Update herarchical phrase-based translation

Section04-Phrasal-and-Syntactic-Models/section04.tex

@@ -3586,12 +3586,77 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
 %%%  关于文法的约束
 \begin{frame}{文法的约束}
 % 把文法限制在合理的范围内，使得系统可以处理
+\begin{itemize}
+\item 按照上面的方法可以抽取到大量的规则，规则太多会降低训练和解码的效率，甚至影响翻译性能，因此需要加入一些\alert{约束}来限制文法规则的数目
+\vspace{0.3em}
+\begin{center}
+\begin{tikzpicture}
+
+\begin{scope}[minimum height = 18pt]
+%\node[anchor=east] (s0) at (0, 0) {$\textrm{X} \ \to \  <\textrm{X}_1\ \textrm{希望}\ \textrm{X}_2,\ \textrm{X}_1\ \textrm{wish to}\ \textrm{X}_2>$};
+\node[anchor=north west] (s1) at (0, 0) {$\textrm{X} \ \to \  <\textrm{X}_1\  \textrm{X}_2 \  \textrm{之一},\ \textrm{one of}\ \textrm{X}_1\ \textrm{X}_2>$};
+\node[anchor=north west] (s2) at ([yshift=0.1em]s1.south west) {$\textrm{X} \ \to \  <\textrm{X}_1\ \textrm{X}_2\ \textrm{是}\ \textrm{X}_3,\ \textrm{X}_1\ \textrm{X}_2\ \textrm{is}\ \textrm{X}_3>$};
+\node[anchor=north west] (s3) at ([yshift=0.1em]s2.south west) {$\textrm{X} \ \to \  <\textrm{X}_1\ \textrm{希望...}\ \textrm{X}_2,\ \textrm{X}_1\ \textrm{wish to...}\ \textrm{X}_2>$};
+\draw[decorate,decoration={brace,amplitude=0.4em,mirror},red,thick] ([xshift=1.3em,yshift=0.3em]s3.south) -- ([xshift=8.0em,yshift=0.3em]s3.south);
+\node[anchor=north] (wi) at ([xshift=4.7em,yshift=-0.0em]s3.south) {\scriptsize{\alert{超过10个词}}};
+\visible<2->{
+\draw[-,red] (s1.west)--(s1.east);
+\draw[-,red] (s2.west)--(s2.east);
+\draw[-,red] (s3.west)--(s3.east);
+}
+\end{scope}
+\end{tikzpicture}
+\end{center}
+\vspace{-0.5em}
+\visible<2->{
+具体包含如下约束
+}
+    \begin{enumerate}
+    \item<2-> 规则中的非终结符不可以连续的出现
+    \item<2-> 每条规则最多包含两个非终结符
+    \item<2-> 抽取规则最多可以跨越10个单词
+    \end{enumerate}
+
+\item<3-> 除此之外，不同的语言会有不同的文法约束，可参考
+\visible<3->{
+\textbf{Hierarchical Phrase-Based Translation}\\
+\textbf{Chiang, Computational Linguistics, 2007}
+}
+\end{itemize}
+
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------
 %%%  特征
 \begin{frame}{特征}
 % 还是David Chiang的论文
+\begin{itemize}
+\item 与短语模型一样，层次短语模型也使用判别式模型进行建模 - $\textrm{P}(d,\textbf{t}|\textbf{s}) = \frac{\exp(\sum_{i=1}^{M} \lambda_i \cdot h_i(d,\textbf{s},\textbf{t}))}{\sum_{d',t'}\exp(\sum_{i=1}^{M} \lambda_i \cdot h_i(d',\textbf{s},\textbf{t}'))}$。其中特征权重$\{\lambda_i\}$可以使用最小错误率训练进行调优，特征函数$\{h_i\}$需要用户定义。
+\item<2-> 这里，所有层次短语规则满足$\langle\ \alpha, \beta, \sim\ \rangle$的形式
+    \begin{itemize}
+    \item $\alpha$和$\beta$表示源语和目标语的规则串，$\sim$表示他们的对应关系
+    \item 此外，定义$\tau(\alpha)$和$\tau(\beta)$为源语端和目标语端的规则序列。例如
+        \vspace{-0.8em}
+        \begin{eqnarray}
+        \tau(\alpha) & = & \textrm{对}\ \textrm{X}_1\ \textrm{感到}\ \textrm{X}_2 \nonumber \\
+        \tau(\beta) & = & \textrm{be}\ \textrm{X}_2\ \textrm{with}\ \textrm{X}_1 \nonumber
+        \end{eqnarray}
+    \end{itemize}
+\item<3-> \textbf{特征1-2： 短语翻译概率}，即正向翻译概率$\Pr(\tau(\alpha)|\tau(\beta))$和反向翻译概率$\Pr(\tau(\alpha)|\tau(\beta))$。这里，$\tau(\alpha)$和$\tau(\beta)$ 都被看做短语，因此可以直接复用短语系统的方法，使用极大似然估计进行计算。
+\end{itemize}
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%%  特征
+\begin{frame}{特征(续)}
+% 给出特征列表
+\begin{itemize}
+\item \textbf{特征3-4： 词汇翻译概率}，即正向词汇翻译概率$\Pr_{lex}(\bar{t}|\bar{s})$和反向词汇翻译概率$\Pr_{lex}(\bar{s}|\bar{t})$。用来描述短语对中源语端单词和目标语端单词的对应关系
+\item \textbf{特征5： $n$-gram语言模型}，即$\textrm{P}_{\textrm{lm}}(\textbf{t})$。度量译文的流畅度，可以使用大规模目标语单语数据得到。
+\item<2-> \textbf{特征6：译文长度}，即$|\textbf{t}|$。避免模型倾向于短译文，同时让系统自动学习对译文长度的偏好。
+\item<2-> \textbf{特征7：翻译规则数量}。这个特征是为了避免模型仅仅使用少量特征构成翻译推导(因为翻译概率相乘，因子少结果一般会大一些)，同时让系统自动学习对使用规则数量的偏好。
+\item<2-> \textbf{特征8：源语言被翻译为空的单词数量}。注意，空翻译规则(或特征)有时也被称作evil feature，这类特征在一些数据集上对BLEU有很好的提升作用，但是会造成人工评价的下降，因此需要谨慎使用。
+\end{itemize}
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------
@@ -3601,6 +3666,129 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
 %%%  CYK解码
 \begin{frame}{CYK解码}
 % 看NiuTrans Manual
+\begin{itemize}
+\item 基于层次短语的翻译解码与基于短语的模型类似，都是要找到使$\textrm{score}(d)$达到最大的翻译推导$d$
+\vspace{-0.5em}
+\begin{displaymath}
+\hat{d} = \argmax_{d \in D} \textrm{score}(d)
+\end{displaymath}
+\vspace{-0.8em}
+    \begin{itemize}
+    \item 由于翻译推导由SCFG构成，使用CYK算法进行解码
+	\item CYK算法解码是一个用来判定任意给定的字符串 是否属于一个上下文无关文法的算法，具体流程如下
+    \end{itemize}
+\vspace{0.5em}
+\begin{center}
+\begin{tikzpicture}
+\node [anchor=south west,rectangle,draw=ublue,thick,inner sep=0.4em,fill=white,drop shadow] (sourceG) at (0,0) {{\color{ublue} \footnotesize{\textbf{S端文法}}}};
+\node [anchor=west,rectangle,draw=ublue,thick,inner sep=0.4em,fill=white,drop shadow] (chom) at ([xshift=3.5em]sourceG.east) {{\color{ublue} \footnotesize{\textbf{乔姆斯基范式}}}};
+\node [anchor=west,rectangle,draw=ublue,thick,inner sep=0.4em,fill=white,drop shadow] (targetG) at ([xshift=3.5em]chom.east) {{\color{ublue} \footnotesize{\textbf{T端文法}}}};
+
+\draw[->,very thick] ([xshift=0.1em]sourceG.east) -- ([xshift=-0.1em]chom.west);
+\draw[->,very thick] ([xshift=-0.1em]targetG.west) -- ([xshift=0.1em]chom.east);
+
+\node [anchor=north west,rectangle,draw=ublue,thick,inner sep=0.4em,fill=white,drop shadow,minimum height=1.2cm] (sourceS) at ([yshift=-1em]sourceG.south west) {{\color{ublue} \footnotesize{\textbf{S端句子}}}};
+\node [anchor=north west,rectangle,draw=ublue,thick,inner sep=0.4em,fill=white,drop shadow,minimum height=1.2cm] (targetS) at ([yshift=-1em]targetG.south west) {{\color{ublue} \footnotesize{\textbf{T端句子}}}};
+\node [anchor=north,rectangle,draw=ublue,thick,inner sep=0.4em,fill=white,drop shadow,minimum height=1.2cm] (parse) at ([yshift=-1em]chom.south) {{\color{ublue} \footnotesize{\textbf{解析得到最好的翻译}}}};
+
+\draw[->,very thick] ([xshift=0.1em]sourceS.east) -- ([xshift=-0.1em]parse.west);
+\draw[->,very thick] ([xshift=0.1em]parse.east) -- ([xshift=-0.1em]targetS.west);
+\draw[->,very thick] ([yshift=-0.1em]chom.south) -- ([yshift=0.1em]parse.north);
+\end{tikzpicture}
+\end{center}
+\vspace{0.3em}
+\item 由于对文法中的非终结符进行了限制，可以直接使用CYK算法进行解码，无需转换成乔姆斯基范式
+\end{itemize}
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%%  CYK解码
+\begin{frame}{CYK解码（续）}
+% 看NiuTrans Manual
+\begin{itemize}
+\item CYK解码提出了一种cell的数据结构，用来记录所有可能出现的翻译假设。
+    \begin{itemize}
+    \item<2-> 对于每个源语句子，使用短语规则表初始化它的cell
+    \item<3-> 自底向上对cell中的每个子cell进行重新组合（正向、反向）
+    \item<4-> 计算每个推导的得分并记录下来，最终选择最优推导所对应的译文作为输出
+    \end{itemize}
+\end{itemize}
+\vspace{-0.8em}
+\begin{center}
+\begin{tikzpicture}
+\visible<2->{
+\node [anchor=west] (s1) at (0,0) {\small{\textbf{进口}}};
+\node [anchor=west] (s2) at ([xshift=4em]s1.east) {\small{\textbf{大幅度}}};
+\node [anchor=west] (s3) at ([xshift=2.8em]s2.east) {\small{\textbf{下降}}};
+\node [anchor=west] (s4) at ([xshift=2.8em]s3.east) {\small{\textbf{了}}};
+
+\node [anchor=north] (t11) at ([yshift=-0.4em]s1.south) {\scriptsize{Imports}};
+\node [anchor=west] (t12) at ([yshift=-1em]t11.west) {\scriptsize{The imports}};
+\node [anchor=west] (t13) at ([yshift=-0.7em]t12.west) {\scriptsize{...}};
+
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+
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+\node [anchor=west] (t33) at ([yshift=-0.7em]t32.west) {\scriptsize{...}};
+
+\node [anchor=north] (t41) at ([yshift=-0.4em]s4.south) {\scriptsize{have}};
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+}
+\visible<3->{
+\node [anchor=west] (t51) at ([xshift=2em,yshift=-1.8em]t23.west) {\scriptsize{drastically \ fallen}};
+\node [anchor=west] (t53) at ([yshift=-0.7em]t51.west) {\scriptsize{...}};
+}
+\visible<4->{
+
+\node [anchor=west] (t61) at ([xshift=3em,yshift=-1.8em]t53.west) {\scriptsize{have \ drastically \ fallen}};
+\node [anchor=west] (t62) at ([yshift=-0.7em]t61.west) {\scriptsize{...}};
+
+\node [anchor=west] (t71) at ([xshift=-6em,yshift=-1.8em]t62.west) {\scriptsize{The \ imports}};
+\node [anchor=west] (t72) at ([xshift=0.2em]t71.east) {\scriptsize{have \ drastically \ fallen}};
+\node [anchor=west] (t73) at ([yshift=-0.7em]t71.west) {\scriptsize{...}};
+}
+\begin{pgfonlayer}{background}
+\visible<2->{
+\node [rectangle,inner sep=0.05em,fill=red!20] [fit = (t11) (t12) (t13)] (box1) {};
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+
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+\node [anchor=south east,inner sep=1pt,fill=black] (tl3) at (box3.south east) {\tiny{{\color{white} \textbf{3}}}};
+\node [anchor=south east,inner sep=1pt,fill=black] (tl4) at (box4.south east) {\tiny{{\color{white} \textbf{4}}}};
+}
+
+\visible<3->{
+\draw [->,thick] (t22.south) .. controls +(south:0.5) and +(north:0.5) .. (t51.north);
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+\node [anchor=south east,inner sep=1pt,fill=black] (tl5) at (box5.south east) {\tiny{{\color{white} \textbf{2-3}}}};
+}
+\visible<4->{
+\draw [->,thick] (t51.south) .. controls +(south:0.5) and +(north:0.5) .. (t61.north);
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+}
+\end{tikzpicture}
+\end{center}
 \end{frame}
 
 %%%------------------------------------------------------------------------------------------------------------
@@ -3611,14 +3799,138 @@ d = r_1 \circ r_2 \circ r_3 \circ r_4
 \begin{frame}{立方剪枝(Cube Pruning)}
 % 问题
 % 解决方法
+\begin{itemize}
+\item 前面介绍的解码方法由于搜索空间非常大，速度很慢，通常使用剪枝的方法来加速这个过程
+    \begin{itemize}
+    \item 解码时对来自不同的cell进行合并时，第一个cell包含$n$个条目，第二个cell包含$m$个条目，就会产生$n \times m$个新条目
+\vspace{0.8em}
+\begin{center}
+\begin{tikzpicture}
+\node [anchor=west] (s1) at (0,0) {\footnotesize{$\textrm{X} \to <\textrm{从}\ \textrm{X}_1,\ \textrm{from}\ \textrm{X}_1>$}};
+\node [anchor=east] (s2) at ([yshift=-2em]s1.east) {\footnotesize{$\textrm{X} \to <\textrm{从}\ \textrm{X}_1,\ \textrm{since}\ \textrm{X}_1>$}};
+\node [anchor=east] (s3) at ([yshift=-2em]s2.east) {\footnotesize{$\textrm{X} \to <\textrm{从}\ \textrm{X}_1,\ \textrm{from the}\ \textrm{X}_1>$}};
+\node [anchor=east] (s4) at ([yshift=-2em]s3.east) {\footnotesize{$\textrm{X} \to <\textrm{从}\ \textrm{X}_1,\ \textrm{through}\ \textrm{X}_1>$}};
+
+\node [anchor=west] (t1) at ([xshift=2.5em]s1.east) {\footnotesize{$\textrm{X} \to <\textrm{计划},\ \textrm{plan}>$}};
+\node [anchor=west] (t2) at ([xshift=2.5em]s2.east) {\footnotesize{$\textrm{X} \to <\textrm{方案},\ \textrm{scheme}>$}};
+\node [anchor=west] (t3) at ([xshift=2.5em]s3.east) {\footnotesize{$\textrm{X} \to <\textrm{项目},\ \textrm{project}>$}};
+\node [anchor=west] (t4) at ([xshift=2.5em]s4.east) {\footnotesize{$\textrm{X} \to <\textrm{时期},\ \textrm{times}>$}};
+
+\foreach \x in {1,2,...,4}
+	\foreach \y in {1,2,...,4}
+    \draw[->] ([xshift=0.1em]s\x.east) -- ([xshift=-0.1em]t\y.west);
+
+\begin{pgfonlayer}{background}
+\node [rectangle,inner sep=0.3em,fill=red!20] [fit = (s1) (s3) (s4)] (box1) {};
+\node [rectangle,inner sep=0.3em,fill=green!20] [fit = (t1) (t2) (t3) (t4)] (box2) {};
+\end{pgfonlayer}
+
+\end{tikzpicture}
+\end{center}
+\vspace{0.3em}
+    \item 当$n$和$m$都很大时，会产生很多新的条目，可以通过限制栈的大小来舍弃大部分条目
+	\item 另一个思路就是如何只生成有机会被选中的条目，这就是\alert{立方剪枝（cube pruning）}的思想
+    \end{itemize}
+\end{itemize}
+\end{frame}
+
+%%%------------------------------------------------------------------------------------------------------------
+%%%  立方剪枝
+\begin{frame}{立方剪枝(Cube Pruning)(续)}
+% 问题
+% 解决方法
+\begin{itemize}
+\item 不是考虑所有可能的组合，而是从\alert{最优}候选开始选择
+    \begin{itemize}
+    \item 根据代价估计对每个cell中的条目进行排序，最好的候选在最顶层，次优候选排在后面
+    \item<2-> 计算所有邻居的代价，选择最优的条目，再计算其邻居的代价，不断进行迭代
+    \item<3-> 直到产生的条目达到一定的数量（如栈容量）或者新加入的条目被其他剪枝策略丢弃，则终止算法
+    \end{itemize}
+\end{itemize}
+\begin{center}
+\begin{tikzpicture}
+\tikzstyle{alignmentnode} = [rectangle,fill=blue!30,minimum size=0.4em,text=white,inner sep=0.1pt]
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+
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+\node [anchor=center,selectnode] (c2) at (alig11.center) {\footnotesize{5.1}};
+\node [anchor=center,selectnode] (c3) at (alig2.center) {\footnotesize{5.5}};
+\node [anchor=center,selectnode,fill=red!20] (c4) at (alig12.center) {\footnotesize{8.2}};
+\node [anchor=center,selectnode,fill=red!20] (c5) at (alig21.center) {\footnotesize{8.5}};
+\node [anchor=center,selectnode,fill=red!20] (c6) at (alig3.center) {\footnotesize{7.7}};
+}
+\end{scope}
+
+\end{tikzpicture}
+\end{center}
 \end{frame}
 
+
 %%%------------------------------------------------------------------------------------------------------------
 %%%  BLEU等评价
 \begin{frame}{效果}
 % 实验结果
-\end{frame}
+\begin{itemize}
+\item 从实验结果中可以看出，基于层次短语的翻译模型性能要优于基于短语的翻译模型
+\item 选择使用层次短语信息实际上增加了模型的复杂度，但是可以通过借鉴基于短语的翻译模型模型以及CYK解码和立方剪枝等技术来解决
+\item 可以考虑加入更多句法信息来进一步提升模型性能
+\end{itemize}
+%\vspace{-1em}
+\begin{center}
+\begin{tabular}{l | l | l | l}
+\multicolumn{2}{c|}{模型} & 开发集 & 测试集  \\
+\multicolumn{2}{c|}{} & (BLEU[\%]) & (BLEU[\%])  \\ \hline
+\multicolumn{2}{l|}{短语(Moses)} & 36.51  & 34.93 \\
+\multicolumn{2}{l|}{短语(NiuTrans)} & 36.99 & 35.29 \\ \hline
+\multicolumn{2}{l|}{层次短语(Moses)} & 36.65 & 34.79 \\
+\multicolumn{2}{l|}{层次短语(NiuTrans)} & 37.41 & 35.35 \\ \hline
+\end{tabular}
+\end{center}
 
+\vspace{-0.5em}
+\scriptsize{* 以上结果来自 NiuTrans: An Open Source Toolkit for Phrase-based Machine Translation}\\
+\scriptsize{* 开发集：NIST MT03，测试集：NIST MT05}\\
+\end{frame}
 %%%------------------------------------------------------------------------------------------------------------
 \section{基于语言学句法的模型}