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diff --git a/report/SCFGs.tex b/report/SCFGs.tex new file mode 100644 index 00000000..0002405d --- /dev/null +++ b/report/SCFGs.tex @@ -0,0 +1,46 @@ + +\chapter{Synchronous context free grammars} \label{sec:scfg} + +%\subsubsection*{Synchronous context free grammar} \label{sec:scfg} +\begin{figure}[t] +\begin{center} +\includegraphics[width=0.6\columnwidth]{example_derivation2.pdf} +\end{center} +\caption[Derivation]{An example SCFG derivation from a Chinese source sentence which yields the English sentence: {\em ``Brown arrived in Shanghai from Beijing late last night.''}. The non-terminal alignment $\mathbf{a}$ is specified by the variable subscripts.} +\label{fig:intro_example_derivation} +\end{figure} + +The translation models discussed explored in this workshop are based on synchronous grammars. +Here we provide a short definition of the formalism we've employed: synchronous context free grammar (SCFG). + +A synchronous context free grammar (SCFG, \cite{lewis68scfg}) generalizes context-free grammars to generate strings concurrently in two (or more) languages. A string pair is generated by applying a series of paired rewrite rules of the form, $X \rightarrow \langle \mathbf{e}, \mathbf{f}, \mathbf{a} \rangle$, where $X$ is a non-terminal, $\mathbf{e}$ and $\mathbf{f}$ are strings of terminals and non-terminals and $\mathbf{a}$ specifies a one-to-one alignment between non-terminals in $\mathbf{e}$ and $\mathbf{f}$. +In the context of SMT, by assigning the source and target languages to the respective sides of a probabilistic SCFG it is possible to describe translation as the process of parsing the source sentence, which induces a parallel tree structure and translation in the target language \cite{chiang07hierarchical}. +Terminal are rewritten as pairs of strings of terminal symbols in the source and target languages. Additionally, one side of a terminal expansion may be the special symbol $\epsilon$, which indicates a null alignment which permits arbitrary insertions and deletions. +Figure \ref{fig:intro_example_derivation} is an example derivation for Chinese to English translation using an SCFG of the form that I propose to learn using non-parametric Bayesian models. + +The generative story is as follows. +In the beginning was the grammar, in which we allow two types of rules: {\emph non-terminal} and {\emph terminal} expansions. +The former rewrites a non-terminal symbol as a string of two or three non-terminals along with an alignment $\mathbf{a}$, specifying the corresponding ordering of the child trees in the source and target language. +Terminal expansion rewrite a non-terminal as a pair of terminal n-grams, where either but not both may be empty. +Given a grammar, each sentence is generated as follows, starting with the distinguished root non-terminal, $S$. +Rewrite each frontier non-terminal, $c$, using a rule chosen from our grammar expanding $c$. +Repeat until there are no remaining frontier non-terminals. +The sentences in both languages can then be read off the leaves, using the rules' alignments to find the right ordering. + +\begin{figure}[t] + \centering + \subfigure{\includegraphics[scale=0.7]{intro_slides/PhraseExtraction1.pdf}} + \subfigure{\includegraphics[scale=0.7]{intro_slides/HieroExtraction2.pdf}} +\caption{Extracting translation rules from aligned sentences. All the phrases obtained using the standard phrase extraction heuristics are depicted in the left figure, these are: $\langle$ Je, I $\rangle$, $\langle$ veux, want to $\rangle$, $\langle$ travailler, work $\rangle$, $\langle$ ne veux pas, do not want to $\rangle$, $\langle$ ne veux pas travailler, do not want to work $\rangle$, $\langle$ Je ne veux pas, I do not want to $\rangle$, $\langle$ Je ne veux pas travailler, I do not want to work $\rangle$. On the right is shown how a discontiguous SCFG rule is created by generalising a phrase embedded in another phrase, the extracted rule is: X $\rightarrow$ $\langle$ ne X$_1$ pas, do not X$_1$ $\rangle$.} +\label{fig:intro_rule_extraction} +\end{figure} + +The process for extracting SCFG rules is based on that used to extract translation phrases in phrase based translation systems. +The phrase based approach \cite{koehn03} uses heuristics to extract phrase translation pairs from a word-aligned corpus. +The phrase extraction heuristic is illustrated in Figure \ref{fig:intro_rule_extraction}. +This heuristic extracts all phrases whose words are either not aligned, or aligned with only other words in the same phrase. +The phrase translation probabilities are then calculated using a maximum likelihood estimation. + +The Hiero \cite{chiang07hierarchical} SCFG extraction heuristic starts from a grammar consisting of the set of contiguous phrases, wherever a phrase is wholly embedded within another a new rule is add with the embedded phrase replace by the non-terminal X. +This process continues until all possible rules have been extracted, subject to the constraints that every rule must contain a terminal on the source side, a rule may only contain two non-terminals on its right side and that those non-terminals may not be adjacent. +The left example in Figure \ref{fig:intro_rule_extraction} depicts this rule generalisation process. diff --git a/report/introduction.tex b/report/introduction.tex index 12cc2705..41d1e81b 100644 --- a/report/introduction.tex +++ b/report/introduction.tex @@ -122,50 +122,3 @@ The algorithms we explored were Maximum Expected Bleu \cite{smith,li} and MIRA \ Chapter \ref{chap:training} describes this work. The remainder of this introductory chapter provides a formal definition of SCFGs and describes the language pairs that we experimented with. - -\section{Synchronous context free grammar} \label{sec:scfg} -{\em This section will be moved to the start of Chapter 2} - -%\subsubsection*{Synchronous context free grammar} \label{sec:scfg} -\begin{figure}[t] -\begin{center} -\includegraphics[width=0.6\columnwidth]{example_derivation2.pdf} -\end{center} -\caption[Derivation]{An example SCFG derivation from a Chinese source sentence which yields the English sentence: {\em ``Brown arrived in Shanghai from Beijing late last night.''}. The non-terminal alignment $\mathbf{a}$ is specified by the variable subscripts.} -\label{fig:intro_example_derivation} -\end{figure} - -The translation models discussed explored in this workshop are based on synchronous grammars. -Here we provide a short definition of the formalism we've employed: synchronous context free grammar (SCFG). - -A synchronous context free grammar (SCFG, \cite{lewis68scfg}) generalizes context-free grammars to generate strings concurrently in two (or more) languages. A string pair is generated by applying a series of paired rewrite rules of the form, $X \rightarrow \langle \mathbf{e}, \mathbf{f}, \mathbf{a} \rangle$, where $X$ is a non-terminal, $\mathbf{e}$ and $\mathbf{f}$ are strings of terminals and non-terminals and $\mathbf{a}$ specifies a one-to-one alignment between non-terminals in $\mathbf{e}$ and $\mathbf{f}$. -In the context of SMT, by assigning the source and target languages to the respective sides of a probabilistic SCFG it is possible to describe translation as the process of parsing the source sentence, which induces a parallel tree structure and translation in the target language \cite{chiang07hierarchical}. -Terminal are rewritten as pairs of strings of terminal symbols in the source and target languages. Additionally, one side of a terminal expansion may be the special symbol $\epsilon$, which indicates a null alignment which permits arbitrary insertions and deletions. -Figure \ref{fig:intro_example_derivation} is an example derivation for Chinese to English translation using an SCFG of the form that I propose to learn using non-parametric Bayesian models. - -The generative story is as follows. -In the beginning was the grammar, in which we allow two types of rules: {\emph non-terminal} and {\emph terminal} expansions. -The former rewrites a non-terminal symbol as a string of two or three non-terminals along with an alignment $\mathbf{a}$, specifying the corresponding ordering of the child trees in the source and target language. -Terminal expansion rewrite a non-terminal as a pair of terminal n-grams, where either but not both may be empty. -Given a grammar, each sentence is generated as follows, starting with the distinguished root non-terminal, $S$. -Rewrite each frontier non-terminal, $c$, using a rule chosen from our grammar expanding $c$. -Repeat until there are no remaining frontier non-terminals. -The sentences in both languages can then be read off the leaves, using the rules' alignments to find the right ordering. - -\begin{figure}[t] - \centering - \subfigure{\includegraphics[scale=0.7]{intro_slides/PhraseExtraction1.pdf}} - \subfigure{\includegraphics[scale=0.7]{intro_slides/HieroExtraction2.pdf}} -\caption{Extracting translation rules from aligned sentences. All the phrases obtained using the standard phrase extraction heuristics are depicted in the left figure, these are: $\langle$ Je, I $\rangle$, $\langle$ veux, want to $\rangle$, $\langle$ travailler, work $\rangle$, $\langle$ ne veux pas, do not want to $\rangle$, $\langle$ ne veux pas travailler, do not want to work $\rangle$, $\langle$ Je ne veux pas, I do not want to $\rangle$, $\langle$ Je ne veux pas travailler, I do not want to work $\rangle$. On the right is shown how a discontiguous SCFG rule is created by generalising a phrase embedded in another phrase, the extracted rule is: X $\rightarrow$ $\langle$ ne X$_1$ pas, do not X$_1$ $\rangle$.} -\label{fig:intro_rule_extraction} -\end{figure} - -The process for extracting SCFG rules is based on that used to extract translation phrases in phrase based translation systems. -The phrase based approach \cite{koehn03} uses heuristics to extract phrase translation pairs from a word-aligned corpus. -The phrase extraction heuristic is illustrated in Figure \ref{fig:intro_rule_extraction}. -This heuristic extracts all phrases whose words are either not aligned, or aligned with only other words in the same phrase. -The phrase translation probabilities are then calculated using a maximum likelihood estimation. - -The Hiero \cite{chiang07hierarchical} SCFG extraction heuristic starts from a grammar consisting of the set of contiguous phrases, wherever a phrase is wholly embedded within another a new rule is add with the embedded phrase replace by the non-terminal X. -This process continues until all possible rules have been extracted, subject to the constraints that every rule must contain a terminal on the source side, a rule may only contain two non-terminals on its right side and that those non-terminals may not be adjacent. -The left example in Figure \ref{fig:intro_rule_extraction} depicts this rule generalisation process. diff --git a/report/report.tex b/report/report.tex index 2b8e045f..71aa668f 100755 --- a/report/report.tex +++ b/report/report.tex @@ -93,6 +93,7 @@ We especially would like to thank Fred Jelinek for heading the Summer School eff \include{introduction} +\include{SCFGs} \include{np_clustering} \include{pr-clustering/posterior} \include{training} |