diff options
Diffstat (limited to 'report/introduction.tex')
| -rw-r--r-- | report/introduction.tex | 53 |
1 files changed, 31 insertions, 22 deletions
diff --git a/report/introduction.tex b/report/introduction.tex index 3b673c8e..12cc2705 100644 --- a/report/introduction.tex +++ b/report/introduction.tex @@ -81,7 +81,7 @@ We structured the workshop into three parallel but interdependent streams: \begin{figure} \centering - \subfigure{\includegraphics[scale=0.5]{intro_slides/JeNeVeuxPasTravailler-hiero-labelled.pdf}} + \includegraphics[scale=0.5]{intro_slides/JeNeVeuxPasTravailler-hiero-labelled.pdf} \caption{Example derivation using the Hiero grammar extraction heuristics where non-terminals have been clustered into unsupervised syntactic categories denoted by $X?$.} \label{fig:intro_labelled_hiero} \end{figure} @@ -124,31 +124,24 @@ 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:scfg} shows an example derivation for Japanese to English translation using an SCFG. - -\begin{figure}Grammar fragment: -\begin{eqnarray*} -\label{rule:discont}X & \rightarrow & \langle \nt{X}{1}\ \nt{X}{2}\ \nt{X}{3},\ \nt{X}{1}\ \nt{X}{3}\ \nt{X}{2} \rangle \\ -X & \rightarrow & \langle \textrm{\emph{John-ga}},\ \textrm{\emph{John}} \rangle \\ -X & \rightarrow & \langle \textrm{\emph{ringo-o}},\ \textrm{\emph{an apple}} \rangle \\ -X & \rightarrow & \langle \textrm{\emph{tabeta}},\ \textrm{\emph{ate}} \rangle -\end{eqnarray*} -Sample derivation: -\begin{eqnarray*} -\label{derivationt} -& &\langle \nt{S}{1},\nt{S}{1} \rangle \Rightarrow \langle \nt{X}{2},\ \nt{X}{2} \rangle \\ - & \Rightarrow& \langle \nt{X}{3}\ \nt{X}{4}\ \nt{X}{5},\ \nt{X}{3}\ \nt{X}{5}\ \nt{X}{4} \rangle \\ - & \Rightarrow &\langle \textrm{\emph{John-ga}}\ \nt{X}{4}\ \nt{X}{5},\ \textrm{\emph{John}}\ \nt{X}{5}\ \nt{X}{4} \rangle \\ - & \Rightarrow &\langle \textrm{\emph{John-ga}}\ \textrm{\emph{ringo-o}}\ \nt{X}{5},\ \textrm{\emph{John}}\ \nt{X}{5}\ \textrm{\emph{an apple}} \rangle \\ - & \Rightarrow &\langle \textrm{\emph{John-ga ringo-o tabeta}},\ \textrm{\emph{John ate an apple}} \rangle -\end{eqnarray*} -\caption{A fragment of an SCFG with a ternary non-terminal expansion and three terminal rules.} -\label{fig:scfg} -\end{figure} +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. @@ -159,4 +152,20 @@ Rewrite each frontier non-terminal, $c$, using a rule chosen from our grammar ex 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. |