/
mac_13_19.tex
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mac_13_19.tex
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\documentclass{beamer}
%\usepackage[table]{xcolor}
\mode<presentation> {
\usetheme{Boadilla}
% \usetheme{Pittsburgh}
%\usefonttheme[2]{sans}
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%\usepackage{lmodern}
%\usepackage[T1]{fontenc}
%\usepackage{palatino}
%\usepackage{cmbright}
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\useinnertheme{rectangles}
}
%\usepackage{normalem}{ulem}
%\usepackage{colortbl, textcomp}
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\usepackage{array}
\beamertemplatesolidbackgroundcolor{white} \setbeamercolor{alerted
text}{fg=red}
\setbeamertemplate{caption}[numbered]\newcounter{mylastframe}
%\usepackage{color}
\usepackage{tikz}
\usetikzlibrary{arrows}
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%$A = B$.
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\renewcommand{\familydefault}{cmss}
%\usepackage[all]{xy}
\usepackage{tikz}
\usepackage{lipsum}
\newenvironment{changemargin}[3]{%
\begin{list}{}{%
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\setlength{\leftmargin}{#1}%
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\usetikzlibrary{arrows}
%\usepackage{palatino}
%\usepackage{eulervm}
\usecolortheme{lily}
\newtheorem{com}{Comment}
\newtheorem{lem} {Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{defn}{Definition}
\newtheorem{cor}{Corollary}
\newtheorem{obs}{Observation}
\numberwithin{equation}{section}
%\usepackage[latin1]{inputenc}
\title[Text as Data] % (optional, nur bei langen Titeln nötig)
{Text as Data}
\author{Justin Grimmer}
\institute[Stanford University]{Professor\\Department of Political Science \\ Stanford University}
\vspace{0.3in}
\date{May 15th, 2019}%[Big Data Workshop]
%\date{\today}
\begin{document}
\begin{frame}
\titlepage
\end{frame}
\begin{frame}
\huge
Measurement via repurposed discovery methods
\begin{itemize}
\item[1)] Discovery categories, measure prevalence of categories
\item[2)] Once we fix \alert{interpretation}, accuracy/precision/recall well defined
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{LDA Revisited}
\only<1>{\begin{eqnarray}
\boldsymbol{\theta}_{k} & \sim & \text{Dirichlet}(\boldsymbol{1}) \nonumber \\
\boldsymbol{\pi}_{i}|\boldsymbol{\alpha} & \sim & \text{Dirichlet}(\boldsymbol{\alpha}) \nonumber \\
\boldsymbol{\tau}_{im}| \boldsymbol{\pi}_{i} & \sim & \text{Multinomial}(1, \boldsymbol{\pi}_{i}) \nonumber \\
x_{im} | \boldsymbol{\theta}_{k}, \tau_{imk} = 1 & \sim & \text{Multinomial}(1, \boldsymbol{\theta}_{k}) \nonumber
\end{eqnarray}}
\only<2>{\begin{eqnarray}
\textbf{Unigram Model}_{k} & \sim & \text{Dirichlet}(\boldsymbol{1}) \nonumber \\
\textbf{Doc. Prop}_{i} & \sim & \text{Dirichlet}(\textbf{Pop. Proportion}) \nonumber \\
\textbf{Word Topic}_{im} & \sim & \text{Multinomial}(1, \textbf{Doc. Prop}_{i}) \nonumber \\
\text{Word}_{im} & \sim & \text{Multinomial}(1, \textbf{Unigram Model}_{k}) \nonumber
\end{eqnarray}}
\end{frame}
\begin{frame}
\frametitle{A General Hierarchical Structure}
LDA:
\begin{tikzpicture}
\node (col) at (0, 10) [] {\textbf{Pop. Proportion}} ;
\invisible<1>{
\node (doc1) at (-5, 8) [] {\textbf{Doc. Prop}$_{1}$} ;
\node (doc2) at (-1, 8) [] {\textbf{Doc. Prop}$_{2}$} ;
\node (dots) at ( 2, 8) [] {$\hdots$} ;
\node (docN) at (4, 8) [] {\textbf{Doc. Prop}$_{N}$} ;
\draw[->, line width=1.5pt] (col) to [out=240, in = 90] (doc1);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (doc2);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (docN);
}
\invisible<1-2>{
\node (word11) at (-5, 7) [] {\textbf{Word Topics}$_{1}$} ;
\node (word22) at (-1, 7) [] {\textbf{Word Topics}$_{2}$} ;
\node (wordnn) at (4, 7) [] {\textbf{Word Topics}$_{N}$ } ;
\draw[->, line width=1.5pt] (doc1) to [out=270, in=90] (word11) ;
\draw[->, line width=1.5pt] (doc2) to [out=270, in=90] (word22) ;
\draw[->, line width=1.5pt] (docN) to [out=270, in=90] (wordnn) ;
}
\invisible<1-3>{
\node (wordaa) at (-5, 6) [] {\textbf{Words}$_{1}$} ;
\node (wordbb) at (-1, 6) [] {\textbf{Words}$_{2}$} ;
\node (wordcc) at (4, 6) [] {\textbf{Words}$_{N}$ } ;
\draw[->, line width = 1.5pt] (word11) to [out = 270, in = 90] (wordaa);
\draw[->, line width = 1.5pt] (word22) to [out = 270, in = 90] (wordbb);
\draw[->, line width = 1.5pt] (wordnn) to [out = 270, in = 90] (wordcc);
\node (topics) at (-1, 4) [] {$\textbf{Unigram Models}$} ;
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordaa);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordbb);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordcc);
}
\end{tikzpicture}
\pause \pause \pause
\end{frame}
\begin{frame}
\frametitle{A General Hierarchical Structure}
Dynamic Topic Model (Quinn et al 2010)
\begin{tikzpicture}
\node (col) at (0, 10) [] {\textbf{Dynamic Prior Across Days}} ;
\invisible<1>{
\node (doc1) at (-5, 8) [] {\textbf{Day Prop}$_{1}$} ;
\node (doc2) at (-1, 8) [] {\textbf{Day Prop}$_{2}$} ;
\node (dots) at ( 2, 8) [] {$\hdots$} ;
\node (docN) at (4, 8) [] {\textbf{Day Prop}$_{N}$} ;
\draw[->, line width=1.5pt] (col) to [out=240, in = 90] (doc1);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (doc2);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (docN);
}
\invisible<1-2>{
\node (word11) at (-5, 7) [] {\textbf{Speech Topics}$_{1}$} ;
\node (word22) at (-1, 7) [] {\textbf{Speech Topics}$_{2}$} ;
\node (wordnn) at (4, 7) [] {\textbf{Speech Topics}$_{N}$ } ;
\draw[->, line width=1.5pt] (doc1) to [out=270, in=90] (word11) ;
\draw[->, line width=1.5pt] (doc2) to [out=270, in=90] (word22) ;
\draw[->, line width=1.5pt] (docN) to [out=270, in=90] (wordnn) ;
}
\invisible<1-3>{
\node (wordaa) at (-5, 6) [] {\textbf{Speeches}$_{1}$} ;
\node (wordbb) at (-1, 6) [] {\textbf{Speeches}$_{2}$} ;
\node (wordcc) at (4, 6) [] {\textbf{Speeches}$_{N}$ } ;
\draw[->, line width = 1.5pt] (word11) to [out = 270, in = 90] (wordaa);
\draw[->, line width = 1.5pt] (word22) to [out = 270, in = 90] (wordbb);
\draw[->, line width = 1.5pt] (wordnn) to [out = 270, in = 90] (wordcc);
\node (topics) at (-1, 4) [] {$\textbf{Unigram Models}$} ;
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordaa);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordbb);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordcc);
}
\end{tikzpicture}
\pause \pause \pause
\end{frame}
\begin{frame}
\frametitle{A General Hierarchical Structure}
Expressed Agenda Model (Grimmer 2010)
\begin{tikzpicture}
\node (col) at (0, 10) [] {\textbf{Average Attention Across Authors}} ;
\invisible<1>{
\node (doc1) at (-5, 8) [] {\textbf{Author Prop}$_{1}$} ;
\node (doc2) at (-1, 8) [] {\textbf{Author Prop}$_{2}$} ;
\node (dots) at ( 2, 8) [] {$\hdots$} ;
\node (docN) at (4, 8) [] {\textbf{Author Prop}$_{N}$} ;
\draw[->, line width=1.5pt] (col) to [out=240, in = 90] (doc1);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (doc2);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (docN);
}
\invisible<1-2>{
\node (word11) at (-5, 7) [] {\textbf{Text Topics}$_{1}$} ;
\node (word22) at (-1, 7) [] {\textbf{Text Topics}$_{2}$} ;
\node (wordnn) at (4, 7) [] {\textbf{Text Topics}$_{N}$ } ;
\draw[->, line width=1.5pt] (doc1) to [out=270, in=90] (word11) ;
\draw[->, line width=1.5pt] (doc2) to [out=270, in=90] (word22) ;
\draw[->, line width=1.5pt] (docN) to [out=270, in=90] (wordnn) ;
}
\invisible<1-3>{
\node (wordaa) at (-5, 6) [] {\textbf{Texts}$_{1}$} ;
\node (wordbb) at (-1, 6) [] {\textbf{Texts}$_{2}$} ;
\node (wordcc) at (4, 6) [] {\textbf{Texts}$_{N}$ } ;
\draw[->, line width = 1.5pt] (word11) to [out = 270, in = 90] (wordaa);
\draw[->, line width = 1.5pt] (word22) to [out = 270, in = 90] (wordbb);
\draw[->, line width = 1.5pt] (wordnn) to [out = 270, in = 90] (wordcc);
\node (topics) at (-1, 4) [] {$\textbf{Unigram Models}$} ;
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordaa);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordbb);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordcc);
}
\end{tikzpicture}
\pause \pause \pause
\end{frame}
\begin{frame}
\frametitle{A General Hierarchical Structure}
Structural Topic Model (Roberts, Stewart, Airoldi 2014)
\begin{tikzpicture}
\node (col) at (0, 10) [] {$g(\boldsymbol{W}, \boldsymbol{\gamma}) $} ;
\invisible<1>{
\node (doc1) at (-5, 8) [] {\textbf{Strata Prop}$_{1}$} ;
\node (doc2) at (-1, 8) [] {\textbf{Strata Prop}$_{2}$} ;
\node (dots) at ( 2, 8) [] {$\hdots$} ;
\node (docN) at (4, 8) [] {\textbf{Strata Prop}$_{N}$} ;
\draw[->, line width=1.5pt] (col) to [out=240, in = 90] (doc1);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (doc2);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (docN);
}
\invisible<1-2>{
\node (word11) at (-5, 7) [] {\textbf{Text Topics}$_{1}$} ;
\node (word22) at (-1, 7) [] {\textbf{Text Topics}$_{2}$} ;
\node (wordnn) at (4, 7) [] {\textbf{Text Topics}$_{N}$ } ;
\draw[->, line width=1.5pt] (doc1) to [out=270, in=90] (word11) ;
\draw[->, line width=1.5pt] (doc2) to [out=270, in=90] (word22) ;
\draw[->, line width=1.5pt] (docN) to [out=270, in=90] (wordnn) ;
}
\invisible<1-3>{
\node (wordaa) at (-5, 6) [] {\textbf{Texts}$_{1}$} ;
\node (wordbb) at (-1, 6) [] {\textbf{Texts}$_{2}$} ;
\node (wordcc) at (4, 6) [] {\textbf{Texts}$_{N}$ } ;
\draw[->, line width = 1.5pt] (word11) to [out = 270, in = 90] (wordaa);
\draw[->, line width = 1.5pt] (word22) to [out = 270, in = 90] (wordbb);
\draw[->, line width = 1.5pt] (wordnn) to [out = 270, in = 90] (wordcc);
\node (topics) at (-1, 4) [] {$\textbf{Unigram Models}$} ;
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordaa);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordbb);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordcc);
}
\invisible<1-4>{
\node (reg) at (3, 4) [] {$h(\tilde{\boldsymbol{W}}, \boldsymbol{\kappa})$ };
\draw[->, line width = 1.5pt] (reg) to [out = 180, in = 0] (topics);
}
\end{tikzpicture}
\pause \pause \pause \pause
\end{frame}
\begin{frame}
{\tt R Code}
\end{frame}
\begin{frame}
\frametitle{A General Hierarchical Structure}
Conditioning on Unknown Covariates$\leadsto$ levels of mixtures at proportions (Grimmer 2013; Wallach 2008)
\begin{tikzpicture}
\only<1>{\node (col_on) at (0, 10)[] {\textbf{Mixture of Top. Attn. Models}} ; }
\invisible<1>{\node (col1) at (-2, 10) [] {\textbf{Strata Indic.} } ;
\node (col) at (2, 10) [] {\textbf{Topic Attention Models} } ; }
\invisible<1-2>{
\node (doc1) at (-5, 8) [] {\textbf{Strata Prop}$_{1}$} ;
\node (doc2) at (-1, 8) [] {\textbf{Strata Prop}$_{2}$} ;
\node (dots) at ( 2, 8) [] {$\hdots$} ;
\node (docN) at (4, 8) [] {\textbf{Strata Prop}$_{N}$} ;
\draw[->, line width=1.5pt, red] (col1) to [out=270, in = 135] (doc1);
\draw[->, line width=1.5pt, red] (col1) to [out=270, in = 135] (doc2);
\draw[->, line width=1.5pt, red] (col1) to [out=270, in = 135] (docN);
}
\invisible<1-3>{
\draw[->, line width=1.5pt] (col) to [out=270, in = 45] (doc1);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (doc2);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (docN);
}
\invisible<1-4>{
\node (word11) at (-5, 7) [] {\textbf{Text Topics}$_{1}$} ;
\node (word22) at (-1, 7) [] {\textbf{Text Topics}$_{2}$} ;
\node (wordnn) at (4, 7) [] {\textbf{Text Topics}$_{N}$ } ;
\draw[->, line width=1.5pt] (doc1) to [out=270, in=90] (word11) ;
\draw[->, line width=1.5pt] (doc2) to [out=270, in=90] (word22) ;
\draw[->, line width=1.5pt] (docN) to [out=270, in=90] (wordnn) ;
}
\invisible<1-5>{
\node (wordaa) at (-5, 6) [] {\textbf{Texts}$_{1}$} ;
\node (wordbb) at (-1, 6) [] {\textbf{Texts}$_{2}$} ;
\node (wordcc) at (4, 6) [] {\textbf{Texts}$_{N}$ } ;
\draw[->, line width = 1.5pt] (word11) to [out = 270, in = 90] (wordaa);
\draw[->, line width = 1.5pt] (word22) to [out = 270, in = 90] (wordbb);
\draw[->, line width = 1.5pt] (wordnn) to [out = 270, in = 90] (wordcc);
\node (topics) at (-1, 4) [] {$\textbf{Unigram Models}$} ;
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordaa);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordbb);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordcc);
}
\end{tikzpicture}
\pause \pause \pause \pause \pause
\end{frame}
\begin{frame}
\frametitle{A General Hierarchical Structure}
Conditioning on Unknown Covariates for Topics$\leadsto$ hierarchy of topics (Li and McCallum 2006; Blaydes, Grimmer, and McQueen 2017)
\begin{tikzpicture}
\node (col) at (-1, 10)[] {\textbf{Population attention}} ;
\invisible<1>{
\node (doc1) at (-5, 8) [] {\textbf{Strata Prop}$_{1}$} ;
\node (doc2) at (-1, 8) [] {\textbf{Strata Prop}$_{2}$} ;
\node (dots) at ( 2, 8) [] {$\hdots$} ;
\node (docN) at (4, 8) [] {\textbf{Strata Prop}$_{N}$} ;
\draw[->, line width=1.5pt] (col) to [out=270, in = 45] (doc1);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (doc2);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (docN);
}
\invisible<1-2>{
\node (word11) at (-5, 7) [] {\textbf{Text Topics}$_{1}$} ;
\node (word22) at (-1, 7) [] {\textbf{Text Topics}$_{2}$} ;
\node (wordnn) at (4, 7) [] {\textbf{Text Topics}$_{N}$ } ;
\draw[->, line width=1.5pt] (doc1) to [out=270, in=90] (word11) ;
\draw[->, line width=1.5pt] (doc2) to [out=270, in=90] (word22) ;
\draw[->, line width=1.5pt] (docN) to [out=270, in=90] (wordnn) ;
}
\invisible<1-3>{
\node (wordaa) at (-5, 6) [] {\textbf{Texts}$_{1}$} ;
\node (wordbb) at (-1, 6) [] {\textbf{Texts}$_{2}$} ;
\node (wordcc) at (4, 6) [] {\textbf{Texts}$_{N}$ } ;
\draw[->, line width = 1.5pt] (word11) to [out = 270, in = 90] (wordaa);
\draw[->, line width = 1.5pt] (word22) to [out = 270, in = 90] (wordbb);
\draw[->, line width = 1.5pt] (wordnn) to [out = 270, in = 90] (wordcc);
\node (topics) at (-1, 4) [] {$\textbf{Unigram Models}$} ;
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordaa);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordbb);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordcc);
}
\invisible<1-4>{
\node (mix) at (3, 4) [] {\textbf{Hierarchy of Topics}} ;
\draw[->, line width = 1.5pt] (mix) to [out = 180, in = 0] (topics);
}
\end{tikzpicture}
\pause \pause \pause \pause \pause
\end{frame}
\begin{frame}
\frametitle{Why Encode Structure in Extensions of LDA?}
\pause
\begin{itemize}
\invisible<1>{\item[-] Substantive reasons} \pause
\begin{itemize}
\invisible<1-2>{\item[-] Additional structure corresponds to substantively interesting content} \pause
\invisible<1-3>{\item[-] Avoids potential ad-hoc secondary analysis} \pause
\invisible<1-4>{\item[-] Clear data generating process} \pause
\end{itemize}
\invisible<1-5>{\item[-] Statistical reasons} \pause
\begin{itemize}
\invisible<1-6>{\item[-] \alert{Smoothing}$\leadsto$ borrow information across groups intelligently} \pause
\invisible<1-7>{\item[-] \alert{Uncertainty}$\leadsto$ potential for better uncertainty estimates} \pause
\invisible<1-8>{\item[-] \alert{Improved topics}$\leadsto$ small word conditions, structure could help}
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Plan for the Class}
\begin{itemize}
\item[1)] Discuss model with unknown covariates for strata proportions$\leadsto$ presentational style
\item[2)] Discuss model with hierarchy of topics$\leadsto$ mirrors genre
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Unknown Covariates for Issue Attention: Measuring Attention in Senate Press Releases}
Substantive problem: \pause \\
\invisible<1>{Senators (representatives) regularly engage the public $\rightarrow$ presentational style\\
But we know little about this engagement} \pause \\
\invisible<1-2>{Why? \alert{Hard to Measure} } \pause \\
\invisible<1-3>{Describe model that facilitates estimation of \alert{presentational styles} in Senate press releases} \pause
\begin{itemize}
\invisible<1-4>{\item[-] Characterize representation provided to constituents} \pause
\invisible<1-5>{\item[-] Divide attention over a set of topics} \pause
\invisible<1-6>{\item[-] Given attention to topics, write press releases}
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Presentational Styles$\leadsto$ Objective Function}
\begin{itemize}
\item[-] $\pi_{itk} \equiv$ Attention senator $i$ allocates to
issue $k$ in year $t$
\item[-] $\pi_{itk} \equiv$ Probability press release is
about issue $k$
\item[-] $\boldsymbol{\pi}_{it} = (\pi_{it1},
\hdots, \pi_{it 44}) $
\end{itemize}
\pause
\invisible<1>{Press release-level parameters (press release $j$ from senator $i$
in year $t$)} \pause
\begin{itemize}
\invisible<1-2>{\item[-] \alert{Assume}: Each press release $j$
assigned to one topic.
\item[-] Let
$\boldsymbol{\tau}_{ijt}$ indicate press release $j$'s topic.} \pause
\end{itemize}
\invisible<1-3>{\begin{center} $\boldsymbol{\tau}_{ijt} \sim
\text{Multinomial}(1, \boldsymbol{\pi}_{it}) $ \end{center}} \pause
\begin{itemize}
\invisible<1-4>{\item[-] Conditional on topic, draw document's
content.} \pause
\invisible<1-5>{\item[-] If $\tau_{ijtk} =1$ then
\end{itemize}
\begin{center}$\boldsymbol{x}_{ijt} \sim \text{Multinomial}(n_{ijt}, \boldsymbol{\theta}_k
).$}
\end{center}
\end{frame}
\begin{frame}
\frametitle{Priors}
Each $\boldsymbol{\pi}_{it}$ is a draw from one-of-$S$ styles$\leadsto$ mixture of Dirichlet distributions \pause .
\begin{eqnarray}
\invisible<1>{\boldsymbol{\sigma}_{it} & \sim & \text{Multinomial}(1, \boldsymbol{\beta}). } \pause \nonumber \\
\invisible<1-2>{\boldsymbol{\pi}_{it}|\sigma_{its}=1, \boldsymbol{\alpha}_s & \sim & \text{Dirichlet}(\boldsymbol{\alpha}_s) \nonumber } \pause \\
\invisible<1-3>{\alpha_{ks} & \sim & \text{Gamma}(0.25, 1)} \pause \nonumber
\end{eqnarray}
\invisible<1-4>{Other priors:} \pause
\begin{eqnarray}
\invisible<1-5>{\boldsymbol{\theta}_k & \sim & \text{Multinomial}(\boldsymbol{\lambda}) \nonumber \\} \pause
\invisible<1-6>{\boldsymbol{\beta} & \sim & \text{Multinomial}(\boldsymbol{1})}
\nonumber
\end{eqnarray}
\end{frame}
%\begin{frame}
%\begin{eqnarray}
%\alpha_{sk} & \sim & \text{Gamma}(0.25, 1) \text{ for all } k, s \nonumber \\
%\boldsymbol{\beta} & \sim & \text{Dirichlet}(\boldsymbol{1}) \nonumber \\
%\boldsymbol{\theta}_k & \sim & \text{Dirichlet}(\boldsymbol{\lambda} ) \nonumber \\
%\boldsymbol{\sigma}_{it} | \boldsymbol{\beta} & \sim & \text{Multinomial}(1, \boldsymbol{\beta} ) \text{ for all } i ; t \nonumber \\
%\boldsymbol{\pi}_{it} | \boldsymbol{\sigma}_{its}=1, \boldsymbol{\alpha}_s & \sim & \text{Dirichlet}(\boldsymbol{\alpha}_s) \text{ for all } i ; t \nonumber \\
%\boldsymbol{\tau}_{ijt}|\boldsymbol{\pi}_{it} & \sim & \text{Multinomial}(1, \boldsymbol{\pi}_{it} ) \text{ for all } j ; t ; i \nonumber \\
%\boldsymbol{y}_{ijt} | \boldsymbol{\tau}_{ijtk} = 1,
%\boldsymbol{\theta}_k & \sim & \text{Multinomial}(n_{ijt},
%\boldsymbol{\theta}_k) \text{ for all } j ; t ; i \nonumber
%\end{eqnarray}
%\end{frame}
\begin{frame}
\frametitle{Presentational Styles$\leadsto$ Objective Function}
\pause
\begin{eqnarray}
\invisible<1>{\boldsymbol{\beta}& \sim & \text{Dirichlet}(\boldsymbol{1}) \nonumber } \\
\invisible<1>{\boldsymbol{\theta}_{k} & \sim & \text{Dirichlet}(\boldsymbol{\lambda}) \nonumber} \\
\invisible<1>{\alpha_{ks} & \sim & \text{Gamma}(0.25, 1) \nonumber} \\
\invisible<1-2>{\boldsymbol{\sigma}_{it} & \sim & \text{Multinomial}(1, \boldsymbol{\beta}) \nonumber } \\
\invisible<1-3>{\boldsymbol{\pi}_{it}| \sigma_{its} = 1, \boldsymbol{\alpha}_{s} & \sim & \text{Dirichlet}(\boldsymbol{\alpha}_{s})\nonumber} \\
\invisible<1-4>{\boldsymbol{\tau}_{ijt} | \boldsymbol{\pi}_{it} & \sim & \text{Multinomial}(1, \boldsymbol{\pi}_{it}) \nonumber \\}
\invisible<1-5>{\boldsymbol{x}_{ijt}| \tau_{ijtk} = 1, \boldsymbol{\theta}_{k} & \sim & \text{Multinomial}(n_{ijt}, \boldsymbol{\theta}_{k})\nonumber }
\end{eqnarray}
\pause \pause \pause \pause \pause
\end{frame}
\begin{frame}
\frametitle{Mixture of Styles, Mixture of Topics}
\begin{tikzpicture}
\node (col1) at (-2, 10) [] {\textbf{Style Indicators} } ;
\node (col) at (2, 10) [] {\textbf{Dirichlet Distributions} } ;
\node (doc1) at (-5, 8) [] {\textbf{Senator Prop}$_{1}$} ;
\node (doc2) at (-1, 8) [] {\textbf{Senator Prop}$_{2}$} ;
\node (dots) at ( 2, 8) [] {$\hdots$} ;
\node (docN) at (4, 8) [] {\textbf{Senator Prop}$_{N}$} ;
\draw[->, line width=1.5pt, red] (col1) to [out=270, in = 135] (doc1);
\draw[->, line width=1.5pt, red] (col1) to [out=270, in = 135] (doc2);
\draw[->, line width=1.5pt, red] (col1) to [out=270, in = 135] (docN);
\draw[->, line width=1.5pt] (col) to [out=270, in = 45] (doc1);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (doc2);
\draw[->, line width=1.5pt] (col) to [out=270, in = 90] (docN);
\node (word11) at (-5, 7) [] {\textbf{Press Topics}$_{1}$} ;
\node (word22) at (-1, 7) [] {\textbf{Press Topics}$_{2}$} ;
\node (wordnn) at (4, 7) [] {\textbf{Press Topics}$_{N}$ } ;
\draw[->, line width=1.5pt] (doc1) to [out=270, in=90] (word11) ;
\draw[->, line width=1.5pt] (doc2) to [out=270, in=90] (word22) ;
\draw[->, line width=1.5pt] (docN) to [out=270, in=90] (wordnn) ;
\node (wordaa) at (-5, 6) [] {\textbf{Press}$_{1}$} ;
\node (wordbb) at (-1, 6) [] {\textbf{Press}$_{2}$} ;
\node (wordcc) at (4, 6) [] {\textbf{Press}$_{N}$ } ;
\draw[->, line width = 1.5pt] (word11) to [out = 270, in = 90] (wordaa);
\draw[->, line width = 1.5pt] (word22) to [out = 270, in = 90] (wordbb);
\draw[->, line width = 1.5pt] (wordnn) to [out = 270, in = 90] (wordcc);
\node (topics) at (-1, 4) [] {$\textbf{Unigram Models}$} ;
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordaa);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordbb);
\draw[->, line width = 1.5pt] (topics) to [out = 90, in = 270] (wordcc);
\end{tikzpicture}
\end{frame}
\begin{frame}
Posterior: \tiny
\begin{eqnarray}
p(\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\theta},
\boldsymbol{\sigma}, \boldsymbol{\pi},
\boldsymbol{\tau}|\boldsymbol{X}) & \propto &
\prod_{k=1}^{K}\prod_{s=1}^{S} \frac{\exp( -
\frac{\alpha_{ks}}{1/4})}{1/4} \times \frac{\Gamma(\sum_{w=1}^{W}
\lambda_w) }{\prod_{w=1}^{W} \Gamma(\lambda_w) } \prod_{w=1}^{W}
\theta_{k,w}^{\lambda_w - 1}
\times \nonumber \\
& & \prod_{i=1}^{N} \prod_{t=2005}^{2007} \prod_{s=1}^{S} \left[
\beta_s \frac{\Gamma(\sum_{k=1}^{K} \alpha_{ks})}{\prod_{k=1}^{K}
\Gamma(\alpha_{ks} )} \prod_{k=1}^{K} \pi_{itk}^{\alpha_{ks}-1}
\prod_{j=1}^{D_{it} }\prod_{k=1}^{K} \left[ \pi_{itk}
\prod_{w=1}^{W} \theta_{kw} ^{x_{ijtw} }
\right]^{\tau_{ijtk}} \right]^{\sigma_{its}} \nonumber
\end{eqnarray}
\pause
\normalsize
\begin{itemize}
\invisible<1>{\item[1)] Estimate with Variational Approximation} \pause
\invisible<1-2>{\item[2)] Determining number of clusters at top? (Grimmer, Shorey, Wallach, and Zlotnick, In Progress)} \pause
\begin{itemize}
\invisible<1-3>{\item[-] Non-parametric model$\leadsto$ statistical selection} \pause
\invisible<1-4>{\item[-] Experiments/Coding Exercises to assess}
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}
\only<1>{\scalebox{0.35}{\includegraphics{ShelbyPress.pdf}}}
\only<2>{\scalebox{0.35}{\includegraphics{SessionsPress.pdf}}}
\end{frame}
\begin{frame}
\frametitle{Notions of validity: From Quinn, Monroe, et al (2010) }
\begin{enumerate}
\item[-] \alert{Semantic Validity:} All categories are coherent and meaningful
\item[-] \alert{Convergent Construct Validity:} Measures concur with existing measures in critical details.
\item[-] \alert{Discriminant Construct Validity}: Measures differ from existing measures in productive ways.
\item[-] \alert{Predictive Measure:} Measures from the model corresponds to external events in expected ways.
\item[-] \alert{Hypothesis Validity:} Measures generated from the model can be used to test substantive hypotheses.
\end{enumerate}
To establish utility of new measures, demonstrate variety of \alert{validations}\\
\alert{None of these validations are performed using a canned statistic}\\
\alert{All}: require substantive knowledge on areas (and what we expect!) [
\end{frame}
\begin{frame}
\frametitle{Home Style Measures, Semantic Validity}
\alert{Must}: Demonstrate to reader that topics are coherent and semantically meaningful
\begin{tabular}{lll}
\hline\hline
Description & Stems & \% \\
\hline
Honorary& honor,prayer,rememb,fund,tribut& 5.0\\
Transp. Grants& airport,transport,announc,urban,hud&4.8\\
Iraq& iraq,iraqi,troop,war,sectarian& 4.7\\
DHS Policy& homeland,port,terrorist,dh,fema&4.1\\
Judicial Nom.& judg,court,suprem,nomin,nomine&3.8\\
Fire Dept. Grant& firefight,homeland,afgp,award,equip&3.7\\
\hline
\end{tabular}
How: \alert{examples} in text are also useful.
\end{frame}
\begin{frame}
\frametitle{Home Style Measures, Convergent Validity}
\only<1-3>{\alert{Over time variation} }
\only<4>{\alert{Supervised/Unsupervised Convergence} }
\only<1>{\scalebox{0.4}{\includegraphics{ImmigrationPlot.pdf}}}
\only<2>{\scalebox{0.4}{\includegraphics{IraqWarPlot.pdf}}}
%\only<3>{\scalebox{0.4}{\includegraphics{Worker5.pdf}}}
\only<3>{\scalebox{0.4}{\includegraphics{HonorPlot.pdf}}}
\only<4>{\scalebox{0.3}{\includegraphics{SupervisedUnsupervised.pdf}}}
\only<5>{\scalebox{0.3}{\includegraphics{ConvValid.pdf}}}
\end{frame}
\begin{frame}
\frametitle{Discriminant Construct Validity}
\scalebox{0.45}{\includegraphics{IdealAttn.pdf} }
\end{frame}
\begin{frame}
\frametitle{Predictive Validity}
\scalebox{0.4}{\includegraphics{CompareLeaders.pdf} }
\end{frame}
\begin{frame}
\frametitle{Hypothesis Validity}
\scalebox{0.28}{\includegraphics{PrioritiesPlotLabel.pdf}}
\begin{columns}[]
\invisible<1>{\column{0.25\textwidth}
\textcolor{blue}{Senate}\\
\textcolor{blue}{Statesperson}
\begin{itemize}
\item[-] \textcolor{blue}{Iraq War}
\item[-] \textcolor{blue}{Intelligence}
\item[-] \textcolor{blue}{Intl. Relations}
\item[-] \textcolor{blue}{Budget}
\end{itemize}}
\invisible<1-2>{\column{0.25\textwidth}
\textcolor{darkgreen}{Domestic}\\
\textcolor{darkgreen}{Policy}
\begin{itemize}
\item[-] \textcolor{darkgreen}{Environment}
\item[-] \textcolor{darkgreen}{Gas prices}
\item[-] \textcolor{darkgreen}{DHS}
\item[-] \textcolor{darkgreen}{Consumer Safety}
\end{itemize}}
\invisible<1-3>{\column{0.25\textwidth} \textcolor{brown}{Pork \&
Policy}
\begin{itemize}
\item[-] \textcolor{brown}{WRDA grants}
\item[-] \textcolor{brown}{Farming}
\item[-] \textcolor{brown}{Health Care}
\item[-] \textcolor{brown}{Education Policy}
\end{itemize}}
\invisible<1-4>{\column{0.25\textwidth}