381 lines
16 KiB
TeX
381 lines
16 KiB
TeX
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\hypersetup{
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pdftitle={Chapter 2 Notes},
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pdfauthor={Emanuel Rodriguez},
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colorlinks=true,
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linkcolor={blue},
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filecolor={Maroon},
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citecolor={Blue},
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urlcolor={Blue},
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pdfcreator={LaTeX via pandoc}}
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\title{Chapter 2 Notes}
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\author{Emanuel Rodriguez}
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\date{}
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\begin{document}
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\maketitle
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\ifdefined\Shaded\renewenvironment{Shaded}{\begin{tcolorbox}[interior hidden, enhanced, breakable, frame hidden, sharp corners, boxrule=0pt, borderline west={3pt}{0pt}{shadecolor}]}{\end{tcolorbox}}\fi
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In this chapter we step through an example of ``fake'' vs ``real'' news
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to build a framework to determine the probability of real vs fake of a
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new news article titled ``The President has a secret!''
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\begin{Shaded}
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\begin{Highlighting}[]
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\CommentTok{\# libraries}
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\FunctionTok{library}\NormalTok{(bayesrules)}
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\FunctionTok{library}\NormalTok{(dplyr)}
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\FunctionTok{library}\NormalTok{(tidyr)}
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\FunctionTok{library}\NormalTok{(gt)}
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\FunctionTok{data}\NormalTok{(fake\_news)}
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\NormalTok{fake\_news }\OtherTok{\textless{}{-}}\NormalTok{ tibble}\SpecialCharTok{::}\FunctionTok{as\_tibble}\NormalTok{(fake\_news)}
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\end{Highlighting}
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\end{Shaded}
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What is the proportion of news articles that were labeled fake vs real.
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\begin{Shaded}
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\begin{Highlighting}[]
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\NormalTok{fake\_news }\SpecialCharTok{|\textgreater{}} \FunctionTok{glimpse}\NormalTok{()}
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\end{Highlighting}
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\end{Shaded}
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\begin{verbatim}
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Rows: 150
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Columns: 30
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$ title <chr> "Clinton's Exploited Haiti Earthquake ‘to Stea~
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$ text <chr> "0 SHARES Facebook Twitter\n\nBernard Sansaric~
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$ url <chr> "http://freedomdaily.com/former-haitian-senate~
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$ authors <chr> NA, NA, "Sierra Marlee", "Jack Shafer,Nolan D"~
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$ type <fct> fake, real, fake, real, fake, real, fake, fake~
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$ title_words <int> 17, 18, 16, 11, 9, 12, 11, 18, 10, 13, 10, 11,~
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$ text_words <int> 219, 509, 494, 268, 479, 220, 184, 500, 677, 4~
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$ title_char <int> 110, 95, 96, 60, 54, 66, 86, 104, 66, 81, 59, ~
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$ text_char <int> 1444, 3016, 2881, 1674, 2813, 1351, 1128, 3112~
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$ title_caps <int> 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 0~
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$ text_caps <int> 1, 1, 3, 3, 0, 0, 0, 12, 12, 1, 2, 5, 1, 1, 6,~
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$ title_caps_percent <dbl> 0.000000, 0.000000, 6.250000, 0.000000, 0.0000~
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$ text_caps_percent <dbl> 0.4566210, 0.1964637, 0.6072874, 1.1194030, 0.~
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$ title_excl <int> 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0~
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$ text_excl <int> 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0~
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$ title_excl_percent <dbl> 0.0000000, 0.0000000, 2.0833333, 0.0000000, 0.~
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$ text_excl_percent <dbl> 0.00000000, 0.00000000, 0.06942034, 0.00000000~
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$ title_has_excl <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE, FALSE~
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$ anger <dbl> 4.24, 2.28, 1.18, 4.66, 0.82, 1.29, 2.56, 3.47~
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$ anticipation <dbl> 2.12, 1.71, 2.16, 1.79, 1.23, 0.43, 2.05, 1.74~
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$ disgust <dbl> 2.54, 1.90, 0.98, 1.79, 0.41, 1.72, 2.05, 1.35~
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$ fear <dbl> 3.81, 1.90, 1.57, 4.30, 0.82, 0.43, 5.13, 4.25~
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$ joy <dbl> 1.27, 1.71, 1.96, 0.36, 1.23, 0.86, 1.54, 1.35~
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$ sadness <dbl> 4.66, 1.33, 0.78, 1.79, 0.82, 0.86, 2.05, 1.93~
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$ surprise <dbl> 2.12, 1.14, 1.18, 1.79, 0.82, 0.86, 1.03, 1.35~
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$ trust <dbl> 2.97, 4.17, 3.73, 2.51, 2.46, 2.16, 5.13, 3.86~
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$ negative <dbl> 8.47, 4.74, 3.33, 6.09, 2.66, 3.02, 4.10, 4.63~
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$ positive <dbl> 3.81, 4.93, 5.49, 2.15, 4.30, 2.16, 4.10, 4.25~
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$ text_syllables <int> 395, 845, 806, 461, 761, 376, 326, 891, 1133, ~
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$ text_syllables_per_word <dbl> 1.803653, 1.660118, 1.631579, 1.720149, 1.5887~
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\end{verbatim}
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\begin{Shaded}
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\begin{Highlighting}[]
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\NormalTok{fake\_news }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{group\_by}\NormalTok{(type) }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{summarise}\NormalTok{(}
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\AttributeTok{total =} \FunctionTok{n}\NormalTok{(),}
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\AttributeTok{prop =}\NormalTok{ total }\SpecialCharTok{/} \FunctionTok{nrow}\NormalTok{(fake\_news)}
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\NormalTok{ ) }
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\end{Highlighting}
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\end{Shaded}
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\begin{verbatim}
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# A tibble: 2 x 3
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type total prop
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<fct> <int> <dbl>
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1 fake 60 0.4
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2 real 90 0.6
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\end{verbatim}
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If we let \(B\) be the event that a news article is ``fake'' news, and
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\(B^c\) be the event that a news article is ``real'', we can write the
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following:
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\[P(B) = .4\] \[P(B^c) = .6\]
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This is the first ``clue'' or set of data that we have to build into our
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framework. Namely, majority of articles are ``real'', therefore we could
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simply predict that the new article is ``real''. This updated sense or
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reality now becomes our priors.
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Getting additional data, and updating our priors, based on additional
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data. The new observation we make is the use of exclamation marks ``!''.
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We note that the use of ``!'' is more frequent in news articles labeled
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as ``fake''. We will want to incorporate this into our framework to
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decide whether the new incoming should be labelled as real or fake.
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\hypertarget{likelihood}{%
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\subsubsection{Likelihood}\label{likelihood}}
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\begin{tcolorbox}[enhanced jigsaw, coltitle=black, rightrule=.15mm, bottomtitle=1mm, breakable, colframe=quarto-callout-note-color-frame, toprule=.15mm, colback=white, opacityback=0, title=\textcolor{quarto-callout-note-color}{\faInfo}\hspace{0.5em}{Probability and Likelihood}, bottomrule=.15mm, opacitybacktitle=0.6, toptitle=1mm, titlerule=0mm, arc=.35mm, leftrule=.75mm, left=2mm, colbacktitle=quarto-callout-note-color!10!white]
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When the event \(B\) is known, then we can evaluate the uncertainy of
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events \(A\) and \(A^c\) given \(B\)
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\[P(A|B) \text{ vs } P(A^c|B)\]
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If on the other hand, we know event \(A\) then we can evaluate the
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relative compatability of data \(A\) with \(B\) and \(B^c\) using
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likelihood functions
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\[L(B|A) \text{ vs } L(B^c|A)\] \[=P(A|B) \text{ vs } P(A|B^c)\]
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\end{tcolorbox}
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So in our case, we don't know whether this new incoming article is real
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or not, but we do know that the title has an exclamation mark. This
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means we can evaluate how likely this article is real or not given that
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it contains an ``!'' in the title using likelihood functions. We can
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formualte this as:
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\[L(B|A) \text{ vs } L(B^c|A)\]
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And perform the computation in R as follows:
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\begin{Shaded}
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\begin{Highlighting}[]
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\CommentTok{\# if fake, what are the proprotions of ! vs no{-}!}
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\NormalTok{prop\_of\_excl\_within\_type }\OtherTok{\textless{}{-}}\NormalTok{ fake\_news }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{group\_by}\NormalTok{(type, title\_has\_excl) }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{summarise}\NormalTok{(}
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\AttributeTok{total =} \FunctionTok{n}\NormalTok{()}
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\NormalTok{ ) }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{ungroup}\NormalTok{() }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{group\_by}\NormalTok{(type) }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{summarise}\NormalTok{(}
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\AttributeTok{has\_excl =}\NormalTok{ title\_has\_excl,}
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\AttributeTok{prop\_within\_type =}\NormalTok{ total }\SpecialCharTok{/} \FunctionTok{sum}\NormalTok{(total)}
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\NormalTok{ ) }
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\end{Highlighting}
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\end{Shaded}
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\begin{Shaded}
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\begin{Highlighting}[]
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\NormalTok{prop\_of\_excl\_within\_type }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{pivot\_wider}\NormalTok{(}\AttributeTok{names\_from =} \StringTok{"type"}\NormalTok{, }\AttributeTok{values\_from =}\NormalTok{ prop\_within\_type) }\SpecialCharTok{|\textgreater{}}
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\FunctionTok{gt}\NormalTok{() }\SpecialCharTok{|\textgreater{}}
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\NormalTok{ gt}\SpecialCharTok{::}\FunctionTok{cols\_label}\NormalTok{(}
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\AttributeTok{has\_excl =} \StringTok{"Contains Exclamtion"}\NormalTok{,}
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\AttributeTok{fake =} \StringTok{"Fake"}\NormalTok{, }
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\AttributeTok{real =} \StringTok{"Real"}\NormalTok{) }\SpecialCharTok{|\textgreater{}}
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\NormalTok{ gt}\SpecialCharTok{::}\FunctionTok{fmt\_number}\NormalTok{(}\AttributeTok{columns=}\FunctionTok{c}\NormalTok{(}\StringTok{"fake"}\NormalTok{, }\StringTok{"real"}\NormalTok{), }\AttributeTok{decimals =} \DecValTok{3}\NormalTok{) }\SpecialCharTok{|\textgreater{}}
|
||
\NormalTok{ gt}\SpecialCharTok{::}\FunctionTok{cols\_width}\NormalTok{(}\FunctionTok{everything}\NormalTok{() }\SpecialCharTok{\textasciitilde{}} \FunctionTok{px}\NormalTok{(}\DecValTok{100}\NormalTok{))}
|
||
\end{Highlighting}
|
||
\end{Shaded}
|
||
|
||
\begin{longtable}{crr}
|
||
\toprule
|
||
Contains Exclamtion & Fake & Real \\
|
||
\midrule
|
||
FALSE & $0.733$ & $0.978$ \\
|
||
TRUE & $0.267$ & $0.022$ \\
|
||
\bottomrule
|
||
\end{longtable}
|
||
|
||
The table above also shows the likelihoods for the case when an article
|
||
does not contain exclamation point in the title.
|
||
|
||
|
||
|
||
\end{document}
|