.158644e-03 1.753396e-05
[10706,] 6.963066e-06 6.288437e-09 9.999931e-01 1.111351e-08
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[10708,] 1.000000e+00 8.483334e-15 8.121175e-15 1.492278e-10
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[10710,] 6.361768e-07 9.999994e-01 2.003009e-11 7.096176e-11
[10711,] 1.532888e-09 4.672261e-11 1.156087e-07 9.999999e-01
[10712,] 6.682313e-04 5.819224e-04 1.633218e-06 9.987482e-01
[10713,] 9.999998e-01 1.252834e-11 1.135867e-10 2.369377e-07
[10714,] 9.999993e-01 3.291819e-07 2.114992e-08 3.952435e-07
[10715,] 4.877129e-05 9.999512e-01 8.842214e-12 4.891534e-08
[10716,] 3.520330e-03 9.960989e-01 3.807221e-04 1.854645e-09
[10717,] 2.127022e-03 7.182767e-01 2.795962e-01 5.334869e-08
[10718,] 8.729596e-06 9.999913e-01 5.614097e-13 1.443559e-08
[10719,] 1.249680e-07 6.720470e-09 9.999999e-01 3.640889e-09
[10720,] 4.076571e-08 2.158202e-08 1.000000e+00 2.635518e-08
[10721,] 2.743144e-07 1.160892e-10 9.998672e-01 1.325440e-04
[10722,] 1.817957e-06 6.405262e-04 9.993511e-01 6.542934e-06
[10723,] 9.015417e-01 9.253799e-02 5.898821e-03 2.155651e-05
[10724,] 5.611513e-01 1.102179e-05 5.962814e-09 4.388376e-01
[10725,] 4.681316e-05 1.017742e-07 9.999530e-01 1.347623e-08
[10726,] 2.535385e-02 3.503933e-07 9.737232e-01 9.225864e-04
[10727,] 1.549507e-05 4.367622e-10 1.606206e-07 9.999844e-01
[10728,] 9.427398e-01 3.638917e-07 5.725778e-02 2.082326e-06
[10729,] 9.994360e-01 7.438227e-07 5.633148e-04 2.983400e-08
[10730,] 9.999987e-01 3.157986e-09 2.049900e-08 1.318751e-06
[10731,] 6.668143e-10 2.561230e-10 1.000000e+00 1.245776e-12
[10732,] 2.380067e-01 9.922344e-06 7.112833e-02 6.908550e-01
[10733,] 2.899211e-06 9.437844e-05 9.989630e-01 9.397491e-04
[10734,] 1.900591e-06 9.999981e-01 3.085883e-09 2.707151e-09
[10735,] 9.999934e-01 9.697898e-07 5.622467e-06 2.602085e-08
[10736,] 1.384512e-01 2.518930e-08 8.613774e-01 1.713741e-04
[10737,] 2.438191e-04 3.999125e-09 9.997562e-01 4.090927e-08
[10738,] 6.043581e-10 9.999999e-01 6.627106e-08 3.728362e-12
[10739,] 5.987127e-02 1.696282e-07 9.401176e-01 1.099861e-05
[10740,] 9.999945e-01 1.577572e-06 3.948719e-06 1.607027e-08
[10741,] 2.320636e-01 5.935755e-01 7.276930e-03 1.670839e-01
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[10744,] 2.044554e-05 9.999795e-01 3.479821e-08 1.579580e-12
[10745,] 1.238376e-06 7.984716e-08 9.970189e-01 2.979795e-03
[10746,] 9.996831e-01 2.960685e-07 3.165135e-04 6.067872e-09
[10747,] 6.961977e-03 6.138726e-11 9.930378e-01 2.215659e-07
[10748,] 3.937438e-05 2.170402e-04 2.142034e-01 7.855402e-01
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[10750,] 8.085925e-04 2.623948e-06 2.240032e-05 9.991664e-01
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[10794,] 7.813800e-11 2.891191e-11 1.000000e+00 2.297708e-17
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[10799,] 5.018036e-06 9.999949e-01 2.824514e-08 1.015586e-07
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[10801,] 9.982179e-01 8.378393e-05 1.658585e-05 1.681778e-03
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[10809,] 1.186843e-06 9.999951e-01 5.690658e-07 3.108522e-06
[10810,] 8.539782e-06 1.308503e-05 9.987605e-01 1.217938e-03
[10811,] 4.108728e-06 1.111287e-06 2.525340e-05 9.999696e-01
[10812,] 6.222052e-07 9.999992e-01 1.689777e-07 1.244264e-10
[10813,] 1.257650e-03 4.946372e-09 5.331296e-01 4.656127e-01
[10814,] 5.130111e-03 2.687960e-06 9.948081e-01 5.913303e-05
[10815,] 1.769008e-07 2.249442e-10 9.999990e-01 8.179011e-07
[10816,] 7.044740e-01 4.555180e-03 5.093266e-05 2.909199e-01
[10817,] 4.060608e-08 6.623158e-10 5.561960e-10 1.000000e+00
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[10820,] 1.025429e-01 5.109490e-05 3.270154e-05 8.973732e-01
[10821,] 9.999762e-01 9.291118e-10 4.820297e-14 2.384966e-05
[10822,] 4.236335e-08 1.254818e-10 1.000000e+00 6.674229e-09
[10823,] 5.882550e-07 1.154335e-07 1.826507e-03 9.981728e-01
[10824,] 9.122543e-06 7.129628e-10 9.999906e-01 2.018227e-07
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[10830,] 2.430098e-04 6.423129e-11 6.592850e-05 9.996911e-01
[10831,] 1.702291e-02 6.528640e-10 2.242072e-06 9.829748e-01
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[10834,] 9.994135e-01 1.152156e-04 1.191051e-04 3.521628e-04
[10835,] 9.991824e-01 1.570603e-05 6.112648e-04 1.906352e-04
[10836,] 8.832684e-01 6.122250e-06 1.167185e-01 7.069776e-06
[10837,] 3.449768e-07 9.999996e-01 4.563899e-14 1.195117e-09
[10838,] 1.668501e-06 8.003735e-08 6.529814e-02 9.347001e-01
[10839,] 1.047202e-06 4.421320e-10 9.999989e-01 2.329406e-10
[10840,] 1.802354e-05 9.438754e-07 1.919347e-02 9.807875e-01
[10841,] 1.031305e-04 9.998530e-01 3.106959e-07 4.346049e-05
[10842,] 9.998800e-01 1.804336e-06 3.560896e-11 1.182076e-04
[10843,] 1.622222e-05 9.999834e-01 3.689642e-07 1.878684e-08
[10844,] 3.309773e-01 4.828291e-07 6.625183e-01 6.503983e-03
[10845,] 3.445985e-04 9.995745e-01 8.096870e-05 1.349988e-08
[10846,] 1.856174e-06 9.999975e-01 1.860451e-07 4.655651e-07
[10847,] 5.827512e-07 9.999994e-01 1.059981e-14 8.222694e-09
[10848,] 8.015808e-06 9.999920e-01 9.560881e-09 4.708302e-08
[10849,] 2.607987e-10 4.329358e-12 1.000000e+00 5.307323e-13
[10850,] 4.404027e-03 1.213022e-08 9.897475e-01 5.848537e-03
[10851,] 3.895650e-04 9.996104e-01 5.189050e-11 1.073039e-07
[10852,] 4.673634e-03 1.655654e-05 9.953073e-01 2.540155e-06
[10853,] 1.429953e-11 6.981965e-12 2.870323e-11 1.000000e+00
[10854,] 1.184092e-05 1.704640e-04 3.645208e-04 9.994531e-01
[10855,] 7.676779e-06 2.974838e-10 9.999903e-01 2.082341e-06
[10856,] 5.043085e-07 4.799692e-11 9.999995e-01 1.229799e-09
[10857,] 9.999976e-01 6.704566e-09 5.281318e-09 2.407432e-06
[10858,] 3.445985e-04 9.995745e-01 8.096870e-05 1.349988e-08
[10859,] 9.886391e-05 1.060990e-07 9.999011e-01 6.832769e-08
[10860,] 3.949464e-05 1.100196e-09 1.020623e-06 9.999595e-01
[10861,] 8.591472e-05 9.999099e-01 9.395397e-09 4.132871e-06
[10862,] 1.009179e-06 9.999990e-01 2.932487e-11 3.404645e-11
[10863,] 1.545153e-06 1.223714e-06 9.999969e-01 2.848960e-07
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[10866,] 7.066597e-05 5.037354e-09 9.999268e-01 2.555244e-06
[10867,] 2.997501e-07 3.280650e-06 9.210236e-07 9.999955e-01
[10868,] 7.382915e-07 9.895066e-09 7.946842e-06 9.999913e-01
[10869,] 1.077478e-02 4.684831e-04 1.613554e-03 9.871432e-01
[10870,] 2.939462e-05 1.994561e-08 1.743878e-04 9.997962e-01
[10871,] 4.008988e-05 2.740778e-06 2.079875e-02 9.791585e-01
[10872,] 8.557143e-08 1.368551e-09 9.999999e-01 1.838649e-09
[10873,] 9.204997e-06 1.200866e-07 9.999906e-01 8.466925e-08
[10874,] 9.999681e-01 4.176221e-09 2.553445e-05 6.390850e-06
[10875,] 9.973164e-01 2.573323e-03 1.100799e-04 1.995528e-07
[10876,] 9.999998e-01 1.171080e-08 1.300182e-11 2.456077e-07
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[10879,] 3.463478e-06 2.295317e-09 9.999926e-01 3.891937e-06
[10880,] 5.560889e-09 1.342157e-12 1.785894e-05 9.999821e-01
[10881,] 1.370049e-06 9.999986e-01 5.397985e-08 1.418420e-10
[10882,] 4.082503e-05 2.252078e-03 1.461163e-01 8.515909e-01
[10883,] 9.972090e-01 7.303814e-08 2.484549e-03 3.063367e-04
[10884,] 1.304256e-03 9.986957e-01 2.651099e-09 6.667230e-08
[10885,] 3.101650e-07 1.111582e-12 9.998233e-01 1.764297e-04
[10886,] 1.762101e-07 7.018889e-07 2.268947e-08 9.999990e-01
[10887,] 9.993677e-01 6.293043e-04 2.775828e-06 3.575143e-07
[10888,] 4.487897e-01 8.843325e-07 4.235981e-01 1.276112e-01
[10889,] 3.860376e-09 7.196755e-09 7.787412e-09 1.000000e+00
[10890,] 2.122628e-05 2.192624e-07 1.115760e-05 9.999673e-01
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[10892,] 1.811673e-06 1.981589e-08 9.999982e-01 1.483840e-10
[10893,] 3.845048e-06 5.734052e-10 5.958746e-01 4.041215e-01
[10894,] 8.000494e-02 1.147917e-03 8.386037e-01 8.024342e-02
[10895,] 9.999845e-01 1.994526e-06 4.348254e-07 1.300456e-05
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[10899,] 2.502655e-05 8.162534e-09 4.072746e-07 9.999746e-01
[10900,] 9.028269e-07 2.640170e-11 1.958773e-06 9.999971e-01
[10901,] 7.819093e-07 9.999992e-01 8.738314e-09 1.192005e-08
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[10905,] 2.748514e-10 1.921097e-11 2.814636e-06 9.999971e-01
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[10908,] 3.650356e-05 9.999465e-01 2.047701e-13 1.709146e-05
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[10910,] 8.154448e-07 9.999992e-01 2.322390e-08 4.460105e-10
[10911,] 1.305398e-06 9.999987e-01 9.280617e-09 3.356071e-10
[10912,] 3.443341e-08 9.999999e-01 4.492420e-08 2.615639e-10
[10913,] 1.478824e-05 5.485240e-06 2.787968e-03 9.971918e-01
[10914,] 7.232035e-04 5.204329e-06 3.010957e-03 9.962606e-01
[10915,] 6.945230e-05 4.803358e-09 9.999303e-01 1.802156e-07
[10916,] 5.659945e-07 2.050244e-09 9.999994e-01 1.602909e-08
[10917,] 3.806388e-09 1.000000e+00 2.880528e-12 1.189888e-14
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[10919,] 6.246188e-05 1.103229e-07 2.021394e-01 7.977980e-01
[10920,] 6.641627e-07 9.999993e-01 1.398063e-08 2.121137e-08
[10921,] 1.303891e-08 9.999987e-01 1.219585e-13 1.359667e-06
[10922,] 3.914751e-08 1.000000e+00 1.619099e-09 4.152967e-10
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[10926,] 5.155432e-11 6.697817e-14 1.000000e+00 1.447437e-12
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[10934,] 3.177519e-04 3.224126e-09 6.744721e-01 3.252101e-01
[10935,] 1.000000e+00 8.063949e-13 4.131239e-11 4.482823e-09
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[10937,] 5.374760e-05 9.999462e-01 7.849819e-09 4.910366e-11
[10938,] 4.233107e-01 5.742792e-01 2.109840e-03 3.002566e-04
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[10942,] 4.723638e-05 3.639976e-05 9.998893e-01 2.711424e-05
[10943,] 3.904832e-12 5.042018e-13 1.000000e+00 7.568319e-16
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[11937,] 7.666275e-06 9.999924e-01 5.070744e-11 4.611836e-10
[11938,] 2.037639e-07 9.999998e-01 1.298063e-08 4.620440e-09
[11939,] 7.112480e-06 9.999858e-01 7.057158e-06 9.259576e-10
[11940,] 6.316185e-07 9.999963e-01 1.088561e-06 2.017121e-06
[11941,] 1.153003e-09 1.000000e+00 5.360350e-12 3.361907e-09
[11942,] 1.097024e-06 9.999989e-01 2.544426e-08 1.128918e-09
[11943,] 2.271316e-01 7.626159e-01 4.508595e-05 1.020734e-02
[11944,] 2.242506e-04 9.282817e-01 7.149240e-02 1.678786e-06
[11945,] 9.999639e-01 1.826168e-06 3.425947e-05 5.572575e-08
[11946,] 8.517216e-01 1.450465e-01 3.230878e-03 1.019321e-06
[11947,] 9.989867e-01 1.000278e-03 7.148935e-06 5.912839e-06
[11948,] 7.949712e-01 2.049939e-01 5.218519e-06 2.967900e-05
[11949,] 1.078829e-05 9.999890e-01 4.588974e-13 2.280951e-07
[11950,] 9.986234e-01 1.021995e-05 7.840269e-04 5.824392e-04
[11951,] 1.362832e-05 9.999864e-01 1.539094e-08 3.150091e-09
[11952,] 9.208671e-07 9.999990e-01 1.508258e-10 3.280128e-11
[11953,] 6.987589e-09 9.999987e-01 1.223756e-06 1.452541e-07
[11954,] 8.837843e-08 9.999944e-01 5.528050e-06 3.641612e-13
[11955,] 1.000000e+00 2.052936e-11 4.876988e-12 3.674302e-11
[11956,] 1.000000e+00 1.294850e-10 3.948468e-11 3.513558e-09
[11957,] 2.995979e-06 7.455206e-07 9.999963e-01 6.952910e-10
[11958,] 9.999505e-01 5.309093e-10 1.798553e-05 3.148309e-05
[11959,] 1.000000e+00 4.163120e-13 5.877955e-13 4.152813e-08
[11960,] 1.112754e-05 9.999717e-01 1.715465e-05 1.487498e-10
[11961,] 1.104521e-04 1.686400e-04 9.997204e-01 4.114806e-07
[11962,] 3.226064e-05 9.997708e-01 1.968983e-04 6.378557e-10
[11963,] 9.999996e-01 2.582377e-09 1.865088e-07 8.064613e-08
[11964,] 2.101277e-02 8.369145e-01 3.803556e-03 1.382692e-01
[11965,] 9.970725e-01 2.572835e-05 5.077310e-05 2.851019e-03
[11966,] 3.227015e-06 1.907997e-07 9.999965e-01 1.093236e-08
[11967,] 1.044224e-07 9.996129e-01 1.077284e-05 3.763385e-04
[11968,] 2.437828e-07 9.999998e-01 2.256940e-09 4.621314e-12
[11969,] 4.643009e-07 1.421692e-06 9.999981e-01 2.077166e-08
[11970,] 1.609447e-06 1.500639e-06 9.999968e-01 3.095705e-10
[11971,] 5.399889e-04 9.735521e-01 2.011643e-02 5.791476e-03
[11972,] 5.391050e-04 1.211325e-07 6.345941e-01 3.648667e-01
[11973,] 2.591220e-02 5.538218e-05 9.739204e-01 1.120629e-04
[11974,] 9.601416e-06 4.121187e-05 9.999487e-01 3.420799e-07
[11975,] 8.861831e-04 6.293163e-06 2.669997e-06 9.991048e-01
[11976,] 1.982178e-03 5.362544e-04 5.752582e-02 9.399558e-01
[11977,] 3.997578e-08 2.314683e-09 6.692805e-12 1.000000e+00
[11978,] 9.999760e-01 1.946559e-09 2.386661e-05 1.761948e-07
[11979,] 9.999986e-01 1.473470e-06 3.782312e-09 1.007426e-09
[11980,] 6.359079e-08 1.746522e-11 9.999998e-01 1.732726e-07
[11981,] 7.824713e-08 9.999999e-01 2.094653e-14 2.180049e-09
[11982,] 2.982827e-06 9.999894e-01 7.568047e-06 2.008779e-09
[11983,] 1.222838e-07 9.999999e-01 8.735833e-10 3.825595e-09
[11984,] 2.764024e-05 9.999723e-01 1.464857e-09 9.559138e-10
[11985,] 1.171777e-07 9.999998e-01 4.624147e-11 6.090091e-08
[11986,] 2.751938e-06 9.999964e-01 1.038702e-08 8.597510e-07
[11987,] 6.698787e-07 9.999963e-01 1.026368e-06 2.036487e-06
[11988,] 5.172129e-10 1.000000e+00 1.310508e-11 1.539680e-10
[11989,] 1.132567e-05 6.388167e-03 9.935977e-01 2.742205e-06
[11990,] 9.999837e-01 3.305342e-06 1.217041e-05 8.877961e-07
[11991,] 9.999764e-01 1.949265e-09 1.180741e-05 1.182085e-05
[11992,] 2.352373e-07 9.999974e-01 2.220019e-06 1.250346e-07
[11993,] 9.797132e-05 9.999020e-01 1.221978e-09 3.486313e-09
[11994,] 4.079777e-03 9.945967e-01 2.468909e-07 1.323137e-03
[11995,] 6.418435e-07 9.999993e-01 1.468156e-08 6.397735e-09
[11996,] 1.241889e-01 1.059706e-06 8.758075e-01 2.558085e-06
[11997,] 1.285348e-05 1.316881e-09 9.999871e-01 1.654035e-08
[11998,] 5.302442e-06 7.824432e-10 1.236148e-05 9.999824e-01
[11999,] 3.620960e-05 6.823539e-09 3.683833e-02 9.631255e-01
[12000,] 2.948604e-06 9.999970e-01 8.516562e-11 6.745586e-12
[12001,] 6.210609e-02 5.902051e-06 1.271692e-05 9.378753e-01
[12002,] 1.000000e+00 5.955563e-13 7.063397e-14 7.130112e-11
[12003,] 9.999725e-01 1.011369e-10 2.030986e-09 2.751167e-05
[12004,] 4.692165e-06 4.630108e-07 9.999949e-01 2.595778e-08
[12005,] 9.999951e-01 2.009761e-08 4.884324e-06 3.888959e-08
[12006,] 2.844296e-01 1.752149e-02 6.665122e-01 3.153665e-02
[12007,] 3.615628e-10 1.936549e-08 1.513217e-08 1.000000e+00
[12008,] 2.857392e-06 9.999961e-01 3.090310e-07 6.888620e-07
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[12010,] 8.355659e-07 6.049308e-09 9.999988e-01 3.753304e-07
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[12015,] 1.142441e-05 3.816988e-09 9.999884e-01 1.071314e-07
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[16815,] 1.969357e-06 2.988831e-10 1.461821e-04 9.998518e-01
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[17450,] 5.225135e-07 9.999989e-01 4.411980e-09 6.323941e-07
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[19580,] 9.998952e-01 2.112538e-05 4.696250e-08 8.365614e-05
[19581,] 5.747624e-07 9.999975e-01 1.980257e-06 4.587301e-08
[19582,] 2.844153e-04 5.066937e-03 8.976664e-02 9.048821e-01
[19583,] 9.999864e-01 1.209174e-05 3.097231e-07 1.165104e-06
[19584,] 9.999905e-01 6.537602e-09 9.112081e-06 4.602696e-07
[19585,] 8.230078e-08 1.781534e-11 9.999999e-01 3.088447e-11
[19586,] 4.638891e-08 3.865490e-05 1.306010e-06 9.999601e-01
[19587,] 7.311020e-05 5.238075e-06 9.999216e-01 1.005942e-07
[19588,] 9.507475e-09 1.180320e-10 1.659732e-08 1.000000e+00
[19589,] 3.591912e-06 9.999963e-01 5.052361e-08 2.446121e-10
[19590,] 3.657175e-06 9.999963e-01 2.654648e-13 1.591544e-11
[19591,] 9.702157e-05 1.466736e-10 1.704376e-03 9.981987e-01
[19592,] 1.216304e-05 3.244404e-09 9.999878e-01 2.321380e-09
[19593,] 2.217746e-08 1.000000e+00 1.104696e-13 2.831347e-15
[19594,] 2.712867e-06 9.999909e-01 3.137494e-06 3.184332e-06
[19595,] 9.999977e-01 1.518110e-09 1.999498e-06 2.875560e-07
[19596,] 9.999999e-01 4.252301e-11 6.523143e-08 3.673911e-10
[19597,] 3.696513e-01 1.211427e-04 6.302274e-01 4.766472e-08
[19598,] 9.025846e-06 6.558814e-08 2.036571e-06 9.999888e-01
[19599,] 4.207928e-10 1.000000e+00 3.547209e-11 1.649417e-11
[19600,] 1.792346e-02 4.962723e-06 9.820679e-01 3.674869e-06
[19601,] 7.392958e-05 9.594542e-06 9.999163e-01 1.998869e-07
[19602,] 9.999981e-01 2.452996e-08 2.735739e-10 1.932332e-06
[19603,] 3.468843e-01 9.239076e-08 6.531122e-01 3.397314e-06
[19604,] 6.195281e-01 1.903433e-06 3.803798e-01 9.019135e-05
[19605,] 1.980946e-03 9.968944e-01 3.051213e-05 1.094112e-03
[19606,] 9.981263e-01 6.176217e-09 1.091452e-08 1.873697e-03
[19607,] 1.319672e-09 1.000000e+00 1.637774e-11 7.641856e-10
[19608,] 9.974922e-01 7.806162e-08 2.506966e-03 7.538223e-07
[19609,] 4.843107e-06 9.999942e-01 8.575427e-08 9.215918e-07
[19610,] 9.999999e-01 1.803843e-08 9.573679e-08 1.754318e-08
[19611,] 2.818118e-06 8.816294e-06 6.032755e-05 9.999280e-01
[19612,] 2.074015e-04 9.997054e-01 2.009575e-06 8.515102e-05
[19613,] 2.252374e-12 1.000000e+00 4.256895e-11 1.429400e-14
[19614,] 1.515120e-08 9.999999e-01 1.477863e-09 1.176851e-07
[19615,] 1.820760e-09 1.000000e+00 8.268871e-10 3.768261e-09
[19616,] 1.828415e-06 9.999958e-01 2.271206e-06 1.386610e-07
[19617,] 2.951500e-07 9.999998e-01 3.461697e-10 7.628373e-09
[19618,] 5.745466e-08 1.000000e+00 7.701292e-10 7.871726e-09
[19619,] 9.999928e-01 6.072459e-10 1.808650e-08 7.202276e-06
[19620,] 9.999995e-01 1.743876e-07 2.584567e-07 4.531800e-08
[19621,] 9.963086e-01 4.607866e-07 3.690720e-03 1.592626e-07
[19622,] 2.355215e-08 1.634878e-10 1.000000e+00 5.451353e-11
[19623,] 7.553198e-04 5.983267e-08 9.989895e-01 2.551539e-04
[19624,] 1.857724e-08 1.000000e+00 1.306024e-14 2.511832e-16
[19625,] 4.670418e-01 3.780393e-07 5.329577e-01 5.113366e-08
[19626,] 9.403813e-07 1.136313e-06 9.999974e-01 5.789074e-07
[19627,] 7.579862e-07 9.200448e-09 9.999993e-01 1.588854e-09
[19628,] 7.928049e-04 9.991652e-01 3.641029e-05 5.640055e-06
[19629,] 1.000000e+00 1.871238e-11 1.546905e-08 1.897127e-08
[19630,] 9.766979e-07 9.999990e-01 7.534514e-11 3.722222e-11
[19631,] 5.161836e-08 1.000000e+00 1.358441e-10 1.842461e-09
[19632,] 9.999995e-01 4.706494e-07 1.821582e-09 4.357840e-08
[19633,] 5.928472e-03 9.936971e-01 3.283925e-04 4.613001e-05
[19634,] 1.923479e-03 9.980690e-01 7.598192e-06 3.092423e-08
[19635,] 9.999990e-01 2.709495e-11 1.251436e-12 1.010490e-06
[19636,] 6.820633e-05 4.820651e-11 9.999318e-01 1.695291e-10
[19637,] 3.809666e-06 9.999962e-01 5.705429e-09 8.046473e-11
[19638,] 9.888237e-01 1.116221e-06 1.117515e-02 1.408353e-09
[19639,] 1.309976e-05 1.216670e-10 9.999859e-01 9.147665e-07
[19640,] 1.151413e-08 9.999648e-01 3.513971e-05 4.342721e-08
[19641,] 1.744307e-04 9.998253e-01 3.408803e-07 5.636922e-12
[19642,] 3.276451e-05 9.999672e-01 4.543454e-10 6.529163e-09
[19643,] 1.465953e-07 3.398481e-09 9.506000e-06 9.999903e-01
[19644,] 5.854330e-11 1.000000e+00 8.870472e-11 1.483750e-12
[19645,] 4.370720e-08 1.479763e-08 1.000000e+00 3.399105e-12
[19646,] 9.312404e-01 1.359426e-06 6.873202e-02 2.618290e-05
[19647,] 1.242490e-04 2.960499e-04 4.415394e-06 9.995752e-01
[19648,] 9.999998e-01 1.716720e-09 1.157559e-09 2.437314e-07
[19649,] 8.601779e-01 2.761291e-07 1.398153e-01 6.642056e-06
[19650,] 9.999955e-01 5.662547e-09 7.371731e-07 3.750882e-06
[19651,] 9.677864e-01 1.107245e-04 3.187247e-02 2.303708e-04
[19652,] 3.635492e-04 3.239861e-10 9.996245e-01 1.195928e-05
[19653,] 2.335309e-03 9.976647e-01 1.209947e-08 1.350866e-11
[19654,] 9.959508e-01 1.558613e-06 4.045327e-03 2.214286e-06
[19655,] 9.312069e-04 1.392348e-10 9.990688e-01 1.383005e-10
[19656,] 4.714855e-01 9.974461e-06 5.284926e-01 1.194493e-05
[19657,] 6.362322e-05 2.709737e-08 4.590129e-03 9.953462e-01
[19658,] 9.999905e-01 2.185907e-06 7.213635e-06 1.989652e-08
[19659,] 9.794506e-09 7.768122e-10 1.000000e+00 1.470831e-12
[19660,] 7.324469e-05 9.996576e-01 4.212861e-07 2.687355e-04
[19661,] 5.455594e-08 4.809357e-09 4.050346e-06 9.999959e-01
[19662,] 7.568875e-07 8.479113e-09 3.457923e-08 9.999992e-01
[19663,] 4.529088e-07 9.999487e-01 2.694774e-07 5.053839e-05
[19664,] 2.506810e-07 1.208626e-03 6.742845e-06 9.987844e-01
[19665,] 1.012503e-06 2.061147e-09 1.384027e-08 9.999989e-01
[19666,] 1.289045e-03 9.980348e-01 6.757689e-04 3.053314e-07
[19667,] 4.185843e-02 9.580181e-01 1.234383e-04 4.614208e-08
[19668,] 3.477803e-07 9.999996e-01 1.018357e-10 1.218485e-09
[19669,] 1.867857e-05 1.594006e-08 9.999801e-01 1.163960e-06
[19670,] 2.674912e-04 9.997326e-01 5.609528e-10 1.214400e-10
[19671,] 1.482873e-08 4.245221e-10 1.000000e+00 1.713656e-12
[19672,] 1.082063e-04 9.997212e-01 1.705434e-04 5.437588e-09
[19673,] 9.274929e-05 9.999071e-01 9.800158e-08 3.362276e-08
[19674,] 2.622636e-07 9.999998e-01 3.373074e-14 1.243418e-09
[19675,] 4.942376e-07 1.543626e-10 2.939188e-02 9.706076e-01
[19676,] 2.118823e-07 7.966690e-07 2.924858e-04 9.997064e-01
[19677,] 9.999996e-01 1.379322e-08 6.421295e-09 3.298186e-07
[19678,] 5.604513e-07 2.574742e-04 9.997417e-01 1.428820e-07
[19679,] 3.637530e-09 2.568507e-12 1.627996e-09 1.000000e+00
[19680,] 1.186642e-07 9.999995e-01 3.060306e-07 4.680328e-09
[19681,] 1.000000e+00 4.650553e-10 5.219308e-11 8.872016e-10
[19682,] 5.652873e-05 7.124045e-01 2.873748e-01 1.641712e-04
[19683,] 3.467239e-06 7.003635e-08 5.035515e-05 9.999460e-01
[19684,] 9.998389e-01 6.294771e-07 1.602930e-04 3.283294e-08
[19685,] 4.192657e-05 9.999580e-01 1.302762e-10 1.349347e-09
[19686,] 1.000000e+00 2.522612e-11 7.412415e-12 1.550257e-09
[19687,] 9.999987e-01 1.181040e-06 1.672375e-07 3.581088e-10
[19688,] 1.547634e-01 8.328341e-01 1.228552e-02 1.169601e-04
[19689,] 9.995236e-01 1.272619e-09 4.763972e-04 5.303148e-08
[19690,] 1.078217e-03 3.742707e-08 9.989213e-01 4.877307e-07
[19691,] 1.000000e+00 2.339076e-12 2.417778e-11 4.930175e-09
[19692,] 3.026818e-04 9.996916e-01 5.718007e-06 5.874901e-12
[19693,] 9.999999e-01 9.302590e-08 1.891577e-08 4.157600e-08
[19694,] 1.940581e-05 1.834898e-07 9.999518e-01 2.856670e-05
[19695,] 1.753839e-02 1.235129e-07 9.739776e-01 8.483917e-03
[19696,] 2.187112e-04 1.778216e-08 5.352573e-01 4.645239e-01
[19697,] 4.537728e-06 9.287450e-05 3.372531e-01 6.626495e-01
[19698,] 2.565999e-06 1.149783e-04 9.998823e-01 8.833128e-08
[19699,] 4.681724e-08 1.389013e-09 9.999998e-01 2.416051e-07
[19700,] 2.208594e-07 9.587930e-11 9.997117e-06 9.999897e-01
[19701,] 1.000000e+00 4.763199e-10 3.439928e-08 5.624211e-09
[19702,] 9.999629e-01 4.163294e-08 3.711755e-05 2.400047e-10
[19703,] 1.589534e-03 1.873111e-09 9.984105e-01 7.885431e-09
[19704,] 9.999994e-01 1.275972e-08 5.438638e-07 6.469021e-11
[19705,] 4.699058e-04 1.753226e-07 2.121125e-05 9.995087e-01
[19706,] 3.995511e-06 9.999959e-01 2.082180e-11 4.013283e-12
[19707,] 9.950390e-06 5.669358e-09 9.999748e-01 1.527302e-05
[19708,] 9.999999e-01 1.253059e-11 2.890968e-09 1.256992e-07
[19709,] 7.140245e-01 2.856800e-01 2.909089e-04 4.661119e-06
[19710,] 6.365488e-07 7.278261e-10 9.999994e-01 1.154640e-08
[19711,] 9.999995e-01 6.878265e-09 6.598258e-08 4.016187e-07
[19712,] 2.396016e-02 2.156254e-05 1.918381e-01 7.841801e-01
[19713,] 9.999350e-01 1.340886e-09 1.149923e-09 6.493038e-05
[19714,] 7.283900e-05 8.739401e-06 9.989514e-01 9.668849e-04
[19715,] 1.072972e-07 7.096553e-09 9.999999e-01 2.719006e-09
[19716,] 3.019986e-06 5.614223e-09 1.805267e-03 9.981918e-01
[19717,] 2.961502e-07 1.589421e-06 1.704070e-08 9.999981e-01
[19718,] 1.213864e-06 4.423807e-06 6.412956e-06 9.999880e-01
[19719,] 4.738570e-06 2.812686e-07 3.716248e-04 9.996234e-01
[19720,] 1.345873e-02 4.701444e-08 4.536426e-01 5.328987e-01
[19721,] 8.461098e-07 3.647663e-07 9.999988e-01 1.007480e-09
[19722,] 3.669234e-06 1.303413e-11 9.999963e-01 2.003654e-09
[19723,] 2.720346e-06 9.999973e-01 1.067170e-09 8.725589e-09
[19724,] 6.043246e-07 3.900303e-12 9.999993e-01 1.179823e-07
[19725,] 1.835236e-03 9.981639e-01 1.910649e-07 7.182014e-07
[19726,] 8.798614e-07 1.346776e-07 9.999990e-01 1.304580e-12
[19727,] 1.056240e-05 8.674077e-09 6.148408e-07 9.999888e-01
[19728,] 5.673041e-07 1.987707e-06 9.992162e-01 7.811436e-04
[19729,] 5.752357e-05 1.236378e-08 9.999326e-01 9.775328e-06
[19730,] 1.377940e-08 3.381425e-06 9.999967e-01 1.201776e-10
[19731,] 2.220695e-08 7.303751e-10 6.077873e-07 9.999994e-01
[19732,] 6.308908e-03 4.067362e-01 5.868644e-01 9.051125e-05
[19733,] 1.000000e+00 3.111351e-12 6.856263e-13 8.050429e-12
[19734,] 7.827917e-07 1.996108e-07 9.999989e-01 4.426039e-09
[19735,] 3.711370e-08 8.890220e-08 1.332604e-04 9.998666e-01
[19736,] 1.018548e-04 9.998981e-01 3.279511e-10 8.263220e-10
[19737,] 8.810667e-10 1.000000e+00 1.396768e-09 1.741665e-12
[19738,] 9.999068e-01 2.569541e-08 9.324565e-05 2.521293e-09
[19739,] 2.187563e-07 9.999998e-01 2.591338e-09 1.442164e-14
[19740,] 1.807604e-04 9.998192e-01 2.336685e-10 6.647913e-11
[19741,] 9.300787e-07 9.999990e-01 8.162399e-11 1.511257e-12
[19742,] 9.999989e-01 9.673154e-08 6.996606e-09 9.298861e-07
[19743,] 1.086661e-03 2.968621e-09 9.987893e-01 1.240233e-04
[19744,] 1.586614e-05 9.999841e-01 2.704763e-10 2.842961e-09
[19745,] 2.628458e-07 1.352983e-08 9.999514e-01 4.832733e-05
[19746,] 6.227157e-08 9.999999e-01 2.079268e-10 3.759056e-14
[19747,] 5.297696e-07 1.099497e-06 9.678009e-01 3.219740e-02
[19748,] 1.266809e-09 9.517107e-13 8.507944e-12 1.000000e+00
[19749,] 1.116620e-07 1.278116e-09 6.353547e-09 9.999999e-01
[19750,] 6.331386e-06 1.728886e-11 9.999937e-01 1.953661e-09
[19751,] 2.625262e-05 9.999732e-01 5.242785e-07 6.635608e-11
[19752,] 5.842991e-09 1.659606e-08 1.000000e+00 1.653633e-09
[19753,] 2.742685e-08 5.185467e-09 5.181316e-08 9.999999e-01
[19754,] 6.720239e-07 1.074912e-08 1.471630e-05 9.999846e-01
[19755,] 1.000000e+00 7.525418e-10 1.471075e-08 6.645368e-09
[19756,] 2.674621e-05 9.999732e-01 3.671106e-08 5.452274e-09
[19757,] 9.998484e-01 3.641377e-10 1.435082e-06 1.501480e-04
[19758,] 1.916436e-05 5.296769e-11 9.999807e-01 1.758464e-07
[19759,] 1.590300e-05 2.010814e-06 9.923023e-01 7.679898e-03
[19760,] 2.487410e-04 1.329985e-05 9.996258e-01 1.122003e-04
[19761,] 9.920968e-01 7.347670e-03 4.892366e-04 6.620799e-05
[19762,] 1.915396e-09 3.706499e-10 3.978071e-10 1.000000e+00
[19763,] 9.999998e-01 1.386232e-11 1.108171e-07 7.623170e-08
[19764,] 4.813947e-03 6.692011e-09 9.951860e-01 4.115210e-08
[19765,] 1.000000e+00 9.148517e-09 1.357308e-08 6.039675e-10
[19766,] 4.694462e-08 5.098048e-11 4.706777e-06 9.999952e-01
[19767,] 3.708311e-04 1.943017e-04 9.650324e-01 3.440248e-02
[19768,] 1.211475e-06 9.999988e-01 2.191750e-09 5.855677e-10
[19769,] 9.977023e-01 1.327184e-05 2.680613e-04 2.016418e-03
[19770,] 3.349838e-01 1.681984e-01 5.576499e-03 4.912413e-01
[19771,] 1.196044e-09 2.637550e-12 1.000000e+00 8.380221e-14
[19772,] 9.912792e-17 2.626609e-17 1.228413e-15 1.000000e+00
[19773,] 1.127269e-05 9.999863e-01 2.481205e-06 9.932495e-09
[19774,] 8.416077e-08 1.149049e-08 9.999999e-01 3.376932e-09
[19775,] 9.999756e-01 3.293371e-08 2.309196e-05 1.245322e-06
[19776,] 4.506358e-04 1.863377e-05 9.974647e-01 2.065995e-03
[19777,] 8.125797e-08 3.016174e-08 9.999988e-01 1.022976e-06
[19778,] 2.461177e-09 4.071225e-08 1.186162e-08 1.000000e+00
[19779,] 9.999993e-01 3.196186e-07 2.058341e-07 1.187241e-07
[19780,] 2.269809e-04 9.539075e-07 9.997067e-01 6.526696e-05
[19781,] 5.624192e-08 1.000000e+00 2.815773e-10 1.153255e-10
[19782,] 2.437575e-06 1.199521e-07 9.999975e-01 6.073669e-10
[19783,] 1.762506e-06 3.767861e-09 9.898689e-01 1.012936e-02
[19784,] 2.903835e-07 2.770499e-07 9.999995e-01 1.689957e-09
[19785,] 3.492736e-10 1.368200e-11 4.038323e-09 1.000000e+00
[19786,] 1.986431e-07 9.999998e-01 2.655824e-11 1.113863e-11
[19787,] 8.707010e-05 2.281627e-08 9.999130e-01 1.109199e-08
[19788,] 1.441958e-06 6.565998e-07 9.961258e-01 3.872156e-03
[19789,] 6.891415e-07 4.855177e-10 2.545713e-09 9.999993e-01
[19790,] 1.219953e-07 9.999999e-01 3.278965e-09 2.411808e-11
[19791,] 1.478930e-06 3.062818e-08 9.999986e-01 1.040559e-10
[19792,] 1.471710e-07 3.769667e-10 9.999999e-01 2.626013e-09
[19793,] 9.746873e-01 1.796433e-05 2.507952e-03 2.278680e-02
[19794,] 5.310052e-07 4.116836e-11 3.432537e-03 9.965669e-01
[19795,] 2.374660e-06 4.600605e-07 5.376108e-05 9.999434e-01
[19796,] 1.688453e-01 8.310934e-01 2.480071e-07 6.115528e-05
[19797,] 1.544110e-03 8.187499e-09 9.984558e-01 5.846369e-08
[19798,] 6.909893e-09 4.528912e-10 2.090905e-05 9.999791e-01
[19799,] 1.431567e-09 1.000000e+00 4.947691e-11 2.099304e-11
[19800,] 7.918530e-04 3.617526e-07 9.992035e-01 4.343095e-06
[19801,] 3.418130e-05 2.633985e-04 1.737624e-01 8.259400e-01
[19802,] 9.828375e-09 6.079375e-09 6.094012e-06 9.999939e-01
[19803,] 2.701383e-08 7.304304e-11 1.451117e-03 9.985488e-01
[19804,] 3.437590e-06 3.219823e-07 9.991259e-01 8.703819e-04
[19805,] 7.100790e-11 1.257855e-13 1.031766e-06 9.999989e-01
[19806,] 5.608061e-07 1.492507e-06 1.866292e-06 9.999961e-01
[19807,] 1.582420e-01 1.141463e-04 8.161155e-01 2.552839e-02
[19808,] 9.999995e-01 2.745103e-07 2.278072e-08 2.575144e-07
[19809,] 9.931907e-01 8.841897e-05 6.720574e-03 2.123016e-07
[19810,] 4.121656e-04 6.261242e-08 9.477468e-06 9.995783e-01
[19811,] 5.711357e-07 3.085588e-06 1.392059e-07 9.999962e-01
[19812,] 5.774902e-07 3.604498e-06 4.248263e-04 9.995710e-01
[19813,] 6.211887e-07 9.999664e-01 3.293902e-05 2.768356e-08
[19814,] 1.897432e-10 1.574523e-08 2.678717e-08 1.000000e+00
[19815,] 9.952818e-01 5.657189e-06 4.601997e-03 1.106106e-04
[19816,] 4.261194e-08 3.290213e-09 9.778144e-07 9.999989e-01
[19817,] 1.027183e-10 1.542786e-11 3.688877e-09 1.000000e+00
[19818,] 1.138766e-05 9.999878e-01 8.152287e-07 3.594753e-08
[19819,] 1.313695e-06 5.360671e-09 9.999802e-01 1.846636e-05
[19820,] 5.768002e-05 9.996523e-01 2.901068e-04 3.547577e-08
[19821,] 1.350714e-03 1.741047e-07 4.893045e-07 9.986487e-01
[19822,] 9.958140e-01 6.409742e-04 3.544922e-03 5.959359e-08
[19823,] 7.017252e-06 9.656485e-11 9.999924e-01 5.707475e-07
[19824,] 5.390246e-05 9.799997e-08 9.999460e-01 1.530561e-10
[19825,] 4.522368e-03 9.550298e-05 9.953819e-01 2.428724e-07
[19826,] 5.079768e-04 6.462967e-05 9.994186e-01 8.765011e-06
[19827,] 1.259257e-04 9.998741e-01 4.071490e-11 5.109493e-10
[19828,] 9.999993e-01 4.818812e-09 6.948056e-07 1.669452e-09
[19829,] 1.350515e-05 5.392951e-10 1.611748e-05 9.999704e-01
[19830,] 7.198817e-08 2.985146e-08 2.940648e-08 9.999999e-01
[19831,] 9.999818e-01 1.744286e-05 5.172383e-07 3.369983e-07
[19832,] 1.517761e-02 1.975611e-08 9.848216e-01 8.368256e-07
[19833,] 4.291092e-05 9.999571e-01 4.904976e-09 1.681558e-08
[19834,] 2.390525e-08 1.396638e-09 1.000000e+00 7.962170e-11
[19835,] 3.298821e-07 1.270613e-08 9.998068e-01 1.927998e-04
[19836,] 3.601490e-03 4.292582e-11 9.963959e-01 2.629756e-06
[19837,] 8.417016e-10 1.000000e+00 3.862361e-11 1.870369e-10
[19838,] 7.535697e-04 4.172007e-08 9.992464e-01 2.942241e-08
[19839,] 2.529827e-01 3.510434e-06 7.470134e-01 2.744282e-07
[19840,] 5.955030e-01 2.267305e-04 4.040529e-01 2.173814e-04
[19841,] 7.100790e-11 1.257855e-13 1.031766e-06 9.999989e-01
[19842,] 1.179228e-07 3.173737e-10 1.178003e-03 9.988219e-01
[19843,] 6.461525e-04 9.992460e-01 1.049014e-04 2.954524e-06
[19844,] 1.762008e-06 9.998565e-01 1.281046e-04 1.364326e-05
[19845,] 9.999973e-01 7.462034e-07 7.156403e-07 1.318146e-06
[19846,] 9.998943e-01 6.718479e-07 6.929380e-05 3.584634e-05
[19847,] 9.994387e-01 5.712023e-07 5.563010e-04 4.418144e-06
[19848,] 4.517464e-06 2.510878e-08 9.999955e-01 1.116216e-08
[19849,] 3.132121e-07 3.612808e-10 9.999996e-01 5.389216e-08
[19850,] 9.120296e-06 9.999905e-01 4.379668e-07 5.788736e-09
[19851,] 2.051180e-07 5.109093e-10 9.999998e-01 2.606160e-11
[19852,] 6.087830e-11 1.000000e+00 5.054051e-14 6.215546e-14
[19853,] 1.864940e-06 2.282940e-08 9.999981e-01 9.144042e-11
[19854,] 8.101406e-07 1.112274e-06 9.999487e-01 4.930759e-05
[19855,] 7.550124e-03 9.924480e-01 1.924877e-06 9.826713e-10
[19856,] 1.190175e-04 4.637139e-07 9.998795e-01 1.011796e-06
[19857,] 3.013952e-08 1.744127e-10 1.000000e+00 8.419798e-09
[19858,] 9.993393e-06 9.999900e-01 2.521355e-08 1.903372e-11
[19859,] 5.571473e-05 9.999429e-01 2.423018e-07 1.234309e-06
[19860,] 9.591455e-05 1.213908e-08 9.998430e-01 6.098863e-05
[19861,] 1.278571e-03 9.987129e-01 7.906328e-06 6.109721e-07
[19862,] 9.999968e-01 4.951646e-09 2.807009e-06 3.966207e-07
[19863,] 1.971464e-06 5.327008e-09 9.999980e-01 7.925639e-11
[19864,] 1.821827e-04 1.259128e-08 9.998177e-01 1.517358e-07
[19865,] 4.440979e-05 3.305985e-07 9.971299e-01 2.825392e-03
[19866,] 8.560729e-04 4.672798e-02 2.321923e-01 7.202237e-01
[19867,] 4.874356e-07 9.999995e-01 2.447977e-10 4.559146e-11
[19868,] 6.382118e-08 2.029926e-09 9.999999e-01 1.154171e-12
[19869,] 6.526573e-05 1.725663e-09 9.999347e-01 1.734884e-08
[19870,] 2.496340e-04 9.997296e-01 2.077267e-05 1.260259e-09
[19871,] 3.838832e-03 9.961432e-01 1.590679e-05 2.116763e-06
[19872,] 9.999983e-01 1.215986e-07 6.570542e-09 1.566556e-06
[19873,] 7.216230e-03 3.073808e-05 9.814372e-01 1.131581e-02
[19874,] 8.358821e-08 1.027148e-09 9.999999e-01 6.877428e-09
[19875,] 6.021621e-08 1.330277e-10 3.950982e-08 9.999999e-01
[19876,] 1.778239e-04 9.996291e-01 2.813388e-06 1.901598e-04
[19877,] 9.999995e-01 4.981119e-07 1.339576e-09 3.568315e-09
[19878,] 2.349392e-06 3.512318e-08 9.999976e-01 9.723341e-09
[19879,] 2.055993e-08 2.276930e-09 7.949308e-05 9.999205e-01
[19880,] 1.000000e+00 1.344939e-12 1.275889e-10 5.871650e-08
[19881,] 3.504114e-04 4.723019e-06 9.996445e-01 2.673377e-07
[19882,] 2.483051e-09 4.418479e-12 3.484183e-08 1.000000e+00
[19883,] 2.171461e-04 9.997827e-01 7.103058e-08 5.627554e-11
[19884,] 1.632190e-01 4.484134e-05 1.581209e-04 8.365780e-01
[19885,] 1.579472e-04 1.374219e-09 9.825962e-01 1.724592e-02
[19886,] 1.000000e+00 1.164926e-09 1.813164e-08 5.220077e-10
[19887,] 9.997061e-01 6.937528e-06 2.402496e-04 4.670248e-05
[19888,] 1.000000e+00 2.172846e-10 5.321425e-08 1.845275e-09
[19889,] 4.044256e-07 3.297055e-08 3.556980e-04 9.996439e-01
[19890,] 2.344675e-08 1.267636e-06 1.512796e-05 9.999835e-01
[19891,] 1.434493e-05 9.999857e-01 5.905874e-10 3.774087e-11
[19892,] 3.802825e-11 9.999990e-01 8.419389e-09 1.003631e-06
[19893,] 9.995700e-01 7.564191e-07 4.244638e-04 4.902412e-06
[19894,] 9.988974e-01 7.601736e-08 1.432905e-04 9.592497e-04
[19895,] 4.632911e-06 4.106047e-10 1.056900e-02 9.894264e-01
[19896,] 1.000000e+00 1.669116e-09 1.018971e-08 2.390908e-08
[19897,] 9.994765e-01 3.354686e-08 5.072532e-04 1.631479e-05
[19898,] 5.942345e-02 6.509565e-01 2.540988e-01 3.552127e-02
[19899,] 2.379330e-04 5.496003e-07 7.095224e-05 9.996905e-01
[19900,] 1.000000e+00 4.547232e-08 3.990113e-08 8.868074e-10
[19901,] 9.999944e-01 2.035783e-08 5.507763e-06 1.075827e-07
[19902,] 5.888896e-09 1.000000e+00 1.252313e-13 5.931940e-12
[19903,] 2.712981e-05 3.642949e-07 3.090654e-02 9.690660e-01
[19904,] 1.020730e-03 9.989793e-01 5.442991e-09 6.471184e-10
[19905,] 3.324175e-07 7.772565e-10 9.999996e-01 3.183681e-09
[19906,] 1.759356e-06 1.013654e-11 9.999982e-01 4.162025e-09
[19907,] 1.246392e-07 2.286906e-11 9.999999e-01 5.786180e-11
[19908,] 3.189607e-03 9.968071e-01 3.356545e-06 2.929710e-09
[19909,] 7.651023e-06 2.977746e-07 9.999913e-01 7.886483e-07
[19910,] 3.652123e-08 6.940223e-11 9.999998e-01 2.974300e-07
[19911,] 2.721169e-03 4.578077e-10 2.404665e-04 9.970384e-01
[19912,] 2.301267e-08 1.000000e+00 1.574408e-10 1.197633e-09
[19913,] 9.449776e-07 1.392232e-08 9.999990e-01 2.276358e-09
[19914,] 1.173132e-05 3.051260e-06 9.999847e-01 5.269574e-07
[19915,] 9.993486e-01 5.646427e-04 1.820817e-08 8.674164e-05
[19916,] 3.365744e-06 2.831130e-09 6.554111e-01 3.445855e-01
[19917,] 1.123339e-01 8.876634e-01 2.340352e-06 3.575310e-07
[19918,] 1.026862e-06 4.060732e-09 4.037610e-05 9.999586e-01
[19919,] 6.374791e-09 5.850052e-12 1.000000e+00 3.195394e-12
[19920,] 5.428111e-05 2.325919e-07 9.388100e-01 6.113547e-02
[19921,] 2.824768e-04 9.997169e-01 3.655117e-08 4.677176e-07
[19922,] 9.952011e-01 6.630859e-05 7.065058e-09 4.732516e-03
[19923,] 9.867776e-06 2.102066e-09 9.999900e-01 6.043700e-08
[19924,] 5.132188e-05 3.685221e-07 9.982643e-01 1.684166e-03
[19925,] 1.205473e-07 7.245562e-09 9.999994e-01 4.694852e-07
[19926,] 8.582639e-08 4.348296e-06 6.038456e-08 9.999956e-01
[19927,] 7.912238e-08 9.999999e-01 1.911328e-08 9.565388e-09
[19928,] 2.685546e-03 9.972879e-01 2.568835e-05 9.314210e-07
[19929,] 9.999930e-01 4.357646e-08 4.470596e-10 6.975714e-06
[19930,] 4.730427e-04 1.412045e-04 2.863537e-03 9.965222e-01
[19931,] 4.786376e-05 1.100181e-04 9.772442e-03 9.900697e-01
[19932,] 1.097629e-02 9.126199e-01 7.484459e-02 1.559248e-03
[19933,] 6.213158e-06 3.831862e-10 9.999684e-01 2.535400e-05
[19934,] 1.000000e+00 1.345085e-12 1.652749e-10 9.610766e-12
[19935,] 1.000000e+00 5.012995e-08 1.654008e-10 8.380169e-11
[19936,] 3.349945e-07 5.579148e-10 8.607413e-05 9.999136e-01
[19937,] 8.371517e-03 9.916255e-01 9.235039e-08 3.005103e-06
[19938,] 1.800180e-04 9.998197e-01 1.215864e-07 2.502974e-07
[19939,] 1.000000e+00 4.282110e-13 2.139261e-10 9.681849e-10
[19940,] 2.033711e-07 8.080286e-06 4.089911e-05 9.999508e-01
[19941,] 2.365400e-10 1.658783e-08 1.994595e-08 1.000000e+00
[19942,] 8.411030e-01 6.596532e-02 1.539608e-07 9.293147e-02
[19943,] 3.208609e-02 1.475709e-11 9.679119e-01 1.995874e-06
[19944,] 1.000000e+00 2.499126e-12 2.576723e-10 3.788541e-09
[19945,] 2.733666e-08 1.000000e+00 1.623092e-08 7.800345e-09
[19946,] 5.275178e-08 9.999859e-01 4.081586e-08 1.399996e-05
[19947,] 6.785895e-06 9.999932e-01 6.294198e-09 1.412039e-11
[19948,] 2.729559e-04 9.997266e-01 4.723441e-07 2.548823e-08
[19949,] 1.108172e-01 1.130562e-08 8.891764e-01 6.392265e-06
[19950,] 4.898155e-09 3.882029e-06 1.699266e-07 9.999959e-01
[19951,] 3.416430e-02 1.794470e-07 9.648371e-01 9.983487e-04
[19952,] 2.138161e-07 1.094349e-11 9.976463e-01 2.353494e-03
[19953,] 3.003115e-09 3.863859e-07 5.072743e-08 9.999996e-01
[19954,] 4.217176e-10 1.000000e+00 1.172320e-09 5.120352e-10
[19955,] 1.907099e-06 9.999981e-01 1.645048e-09 1.494597e-09
[19956,] 1.000000e+00 1.102631e-09 3.575213e-08 2.703193e-09
[19957,] 5.825611e-05 2.415975e-06 1.084491e-06 9.999382e-01
[19958,] 2.894965e-05 9.999710e-01 2.590819e-08 1.057665e-09
[19959,] 1.000000e+00 4.341262e-10 5.290079e-10 3.800028e-08
[19960,] 9.958472e-01 1.235905e-04 4.007724e-03 2.159196e-05
[19961,] 9.948783e-01 4.054739e-05 4.901204e-03 1.799713e-04
[19962,] 2.616137e-05 9.999696e-01 4.216170e-07 3.789421e-06
[19963,] 2.026796e-06 3.073667e-08 9.999926e-01 5.278979e-06
[19964,] 1.669096e-07 1.348758e-09 3.942302e-08 9.999998e-01
[19965,] 9.991647e-01 6.109210e-04 2.244616e-04 5.151761e-09
[19966,] 9.244663e-08 3.705893e-09 9.999999e-01 3.566915e-09
[19967,] 6.838501e-08 2.513713e-10 3.395335e-03 9.966046e-01
[19968,] 4.180366e-06 3.566858e-07 9.999944e-01 1.098598e-06
[19969,] 2.061789e-06 4.513066e-07 9.929690e-01 7.028574e-03
[19970,] 5.234708e-08 2.856130e-10 1.860783e-07 9.999998e-01
[19971,] 2.107939e-05 9.999789e-01 6.424550e-11 5.361979e-10
[19972,] 2.057285e-02 9.794194e-01 6.481457e-06 1.366102e-06
[19973,] 9.999998e-01 2.461621e-10 5.531881e-10 2.559202e-07
[19974,] 5.749223e-02 8.425588e-01 9.992955e-02 1.943726e-05
[19975,] 5.564741e-06 3.967067e-11 9.999770e-01 1.744930e-05
[19976,] 8.505558e-03 9.914849e-01 5.283319e-06 4.221591e-06
[19977,] 5.983686e-04 5.468300e-08 9.994005e-01 1.081287e-06
[19978,] 3.131506e-08 4.163538e-08 5.466238e-03 9.945338e-01
[19979,] 1.175256e-09 1.741524e-09 6.152594e-06 9.999938e-01
[19980,] 1.096102e-06 9.999989e-01 5.355218e-10 2.807345e-11
[19981,] 9.999999e-01 1.767502e-07 1.346193e-08 6.048043e-10
[19982,] 4.814161e-06 1.884899e-11 9.999952e-01 2.766510e-12
[19983,] 6.102965e-03 1.457236e-11 9.938964e-01 6.018101e-07
[19984,] 1.701987e-09 1.000000e+00 8.651678e-11 2.671096e-11
[19985,] 8.906946e-06 3.309669e-05 3.391387e-02 9.660442e-01
[19986,] 3.981631e-05 9.999601e-01 1.502684e-07 2.961565e-12
[19987,] 3.474623e-03 9.446291e-08 2.007008e-07 9.965250e-01
[19988,] 9.999880e-01 1.346819e-08 5.094864e-10 1.197168e-05
[19989,] 2.285885e-08 1.353741e-10 2.069507e-07 9.999998e-01
[19990,] 6.110663e-08 9.999999e-01 2.286725e-13 2.742956e-13
[19991,] 2.488498e-07 9.999998e-01 1.166968e-11 1.182097e-11
[19992,] 3.803425e-02 7.127718e-01 9.560955e-04 2.482378e-01
[19993,] 2.039612e-10 1.926064e-09 6.537729e-08 9.999999e-01
[19994,] 5.390921e-05 6.060323e-04 5.739534e-06 9.993343e-01
[19995,] 8.620522e-07 9.999992e-01 1.201091e-08 3.936346e-09
[19996,] 3.084714e-07 9.999996e-01 3.148290e-12 1.796726e-11
[19997,] 9.999920e-01 1.527162e-06 4.089103e-06 2.349877e-06
[19998,] 1.000000e+00 1.260885e-10 5.288500e-08 4.754283e-11
[19999,] 3.643951e-10 1.000000e+00 1.429357e-13 9.338805e-12
[20000,] 4.923410e-06 9.999950e-01 6.091561e-08 7.126618e-09
[20001,] 1.385491e-08 4.566409e-07 5.661834e-06 9.999938e-01
[20002,] 5.139602e-03 1.229702e-07 9.947556e-01 1.046791e-04
[20003,] 9.259182e-09 1.000000e+00 4.641587e-13 9.679459e-12
[20004,] 1.529776e-06 9.358940e-12 9.999985e-01 9.142694e-09
[20005,] 1.033698e-05 6.921187e-07 1.859455e-04 9.998030e-01
[20006,] 4.854073e-09 1.000000e+00 1.712182e-09 4.436118e-09
[20007,] 5.123803e-03 9.948739e-01 2.638035e-08 2.306776e-06
[20008,] 4.573692e-08 1.000000e+00 3.359183e-09 7.244958e-13
[20009,] 1.000000e+00 5.837076e-09 5.835454e-08 6.420404e-09
[20010,] 9.970060e-01 2.869539e-03 3.803260e-05 8.639762e-05
[20011,] 8.774918e-06 2.903355e-08 9.999912e-01 4.365504e-09
[20012,] 2.325541e-07 9.999993e-01 4.860073e-07 2.912259e-11
[20013,] 1.205850e-02 1.918539e-06 9.869947e-01 9.449371e-04
[20014,] 5.510753e-07 7.575451e-11 2.375014e-06 9.999970e-01
[20015,] 2.827755e-07 9.999998e-01 1.531377e-09 1.850351e-11
[20016,] 9.541541e-05 9.999012e-01 3.438889e-06 3.523453e-08
[20017,] 1.402177e-05 9.999840e-01 1.971482e-06 4.671980e-08
[20018,] 2.269416e-04 8.621471e-05 7.810857e-08 9.996868e-01
[20019,] 8.968399e-04 8.085619e-04 2.685415e-06 9.982919e-01
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[20088,] 6.480497e-06 9.999934e-01 1.043357e-07 3.829481e-10
[20089,] 5.161502e-04 9.994804e-01 3.392500e-06 4.786888e-08
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[20091,] 7.033451e-04 9.986093e-01 6.872284e-04 1.099665e-07
[20092,] 9.960609e-01 1.017820e-07 3.874462e-03 6.444693e-05
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[20099,] 1.498540e-04 1.926805e-07 3.719592e-01 6.278908e-01
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[20101,] 4.004015e-07 3.293887e-08 4.744537e-06 9.999949e-01
[20102,] 2.195531e-04 4.727179e-08 1.100144e-03 9.986803e-01
[20103,] 1.138668e-04 9.998848e-01 9.950096e-07 2.525637e-07
[20104,] 1.039121e-05 9.999895e-01 4.069171e-08 2.895269e-13
[20105,] 4.012881e-07 7.312099e-06 9.999924e-01 3.837947e-09
[20106,] 9.923491e-03 2.891241e-05 1.421335e-02 9.758341e-01
[20107,] 3.470098e-05 3.101615e-07 9.668338e-01 3.313114e-02
[20108,] 7.125437e-03 1.283763e-02 4.127526e-03 9.759094e-01
[20109,] 4.323770e-03 9.956762e-01 6.524216e-08 6.735870e-10
[20110,] 2.916485e-05 9.999708e-01 4.303363e-09 3.604205e-09
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[20114,] 6.233028e-08 9.999999e-01 2.859661e-11 1.745791e-10
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[20127,] 4.056028e-06 9.999959e-01 3.026621e-11 1.993223e-14
[20128,] 1.813432e-10 1.000000e+00 4.615110e-10 1.535203e-13
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[20130,] 6.560034e-07 9.999987e-01 6.019320e-07 5.352465e-08
[20131,] 1.000000e+00 1.428203e-11 3.260267e-10 3.712028e-12
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[20134,] 6.820293e-07 5.718043e-08 2.697106e-03 9.973022e-01
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[20146,] 2.021370e-08 3.343095e-09 1.000000e+00 3.919472e-12
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[20901,] 1.000000e+00 5.576504e-17 2.450336e-15 5.852329e-12
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[20961,] 3.004672e-11 1.000000e+00 2.220959e-16 2.806222e-12
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[21985,] 8.588638e-07 4.828239e-11 5.091785e-05 9.999483e-01
[21986,] 1.000000e+00 1.779182e-13 1.478223e-11 2.859577e-09
[21987,] 2.523273e-08 9.994966e-10 2.918875e-06 9.999970e-01
[21988,] 5.550157e-07 2.005002e-08 9.964765e-01 3.522921e-03
[21989,] 1.100447e-04 9.269361e-10 7.928832e-03 9.919612e-01
[21990,] 4.314958e-06 9.957920e-09 1.010146e-06 9.999946e-01
[21991,] 1.157002e-05 6.355728e-10 4.139951e-09 9.999884e-01
[21992,] 1.171117e-04 9.998828e-01 8.450227e-10 1.513210e-08
[21993,] 1.933663e-06 9.999981e-01 2.929095e-08 1.740533e-08
[21994,] 1.151673e-04 9.776490e-08 3.483030e-08 9.998847e-01
[21995,] 7.232460e-06 2.766638e-12 9.242398e-03 9.907504e-01
[21996,] 2.889683e-06 7.859397e-09 1.544386e-03 9.984527e-01
[21997,] 1.370957e-07 1.727631e-05 2.621797e-04 9.997204e-01
[21998,] 8.770035e-06 3.282867e-09 9.889843e-01 1.100695e-02
[21999,] 9.916897e-01 2.475832e-06 6.321336e-06 8.301526e-03
[22000,] 1.026557e-06 3.251491e-10 1.265109e-03 9.987338e-01
[22001,] 1.508085e-08 8.170026e-14 1.000000e+00 3.053338e-12
[22002,] 2.291179e-05 9.194247e-01 8.046921e-02 8.321620e-05
[22003,] 6.815524e-07 2.473924e-07 1.136891e-06 9.999980e-01
[22004,] 1.894984e-02 8.684466e-01 5.630875e-03 1.069726e-01
[22005,] 1.000000e+00 8.473624e-09 1.000067e-08 3.030965e-11
[22006,] 3.870174e-06 3.734676e-05 2.534425e-07 9.999585e-01
[22007,] 9.421188e-09 1.455777e-11 2.456659e-10 1.000000e+00
[22008,] 2.726173e-03 7.760648e-05 1.698657e-09 9.971962e-01
[22009,] 9.999999e-01 2.656088e-11 3.951235e-09 1.382955e-07
[22010,] 9.607127e-06 2.147546e-08 9.999903e-01 8.447400e-09
[22011,] 2.846903e-05 9.999715e-01 3.570649e-11 3.434742e-12
[22012,] 9.999870e-01 1.858210e-06 1.108076e-05 1.758181e-08
[22013,] 4.979420e-06 8.963968e-11 4.057232e-05 9.999545e-01
[22014,] 9.999996e-01 1.727870e-09 3.769910e-11 3.562974e-07
[22015,] 8.151506e-06 4.696967e-08 9.999888e-01 3.052795e-06
[22016,] 4.633213e-03 2.632063e-10 9.953146e-01 5.224734e-05
[22017,] 9.999995e-01 2.525853e-10 1.105182e-07 3.096120e-07
[22018,] 9.999994e-01 9.164409e-08 1.067109e-14 4.974244e-07
[22019,] 4.449186e-04 3.304041e-08 9.995539e-01 1.189711e-06
[22020,] 7.068058e-01 4.649566e-03 2.885304e-01 1.433332e-05
[22021,] 2.246613e-05 9.999597e-01 1.784249e-05 2.898447e-10
[22022,] 9.176160e-04 9.986469e-08 1.226232e-06 9.990810e-01
[22023,] 9.999911e-01 2.128987e-08 5.172209e-07 8.427214e-06
[22024,] 4.824591e-07 7.823753e-07 9.998159e-01 1.829445e-04
[22025,] 6.950811e-04 1.748204e-06 9.992988e-01 4.294011e-06
[22026,] 1.277425e-04 2.289695e-06 5.529297e-01 4.469403e-01
[22027,] 1.408046e-05 9.999859e-01 6.313055e-12 2.355675e-09
[22028,] 1.217317e-03 3.743171e-03 9.938470e-01 1.192565e-03
[22029,] 2.310761e-04 4.501430e-07 3.499354e-05 9.997334e-01
[22030,] 5.998402e-01 3.955533e-01 4.603551e-03 2.988235e-06
[22031,] 7.984132e-02 9.201580e-01 3.744292e-07 2.951504e-07
[22032,] 2.224598e-06 9.999977e-01 1.818972e-09 4.893141e-09
[22033,] 1.386632e-05 3.537185e-10 8.040409e-01 1.959452e-01
[22034,] 1.332407e-07 9.999999e-01 4.603935e-10 8.202733e-11
[22035,] 2.377793e-07 9.999998e-01 2.551794e-10 3.360616e-10
[22036,] 1.114912e-05 9.782977e-09 1.823573e-04 9.998065e-01
[22037,] 2.022789e-08 1.000000e+00 8.176612e-12 4.190668e-10
[22038,] 9.541019e-07 1.129130e-08 9.999990e-01 8.077654e-10
[22039,] 5.977141e-07 1.894784e-10 9.999993e-01 1.472184e-07
[22040,] 1.000000e+00 5.174266e-12 1.029273e-10 2.287242e-08
[22041,] 8.556926e-05 1.020339e-04 9.876361e-01 1.217623e-02
[22042,] 7.771792e-06 7.263539e-08 9.999896e-01 2.568645e-06
[22043,] 3.242890e-10 1.000000e+00 4.653620e-11 7.906584e-11
[22044,] 1.000000e+00 3.816645e-13 8.576848e-12 1.163579e-11
[22045,] 4.169997e-08 4.801390e-10 1.000000e+00 3.936031e-11
[22046,] 5.005347e-08 9.320668e-07 9.999990e-01 2.208578e-09
[22047,] 5.300790e-05 3.142575e-08 6.775124e-08 9.999470e-01
[22048,] 5.995336e-06 9.999940e-01 1.088179e-09 3.901301e-09
[22049,] 6.296348e-06 9.999937e-01 8.393529e-09 3.106739e-10
[22050,] 9.999928e-01 7.098199e-06 1.234348e-09 6.505665e-08
[22051,] 4.892908e-01 4.679656e-06 7.145260e-04 5.099900e-01
[22052,] 1.000000e+00 3.745744e-10 2.612631e-11 2.124718e-08
[22053,] 9.999999e-01 1.878047e-10 1.985627e-10 6.963691e-08
[22054,] 4.010130e-04 7.633814e-09 9.995990e-01 1.713077e-08
[22055,] 1.361834e-06 2.965603e-08 9.994608e-01 5.379187e-04
[22056,] 2.553110e-01 1.742474e-01 5.697492e-01 6.924050e-04
[22057,] 2.356063e-04 9.997640e-01 3.564989e-07 5.482756e-10
[22058,] 9.380897e-07 9.999990e-01 1.774116e-11 1.571096e-08
[22059,] 2.127576e-05 9.974760e-01 1.588909e-07 2.502533e-03
[22060,] 7.983166e-04 1.878904e-06 9.991996e-01 3.117271e-07
[22061,] 2.887124e-06 8.619633e-11 9.999971e-01 2.163098e-10
[22062,] 1.619393e-05 5.402828e-09 1.171121e-08 9.999838e-01
[22063,] 1.000000e+00 9.055257e-09 2.379738e-09 5.141308e-09
[22064,] 9.999995e-01 2.159646e-12 4.363952e-07 1.253603e-08
[22065,] 1.000000e+00 2.602886e-12 7.428101e-11 9.787907e-10
[22066,] 9.999999e-01 7.286800e-08 7.168532e-09 1.536337e-08
[22067,] 9.901927e-05 2.909958e-10 9.998949e-01 6.109154e-06
[22068,] 3.125496e-07 1.794494e-10 9.999996e-01 3.874717e-08
[22069,] 3.398042e-08 1.000000e+00 1.028764e-09 1.340066e-12
[22070,] 6.329763e-03 4.278933e-08 9.445345e-01 4.913570e-02
[22071,] 1.919696e-03 3.586807e-07 9.880653e-01 1.001465e-02
[22072,] 1.186945e-08 1.000000e+00 2.770486e-10 5.689652e-08
[22073,] 7.138732e-06 3.145317e-07 9.999925e-01 5.809587e-09
[22074,] 5.996092e-02 2.514224e-05 9.399859e-01 2.813559e-05
[22075,] 4.550286e-05 1.092919e-08 9.987994e-01 1.155087e-03
[22076,] 6.508450e-05 2.732284e-08 9.999349e-01 3.713265e-09
[22077,] 9.268680e-07 9.999962e-01 2.802294e-06 9.901235e-08
[22078,] 3.451373e-06 9.995271e-01 4.692923e-04 6.692422e-08
[22079,] 7.065070e-05 1.267402e-09 6.232557e-02 9.376038e-01
[22080,] 1.000000e+00 4.626193e-12 2.238469e-11 1.067905e-11
[22081,] 6.785925e-07 6.059458e-10 9.667035e-06 9.999896e-01
[22082,] 4.155872e-08 1.000000e+00 1.616695e-09 7.014729e-10
[22083,] 2.690481e-04 9.775228e-01 2.218223e-02 2.585508e-05
[22084,] 1.399692e-02 8.864124e-05 9.846731e-01 1.241433e-03
[22085,] 1.070694e-02 6.086312e-06 9.892869e-01 4.042761e-09
[22086,] 1.271578e-03 6.493521e-07 9.923795e-01 6.348152e-03
[22087,] 1.847562e-06 9.999981e-01 6.885577e-10 1.984026e-10
[22088,] 3.522190e-07 9.999996e-01 9.605273e-10 2.398389e-08
[22089,] 1.424550e-03 2.218363e-05 9.984788e-01 7.445306e-05
[22090,] 9.998697e-01 3.824027e-08 1.289376e-04 1.238552e-06
[22091,] 1.217746e-06 2.832644e-10 9.999977e-01 1.116554e-06
[22092,] 7.455992e-08 2.254117e-10 4.691204e-01 5.308794e-01
[22093,] 3.176863e-08 8.031267e-12 6.376387e-04 9.993623e-01
[22094,] 4.530035e-06 9.999944e-01 1.518515e-07 9.362568e-07
[22095,] 8.007977e-12 1.000000e+00 7.558856e-16 2.058734e-16
[22096,] 3.551493e-08 9.999944e-01 5.485401e-06 6.197702e-08
[22097,] 1.000000e+00 4.889566e-10 6.757915e-09 8.236292e-09
[22098,] 9.999999e-01 8.549855e-11 1.194562e-09 1.083014e-07
[22099,] 2.880189e-07 2.308358e-10 4.391611e-06 9.999954e-01
[22100,] 1.000000e+00 2.591453e-12 4.701604e-10 7.774345e-11
[22101,] 2.253054e-04 4.052863e-04 9.993694e-01 1.220656e-08
[22102,] 9.999948e-01 1.236204e-06 1.346887e-07 3.910528e-06
[22103,] 8.291360e-01 2.430442e-06 1.684606e-01 2.401069e-03
[22104,] 6.071104e-06 7.868409e-06 9.999861e-01 7.185915e-09
[22105,] 3.227446e-05 4.956717e-04 3.678462e-03 9.957936e-01
[22106,] 9.999986e-01 3.119805e-07 2.024755e-07 9.281794e-07
[22107,] 2.506661e-02 3.448037e-08 9.749206e-01 1.274772e-05
[22108,] 8.132387e-05 1.647355e-05 3.205888e-02 9.678434e-01
[22109,] 1.514887e-05 9.998446e-01 1.393867e-04 8.410024e-07
[22110,] 9.999995e-01 2.083094e-10 3.747650e-10 4.797679e-07
[22111,] 1.060060e-09 1.496403e-09 1.224024e-09 1.000000e+00
[22112,] 9.999343e-01 3.734016e-09 7.961950e-07 6.487964e-05
[22113,] 9.999986e-01 9.625736e-09 2.900912e-13 1.466930e-06
[22114,] 2.047053e-05 5.474003e-09 4.062523e-08 9.999795e-01
[22115,] 1.974288e-08 1.000000e+00 6.874402e-12 3.611686e-10
[22116,] 1.285188e-04 9.998715e-01 7.843441e-09 7.670696e-09
[22117,] 9.037747e-01 2.951206e-03 9.326783e-02 6.275617e-06
[22118,] 1.836557e-06 2.199155e-08 9.566037e-01 4.339449e-02
[22119,] 6.520942e-07 1.304489e-09 2.055074e-01 7.944920e-01
[22120,] 1.211550e-05 1.420150e-05 1.012267e-01 8.987470e-01
[22121,] 9.999999e-01 7.711608e-11 6.338192e-08 8.492975e-09
[22122,] 9.991102e-01 9.718246e-10 5.281077e-07 8.893589e-04
[22123,] 9.521757e-01 4.515385e-02 2.669792e-03 6.678590e-07
[22124,] 1.259021e-02 1.056602e-05 3.686735e-01 6.187258e-01
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[22126,] 1.202016e-05 4.391773e-09 9.994196e-01 5.684260e-04
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[22129,] 7.386347e-03 9.919186e-01 1.717263e-04 5.233021e-04
[22130,] 9.974239e-01 2.562124e-05 2.306336e-06 2.548293e-03
[22131,] 4.447247e-03 2.293545e-09 1.855438e-07 9.955526e-01
[22132,] 4.572462e-04 1.566706e-08 9.995357e-01 7.106419e-06
[22133,] 1.263110e-07 1.088796e-09 1.011906e-04 9.998987e-01
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[22140,] 9.969817e-01 7.612578e-09 2.122344e-03 8.959448e-04
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[24827,] 1.860228e-05 3.784168e-08 9.999814e-01 3.506276e-09
[24828,] 1.325054e-05 2.532605e-05 9.998990e-01 6.239968e-05
[24829,] 6.543517e-08 1.040368e-09 9.999999e-01 6.200328e-11
[24830,] 9.104992e-02 3.430441e-08 3.318864e-01 5.770637e-01
[24831,] 4.337832e-05 9.998022e-01 8.586549e-05 6.869239e-05
[24832,] 9.961215e-01 6.457424e-10 1.220270e-05 3.866300e-03
[24833,] 1.000000e+00 6.221233e-16 4.793647e-15 5.922569e-08
[24834,] 1.881193e-03 3.953045e-07 9.977167e-01 4.017371e-04
[24835,] 1.850291e-08 8.257311e-08 9.999999e-01 1.358587e-09
[24836,] 2.469814e-06 9.999975e-01 5.883440e-08 8.289853e-10
[24837,] 1.038363e-08 5.329525e-06 9.999930e-01 1.749883e-06
[24838,] 1.410678e-01 2.275579e-05 8.589092e-01 1.930189e-07
[24839,] 8.091371e-05 7.193857e-08 9.990766e-01 8.424954e-04
[24840,] 1.345389e-09 4.793039e-05 9.999521e-01 4.118059e-08
[24841,] 7.490995e-03 3.482243e-02 7.878555e-05 9.576078e-01
[24842,] 2.432814e-02 9.756662e-01 4.939866e-06 6.429703e-07
[24843,] 9.999999e-01 1.364572e-10 8.024094e-08 1.630345e-09
[24844,] 9.373236e-01 5.090856e-08 6.261694e-02 5.956093e-05
[24845,] 4.545895e-02 1.709018e-05 9.545229e-01 9.755933e-07
[24846,] 3.484001e-04 9.555516e-01 4.379017e-02 3.098008e-04
[24847,] 8.344529e-02 9.165292e-01 8.147791e-11 2.543962e-05
[24848,] 3.563192e-05 1.562509e-05 9.914016e-01 8.547210e-03
[24849,] 4.594800e-06 1.285918e-05 3.951922e-07 9.999821e-01
[24850,] 2.587375e-05 9.999534e-01 2.077950e-05 2.570450e-08
[24851,] 1.321132e-02 2.867818e-04 9.686000e-05 9.864050e-01
[24852,] 8.159688e-01 1.065816e-04 1.839227e-01 1.831737e-06
[24853,] 1.859633e-01 1.571337e-05 4.598015e-05 8.139750e-01
[24854,] 9.998878e-01 8.294277e-09 8.098550e-05 3.118879e-05
[24855,] 9.999989e-01 5.296507e-09 4.952474e-14 1.036492e-06
[24856,] 9.998350e-01 1.146792e-04 4.676830e-08 5.023862e-05
[24857,] 7.082554e-05 3.197620e-07 9.999288e-01 1.410443e-08
[24858,] 9.016294e-08 7.699735e-10 9.999999e-01 2.538803e-10
[24859,] 8.481727e-01 1.367569e-01 1.010197e-02 4.968332e-03
[24860,] 9.999861e-01 2.667977e-12 2.957791e-09 1.389077e-05
[24861,] 1.159542e-08 1.947979e-10 1.000000e+00 5.537764e-13
[24862,] 3.224722e-05 1.519794e-02 2.607370e-05 9.847437e-01
[24863,] 7.683449e-08 1.198775e-07 9.087931e-05 9.999089e-01
[24864,] 7.879739e-04 9.990121e-01 1.957460e-04 4.205183e-06
[24865,] 9.999985e-01 8.688486e-12 5.474172e-08 1.496495e-06
[24866,] 1.000000e+00 5.898060e-12 6.973700e-12 1.319084e-11
[24867,] 1.302563e-07 6.669519e-09 9.999999e-01 6.756193e-11
[24868,] 5.785643e-10 1.000000e+00 4.060046e-10 5.110569e-09
[24869,] 9.999952e-01 1.656840e-11 3.215590e-09 4.727858e-06
[24870,] 2.695634e-07 1.394349e-04 1.118155e-05 9.998491e-01
[24871,] 2.228673e-02 1.449658e-02 9.629642e-01 2.523781e-04
[24872,] 4.127809e-04 2.135436e-02 9.781582e-01 7.455506e-05
[24873,] 4.786362e-04 9.930388e-01 5.784401e-03 6.982148e-04
[24874,] 1.254962e-04 1.727839e-05 9.998572e-01 4.046633e-10
[24875,] 9.999998e-01 2.880718e-09 1.222504e-07 7.361790e-08
[24876,] 9.933748e-01 9.064121e-09 4.449307e-03 2.176007e-03
[24877,] 1.630618e-03 2.731399e-06 9.982876e-01 7.900615e-05
[24878,] 9.989009e-01 1.092826e-03 5.677137e-06 5.850262e-07
[24879,] 5.713202e-06 6.157566e-09 9.999943e-01 1.784657e-10
[24880,] 5.816429e-06 1.169277e-07 9.999940e-01 6.833060e-10
[24881,] 1.823427e-03 6.977832e-07 9.981747e-01 1.254584e-06
[24882,] 4.374407e-07 1.229846e-07 9.973568e-01 2.642604e-03
[24883,] 8.057901e-03 2.547843e-04 1.497653e-07 9.916872e-01
[24884,] 1.053728e-07 9.999999e-01 3.709287e-13 1.220975e-08
[24885,] 1.471047e-07 9.999999e-01 2.797230e-14 5.104675e-09
[24886,] 2.549828e-03 9.974501e-01 3.488034e-09 7.529366e-08
[24887,] 1.202938e-04 5.805708e-10 2.840670e-02 9.714730e-01
[24888,] 9.312487e-10 9.451666e-11 1.211617e-07 9.999999e-01
[24889,] 1.426923e-08 2.562970e-10 1.417099e-02 9.858290e-01
[24890,] 6.457431e-06 5.043146e-07 5.224138e-06 9.999878e-01
[24891,] 2.998026e-11 1.000000e+00 6.529781e-11 2.139594e-15
[24892,] 5.075933e-04 4.958475e-09 6.803899e-04 9.988121e-01
[24893,] 5.979703e-09 9.648686e-09 3.293563e-07 9.999996e-01
[24894,] 7.249790e-03 4.320000e-02 3.275143e-01 6.220359e-01
[24895,] 3.483555e-09 9.999996e-01 1.213362e-08 3.044645e-07
[24896,] 4.343410e-03 9.956428e-01 1.550993e-08 1.377267e-05
[24897,] 1.111265e-02 1.846802e-02 1.219782e-01 8.484411e-01
[24898,] 2.296330e-11 8.680918e-11 1.002723e-08 1.000000e+00
[24899,] 1.596341e-06 6.846899e-09 3.008097e-04 9.996976e-01
[24900,] 9.999964e-01 8.597317e-10 6.196498e-08 3.453603e-06
[24901,] 3.001610e-09 1.127441e-12 2.892812e-08 1.000000e+00
[24902,] 2.924164e-04 2.957345e-09 5.546975e-04 9.991529e-01
[24903,] 9.999994e-01 2.542031e-08 4.981000e-07 4.366593e-08
[24904,] 3.425586e-04 7.368088e-09 9.995547e-01 1.027034e-04
[24905,] 9.997855e-01 4.435998e-08 5.174279e-09 2.144360e-04
[24906,] 1.039979e-04 3.179704e-05 9.885825e-01 1.128172e-02
[24907,] 9.961703e-01 2.854123e-06 3.806518e-03 2.025032e-05
[24908,] 2.220961e-04 6.098084e-09 9.997765e-01 1.378140e-06
[24909,] 1.000000e+00 3.763685e-13 5.992612e-15 2.259710e-09
[24910,] 9.991972e-01 3.679093e-06 8.581099e-05 7.134069e-04
[24911,] 9.999999e-01 6.469050e-11 4.547127e-08 9.360988e-08
[24912,] 9.999905e-01 4.068381e-07 2.340410e-06 6.779019e-06
[24913,] 9.999995e-01 1.347847e-09 1.561703e-07 4.042937e-07
[24914,] 9.999999e-01 1.963765e-08 7.421993e-08 2.365794e-09
[24915,] 1.000000e+00 6.334597e-10 3.411723e-10 5.925673e-09
[24916,] 9.301801e-01 2.119440e-06 4.929951e-02 2.051829e-02
[24917,] 1.157987e-03 1.341641e-06 9.988084e-01 3.230833e-05
[24918,] 1.800240e-02 9.390152e-01 1.167063e-02 3.131173e-02
[24919,] 1.000000e+00 1.161321e-10 2.215744e-10 8.327555e-11
[24920,] 1.000000e+00 1.323607e-13 6.909774e-13 2.625604e-12
[24921,] 9.999971e-01 1.808164e-09 1.108322e-07 2.716887e-06
[24922,] 1.000000e+00 4.539903e-14 6.836652e-12 1.947875e-10
[24923,] 9.998862e-01 2.831283e-08 1.123541e-04 1.374188e-06
[24924,] 2.613224e-05 2.493926e-06 9.982172e-01 1.754127e-03
[24925,] 4.419748e-09 9.731874e-09 5.809206e-07 9.999994e-01
[24926,] 4.037188e-06 1.362434e-09 4.679506e-06 9.999913e-01
[24927,] 4.752287e-03 6.522589e-07 1.503712e-01 8.448760e-01
[24928,] 7.384086e-02 1.164765e-06 5.670630e-02 8.694518e-01
[24929,] 1.296855e-05 2.639439e-06 9.999844e-01 3.737538e-09
[24930,] 3.487224e-05 5.855280e-09 9.998313e-01 1.336814e-04
[24931,] 2.746256e-07 9.999996e-01 1.810606e-08 9.375138e-08
[24932,] 6.715823e-06 9.999933e-01 1.673670e-08 8.340669e-09
[24933,] 1.000000e+00 2.680730e-09 1.299949e-11 1.112022e-08
[24934,] 9.999926e-01 2.290809e-06 3.780513e-06 1.300753e-06
[24935,] 7.574314e-01 3.572465e-05 2.396854e-04 2.422931e-01
[24936,] 5.235595e-04 2.650776e-07 9.994745e-01 1.798875e-06
[24937,] 2.733425e-05 9.370186e-05 2.292106e-02 9.769579e-01
[24938,] 1.876253e-06 7.692380e-10 7.348877e-03 9.926493e-01
[24939,] 3.036446e-07 2.519385e-08 5.305829e-06 9.999944e-01
[24940,] 1.843719e-04 2.401431e-08 6.535227e-08 9.998156e-01
[24941,] 6.101086e-01 2.186102e-03 2.237642e-01 1.639411e-01
[24942,] 9.440496e-03 2.325323e-07 4.517557e-01 5.388036e-01
[24943,] 9.999655e-01 9.801273e-08 3.436513e-05 6.339788e-08
[24944,] 4.113466e-05 9.999588e-01 1.207556e-09 8.147524e-08
[24945,] 1.293858e-02 3.513840e-07 9.567225e-03 9.774939e-01
[24946,] 1.202629e-04 1.489479e-03 2.466450e-03 9.959238e-01
[24947,] 4.079835e-03 9.893265e-01 2.650195e-05 6.567202e-03
[24948,] 5.715046e-05 9.999428e-01 7.720406e-08 6.524565e-11
[24949,] 2.100062e-05 9.999771e-01 1.856153e-06 1.712980e-08
[24950,] 6.492938e-09 9.999999e-01 4.805790e-09 1.665227e-07
[24951,] 9.999429e-01 1.747126e-05 9.958411e-07 3.868256e-05
[24952,] 1.000000e+00 9.398477e-14 8.620014e-12 5.467066e-11
[24953,] 3.680277e-08 1.317420e-10 9.999850e-01 1.500639e-05
[24954,] 1.696078e-03 4.988264e-11 9.982771e-01 2.685394e-05
[24955,] 1.060313e-03 1.547391e-01 4.082529e-01 4.359477e-01
[24956,] 9.999920e-01 4.682438e-08 6.542411e-10 7.987284e-06
[24957,] 1.084264e-05 9.999892e-01 4.406906e-10 5.288864e-09
[24958,] 9.926271e-12 1.814648e-12 1.496844e-10 1.000000e+00
[24959,] 6.043290e-07 4.569896e-09 6.246418e-02 9.375353e-01
[24960,] 4.274377e-07 9.999995e-01 7.571744e-11 1.276132e-10
[24961,] 1.007663e-06 5.508459e-06 9.999909e-01 2.625836e-06
[24962,] 2.702362e-04 3.647169e-09 2.243245e-03 9.974865e-01
[24963,] 1.247367e-04 8.593484e-03 6.450970e-03 9.848307e-01
[24964,] 5.219466e-07 7.577433e-08 2.305305e-04 9.997688e-01
[24965,] 9.999874e-01 9.442617e-10 1.249273e-05 1.180417e-07
[24966,] 1.534933e-04 9.259065e-08 1.411303e-05 9.998323e-01
[24967,] 6.537075e-04 6.801427e-08 1.621357e-05 9.993300e-01
[24968,] 9.343188e-01 6.542778e-02 1.308364e-05 2.403623e-04
[24969,] 1.173991e-06 2.863640e-05 2.808763e-06 9.999675e-01
[24970,] 7.807380e-05 9.999219e-01 4.072015e-09 5.851803e-09
[24971,] 1.000000e+00 1.389501e-09 2.833615e-08 2.267902e-08
[24972,] 9.989158e-01 2.355543e-09 2.409087e-08 1.084208e-03
[24973,] 3.430154e-04 7.850092e-08 9.957590e-01 3.897961e-03
[24974,] 7.674521e-07 3.588160e-05 9.999447e-01 1.871408e-05
[24975,] 2.848204e-06 8.382645e-09 2.673953e-07 9.999969e-01
[24976,] 1.990293e-04 5.744195e-10 3.936045e-06 9.997970e-01
[24977,] 4.741110e-03 9.952509e-01 7.937636e-06 7.755590e-09
[24978,] 9.994673e-01 4.020005e-04 1.268777e-04 3.757463e-06
[24979,] 9.997130e-01 9.642265e-12 2.868529e-04 1.239708e-07
[24980,] 9.997448e-01 1.935111e-07 2.537188e-04 1.294095e-06
[24981,] 2.894607e-04 3.825694e-08 3.329366e-08 9.997105e-01
[24982,] 2.667605e-04 7.748214e-08 9.997332e-01 2.549384e-08
[24983,] 2.242829e-07 9.999490e-01 1.690815e-10 5.083535e-05
[24984,] 2.607210e-05 1.599933e-07 9.944194e-01 5.554331e-03
[24985,] 2.824751e-06 1.142638e-06 9.999959e-01 4.943394e-09
[24986,] 4.052074e-07 1.012135e-07 9.999995e-01 4.124135e-11
[24987,] 3.811574e-06 3.911646e-08 9.999962e-01 1.340385e-08
[24988,] 1.573666e-07 6.813000e-13 9.999986e-01 1.287706e-06
[24989,] 6.445188e-04 4.279630e-07 6.074657e-01 3.918894e-01
[24990,] 5.746368e-05 4.994410e-04 9.994233e-01 1.987548e-05
[24991,] 1.458784e-05 7.936618e-09 9.999853e-01 1.573099e-07
[24992,] 8.749384e-04 7.157927e-08 9.990706e-01 5.450470e-05
[24993,] 2.304001e-01 1.136195e-05 7.695765e-01 1.204900e-05
[24994,] 9.766603e-04 4.784437e-07 4.042309e-03 9.949805e-01
[24995,] 4.516786e-08 7.917331e-10 1.742682e-08 9.999999e-01
[24996,] 2.886031e-09 9.999999e-01 1.504588e-08 1.519061e-07
[24997,] 4.156973e-05 9.990584e-01 8.650949e-04 3.492786e-05
[24998,] 3.991177e-05 9.999601e-01 3.506295e-09 3.664541e-10
[24999,] 5.560744e-09 1.000000e+00 8.910189e-10 3.554995e-13
 [ reached 'max' / getOption("max.print") -- omitted 5001 rows ]

An Introduction to Text Analysis

Hello

Did you come prepared?

Before NLP and Text Analysis

Tidy Data

Tidy Text

Tokens

Unnesting Tokens

Unnesting Tokens

Unnesting Tokens

The RBI MPC minutes

The RBI MPC minutes

The RBI MPC minutes - removing stop words

The RBI MPC Minutes - Word freq

The RBI MPC Minutes - Word freq

Can do other stuff

Can do other stuff

Can do other stuff

Can do other stuff

Can AI do this

Can do other stuff

Can do other stuff

All this is fine. Where is the cool stuff?

Sentiment Analysis

Sentiment Analysis

Sentiment Analysis - Lexicons

Sentiment Analysis - AFINN

Sentiment Analysis - bing

Sentiment Analysis - nrc

Sentiment Analysis - Use with Care

Subjectivity in Sentiment Analysis

Looking for Sentiments in the RBI MPC Minutes

Looking for Sentiments in the RBI MPC Minutes

MPC Sentiments - Set up

MPC Sentiments - Set up

MPC Sentiments - augment with lexicon

MPC Sentiments - Aggregate at Para level

MPC Sentiments - Bing

MPC Positive Sentiments - Bing

MPC Positive Sentiments - Bing

MPC Negative Sentiments - Bing

MPC Negative Sentiments - Bing

MPC Cumulative Sentiments - Bing

MPC Cumulative Sentiments - Bing

Same stuff using Loughran-McDonald

Same stuff using Loughran-McDonald

Same stuff using Loughran-McDonald

Sentence as Token

Sentence as token

Beyond Descriptive

Topic Modeling

Topic Modeling

LDA

LDA

Applying LDA

Applying LDA

Applying LDA

Applying LDA

Applying LDA

Applying LDA

Applying LDA

Applying LDA

Infering from LDA

Infering from LDA

Infering from LDA

Infering from LDA

Infering from LDA

Inferring from LDA

Finding the right k

Finding the right k

Finding the right k

Finding the right k

Supervised models for text analysis

Dense Neural Netowrks

Dense Neural Network

Dense Neural Network

Dense Neural Network

Dense Neural Network

Dense Neural Network

Dense Neural Networks

Finding the right `k`

Finding the right `k`

Finding the right `k`

Finding the right `k`