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\documentclass{beamer}
\mode<presentation>
{
\usetheme{Boadilla}
\setbeamercovered{transparent}}
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\usepackage{times}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\ws}{\ensuremath{\vec{w}}}
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\newcommand{\bz}{\mathbf{z}}
\newcommand{\bd}{\mathbf{d}}
\newcommand{\by}{\mathbf{y}}
\newcommand\bleu{${B{\scriptstyle LEU}}$}
\title{Clustering of phrases and contexts}
\author{Trevor Cohn}
\date{\today}
\begin{document}
\begin{frame}[t]{Motivation}
%\vspace{1.0cm}
\begin{exampleblock}{Distributional Hypothesis}
\begin{quote}
\emph{Words that occur in the same contexts tend to have similar meanings}
\end{quote}
\hfill (Zellig Harris, 1954)
\end{exampleblock}
\vspace{3ex}
We will leverage this in a translation setting:
\begin{itemize}
\item Use the contexts to \alert{cluster} translation units into groups
\item Units in the same group expected to be semantically and syntactically similar
\item Then use these cluster labels to guide translation
\begin{itemize}
\item lexical selection: translating ambiguous source word/s
\item reordering: consistent syntactic patterns of reordering
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}[t]{Monolingual Example}
Task: cluster words into their parts-of-speech. \\
\vspace{1ex}
Illustrate by starting with the word `deal' (noun or verb):
\only<1>{\includegraphics[width=\columnwidth]{deal_first.pdf} \\ Step 1: Find contexts for `deal'}
\only<2->{\includegraphics[width=\columnwidth]{deal.pdf} \\ Step 2: Find other words which occur in these contexts}
%\only<3>{\includegraphics[width=\columnwidth]{deal_more.pdf} \\ \ldots continue to expand}
\only<3>{
\vspace{1ex}
Notice that the instances of deal can be split into two connected sub-graphs:
\begin{itemize}
\item noun: the left two contexts ``a \ldots with'' and ``a \ldots that''
\item verb: the right two contexts ``to \ldots with'' and ``not \ldots with''
\item neighbouring words of these contexts share the same PoS
\end{itemize}
}
\end{frame}
\begin{frame}[t]{More Formally}
Construct a bipartite graph
\begin{itemize}
\item Nodes on the top layer denote word types (bilingual phrase pairs)
\item Nodes on the bottom layer denote context types (monlingual/bilingual words)
\item Edges connect words and their contexts
\end{itemize}
\includegraphics[width=\columnwidth]{bipartite.pdf}
\end{frame}
\begin{frame}[t]{Clustering}
Task is to cluster the graph into sub-graphs. Nodes in the sub-graphs should be
\begin{itemize}
\item strongly connected to one another
\item weakly connected to nodes outside the sub-graph
\item could formulate as either \emph{hard} or \emph{soft} clustering
\end{itemize}
Choose \alert{soft clustering} to allow for syntactic and semantic ambiguity
\centering
\includegraphics[width=0.7\columnwidth]{bipartite_lda.pdf}
\end{frame}
\begin{frame}[t]{Latent Dirichlet Allocation (LDA)}
LDA is a generative model which treats documents as bags of words
\begin{itemize}
\item each word is assign a \alert{topic} (cluster tag)
\item words are generated from a topic-specific multinomial
\item topics are \alert{tied} across a document using a Dirichlet prior
\item $\alpha < 1$ biases towards \alert{sparse} distributions, i.e., topic reuse
\item inferred $\theta_d$ describes a document and $\phi_t$ describes a topic
\end{itemize}
\vspace{-3ex}
\includegraphics[scale=0.55]{lda.pdf}
\end{frame}
\begin{frame}[t]{LDA over Contexts}
Generative story:
\begin{itemize}
\item for each word type $w$
\item for each of the $L$ contexts
\item first we draw a topic $t$, then generate the context $\vec{c}$ given the topic
\item the Dirichlet prior ties the topics for each $w$
\item we're primarily interested in the learnt $\theta$ values
\end{itemize}
\includegraphics[scale=0.4]{context_lda.pdf}
\end{frame}
\end{document}
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