Commit aacc5f12 by 曹润柘

update chapter3 to 3.4

parent 20d19d47
......@@ -48,7 +48,7 @@
\node [ugreen] (input) at (0,0) {猫喜欢吃鱼};
\node [draw,thick,anchor=west,ublue] (preprocessing) at ([xshift=1em]input.east) {分词系统};
\node [ugreen,anchor=west] (mtinput) at ([xshift=1em]preprocessing.east) {猫/喜欢/吃/鱼};
\node [draw,thick,anchor=west,ublue] (smt) at ([xshift=1em]mtinput.east) {SMT系统};
\node [draw,thick,anchor=west,ublue] (smt) at ([xshift=1em]mtinput.east) {MT系统};
\node [anchor=west] (mtoutput) at ([xshift=1em]smt.east) {...};
\draw [->,thick,ublue] ([xshift=0.1em]input.east) -- ([xshift=-0.2em]preprocessing.west);
\draw [->,thick,ublue] ([xshift=0.2em]preprocessing.east) -- ([xshift=-0.1em]mtinput.west);
......
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%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=3em] (eq1) at (0,0) {$f(s_u|t_v)$};
\node [anchor=west,inner sep=2pt] (eq2) at ([xshift=-2pt]eq1.east) {$=$};
\node [anchor=west,inner sep=2pt] (eq3) at ([xshift=-2pt]eq2.east) {$\lambda_{t_v}^{-1}$};
\node [anchor=west,inner sep=2pt] (eq4) at ([xshift=-2pt]eq3.east) {$\frac{\epsilon}{(l+1)^{m}}$};
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=3em] (eq5) at ([xshift=-2pt]eq4.east) {\footnotesize{$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$}};
\node [anchor=west,inner sep=2pt] (eq6) at ([xshift=-2pt]eq5.east) {\footnotesize{$\sum\limits_{j=1}^{m} \delta(s_j,s_u) \sum\limits_{i=0}^{l} \delta(t_i,t_v)$}};
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=3em] (eq7) at ([xshift=-2pt,yshift=-0pt]eq6.east) {$\frac{f(s_u|t_v)}{\sum_{i=0}^{l}f(s_u|t_i)}$};
\node [anchor=south west,inner sep=2pt] (label1) at ([yshift=1em]eq1.north west) {\footnotesize{\textbf{新的参数值}}};
\node [anchor=south east,inner sep=2pt] (label2) at ([yshift=1em,xshift=-5em]eq7.north east) {\footnotesize{\textbf{旧的参数值}}};
\draw [<-,thick] (label1.south) .. controls +(south:1em) and +(north:1em) .. ([xshift=-1em]eq1.north);
\draw [<-,thick] (label2.south) .. controls +(300:1em) and +(north:1em) .. ([xshift=1em]eq7.north);
\draw [<-,thick] ([xshift=-0.5em]label2.south) .. controls +(240:1em) and +(north:1em) .. ([xshift=1em]eq5.north);
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt,minimum height=2em] (eq1) at (0,0) {$f(s_u|t_v)$};
\node [anchor=west,inner sep=2pt] (eq2) at ([xshift=-2pt]eq1.east) {$=$};
\node [anchor=west,inner sep=2pt,minimum height=2em] (eq3) at ([xshift=-2pt]eq2.east) {$\lambda_{t_v}^{-1}$};
\node [anchor=west,inner sep=2pt,minimum height=3.0em] (eq4) at ([xshift=-3pt]eq3.east) {\footnotesize{$\frac{\epsilon}{(l+1)^{m}} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$}};
\node [anchor=west,inner sep=2pt,minimum height=3.0em] (eq5) at ([xshift=1pt]eq4.east) {\footnotesize{$\sum\limits_{j=1}^{m} \delta(s_j,s_u) \sum\limits_{i=0}^{l} \delta(t_i,t_v)$}};
\node [anchor=west,inner sep=2pt,minimum height=3.0em] (eq6) at ([xshift=1pt]eq5.east) {$\frac{f(s_u|t_v)}{\sum_{i=0}^{l}f(s_u|t_i)}$};
{
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=3.0em] (eq4) at ([xshift=-3pt]eq3.east) {\footnotesize{$\frac{\epsilon}{(l+1)^{m}} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$}};
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{
\node [anchor=west,inner sep=2pt,fill=blue!20,minimum height=3.0em] (eq5) at ([xshift=1pt]eq4.east) {\footnotesize{$\sum\limits_{j=1}^{m} \delta(s_j,s_u) \sum\limits_{i=0}^{l} \delta(t_i,t_v)$}};
}
{
\node [anchor=west,inner sep=2pt,fill=green!20,minimum height=3.0em] (eq6) at ([xshift=1pt]eq5.east) {$\frac{f(s_u|t_v)}{\sum_{i=0}^{l}f(s_u|t_i)}$};
}
{
\node [anchor=south west,inner sep=2pt] (label1) at (eq4.north west) {\textbf{\scriptsize{翻译概率$\textrm{P}(s|t)$}}};
}
{
\node [anchor=south west,inner sep=2pt] (label2) at (eq5.north west) {\textbf{\scriptsize{配对的总次数}}};
\node [anchor=south west,inner sep=2pt] (label2part2) at ([yshift=-3pt]label2.north west) {\textbf{\scriptsize{$(s_u,t_v)$在句对$(s,t)$}}};
}
{
\node [anchor=south west,inner sep=2pt] (label3) at (eq6.north west) {\textbf{\scriptsize{有的$t_i$的相对值}}};
\node [anchor=south west,inner sep=2pt] (label4) at ([yshift=-3pt]label3.north west) {\textbf{\scriptsize{$f(s_u|t_v)$对于所}}};
}
{
\node [anchor=east,rotate=90] (neweq1) at ([yshift=-0em]eq4.south) {=};
\node [anchor=north,inner sep=1pt] (neweq1full) at (neweq1.west) {\large{$\textrm{P}(s|t)$}};
}
{
\draw[decorate,thick,decoration={brace,amplitude=5pt,mirror}] ([yshift=-0.2em]eq5.south west) -- ([yshift=-0.2em]eq6.south east) node [pos=0.4,below,xshift=-0.0em,yshift=-0.3em] (expcount1) {\footnotesize{\textbf{'$t_v$翻译为$s_u$'这个事件}}};
\node [anchor=north west] (expcount2) at ([yshift=0.5em]expcount1.south west) {\footnotesize{\textbf{出现次数的期望的估计}}};
\node [anchor=north west] (expcount3) at ([yshift=0.5em]expcount2.south west) {\footnotesize{\textbf{称之为期望频次expected count}}};
}
\end{tikzpicture}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt] (eq1) at (0,0) {$f(s_u|t_v)$};
\node [anchor=west] (eq2) at (eq1.east) {$=$\ };
\draw [-] ([xshift=0.3em]eq2.east) -- ([xshift=11.6em]eq2.east);
\node [anchor=south west] (eq3) at ([xshift=1em]eq2.east) {$\sum_{i=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[i]},t^{[i]})$};
\node [anchor=north west] (eq4) at (eq2.east) {$\sum_{s_u} \sum_{i=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[i]},t^{[i]})$};
{
\node [anchor=south] (label1) at ([yshift=-6em,xshift=3em]eq1.north west) {利用这个公式计算};
\node [anchor=north west] (label1part2) at ([yshift=0.3em]label1.south west) {新的$f(s_u|t_v)$};
}
{
\node [anchor=west] (label2) at ([xshift=5em]label1.east) {用当前的$f(s_u|t_v)$};
\node [anchor=north west] (label2part2) at ([yshift=0.3em]label2.south west) {计算期望频次$c_{\mathbb{E}}(\cdot)$};
}
{
\node [anchor=west,fill=red!20,inner sep=2pt] (eq1) at (0,0) {$f(s_u|t_v)$};
}
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\node[rectangle,fill=blue!20,inner sep=0] [fit = (eq3) (eq4)] (c) {};
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\node[rectangle,draw,red,inner sep=0] [fit = (label1) (label1part2)] (flabel) {};
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\node[rectangle,draw,ublue,inner sep=0] [fit = (label2) (label2part2)] (clabel) {};
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{
\draw [->,thick] (eq1.south) ..controls +(south:1.5em) and +(north:1.5em).. (flabel.north);
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\draw [->,thick] (c.south) ..controls +(south:1.0em) and +(north:1.0em).. (clabel.north);
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{
\draw [->,thick] ([yshift=1em]flabel.east) -- ([yshift=1em]clabel.west);
\draw [<-,thick] ([yshift=-1em]flabel.east) -- ([yshift=-1em]clabel.west) node [pos=0.5,above,yshift=0.3em] {\footnotesize{\textbf{反复执行}}};
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\end{tikzpicture}
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\definecolor{ugreen}{rgb}{0,0.5,0}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=north west] (line1) at (0,0) {\textbf{IBM模型1的训练(EM算法)}};
\node [anchor=north west] (line2) at ([yshift=-0.3em]line1.south west) {输入: 平行语料${(s^{[1]},t^{[1]}),...,(s^{[N]},t^{[N]})}$};
\node [anchor=north west] (line3) at ([yshift=-0.1em]line2.south west) {输出: 参数$f(\cdot|\cdot)$的最优值};
\node [anchor=north west] (line4) at ([yshift=-0.1em]line3.south west) {1: \textbf{Function} \textsc{TrainItWithEM}($\{(s^{[1]},t^{[1]}),...,(s^{[N]},t^{[N]})\}$) };
\node [anchor=north west] (line5) at ([yshift=-0.1em]line4.south west) {2: \ \ Initialize $f(\cdot|\cdot)$ \hspace{5em} $\rhd$ 比如给$f(\cdot|\cdot)$一个均匀分布};
\node [anchor=north west] (line6) at ([yshift=-0.1em]line5.south west) {3: \ \ Loop until $f(\cdot|\cdot)$ converges};
\node [anchor=north west] (line7) at ([yshift=-0.1em]line6.south west) {4: \ \ \ \ \textbf{foreach} $k = 1$ to $N$ \textbf{do}};
\node [anchor=north west] (line8) at ([yshift=-0.1em]line7.south west) {5: \ \ \ \ \ \ \ \footnotesize{$c_{\mathbb{E}}(s_u|t_v;s^{[k]},t^{[k]}) = \sum\limits_{j=1}^{|s^{[k]}|} \delta(s_j,s_u) \sum\limits_{i=0}^{|t^{[k]}|} \delta(t_i,t_v) \cdot \frac{f(s_u|t_v)}{\sum_{i=0}^{l}f(s_u|t_i)}$}\normalsize{}};
\node [anchor=north west] (line9) at ([yshift=-0.1em]line8.south west) {6: \ \ \ \ \textbf{foreach} $t_v$ appears at least one of $\{t^{[1]},...,t^{[N]}\}$ \textbf{do}};
\node [anchor=north west] (line10) at ([yshift=-0.1em]line9.south west) {7: \ \ \ \ \ \ \ $\lambda_{t_v}^{'} = \sum_{s_u} \sum_{k=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[k]},t^{[k]})$};
\node [anchor=north west] (line11) at ([yshift=-0.1em]line10.south west) {8: \ \ \ \ \ \ \ \textbf{foreach} $s_u$ appears at least one of $\{s^{[1]},...,s^{[N]}\}$ \textbf{do}};
\node [anchor=north west] (line12) at ([yshift=-0.1em]line11.south west) {9: \ \ \ \ \ \ \ \ \ $f(s_u|t_v) = \sum_{k=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[k]},t^{[k]}) \cdot (\lambda_{t_v}^{'})^{-1}$};
\node [anchor=north west] (line13) at ([yshift=-0.1em]line12.south west) {10: \ \textbf{return} $f(\cdot|\cdot)$};
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%%% outline
%-------------------------------------------------------------------------
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\begin{tikzpicture}
\begin{scope}
\node [anchor=west] (s1) at (0,0) {\textbf{}};
\node [anchor=west] (s2) at ([xshift=3em]s1.east) {\textbf{}};
\node [anchor=west] (s3) at ([xshift=3em]s2.east) {\textbf{}};
\node [anchor=west] (s4) at ([xshift=3em]s3.east) {\textbf{表示ʾ}};
\node [anchor=west] (s5) at ([xshift=3em]s4.east) {\textbf{满意}};
\node [anchor=south west] (sentlabel) at ([yshift=-0.5em]s1.north west) {\scriptsize{\textbf{\color{red}{待翻译句子(已经分词):}}}};
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{\small
\node [anchor=north,inner sep=2pt,fill=red!20,minimum height=1.5em,minimum width=2.5em] (t11) at ([yshift=-1em]s1.south) {I};
\node [anchor=north,inner sep=2pt,fill=red!20,minimum height=1.5em,minimum width=2.5em] (t12) at ([yshift=-0.8em]t11.south) {me};
\node [anchor=north,inner sep=2pt,fill=red!20,minimum height=1.5em,minimum width=2.5em] (t13) at ([yshift=-0.8em]t12.south) {I'm};
\node [anchor=north west,inner sep=1pt,fill=black] (tl11) at (t11.north west) {\tiny{{\color{white} \textbf{1}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (tl12) at (t12.north west) {\tiny{{\color{white} \textbf{1}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (tl13) at (t13.north west) {\tiny{{\color{white} \textbf{1}}}};
\node [anchor=north,inner sep=2pt,fill=green!20,minimum height=1.5em,minimum width=2.5em] (t21) at ([yshift=-1em]s2.south) {to};
\node [anchor=north,inner sep=2pt,fill=green!20,minimum height=1.5em,minimum width=2.5em] (t22) at ([yshift=-0.8em]t21.south) {with};
\node [anchor=north,inner sep=2pt,fill=green!20,minimum height=1.5em,minimum width=2.5em] (t23) at ([yshift=-0.8em]t22.south) {for};
\node [anchor=north west,inner sep=1pt,fill=black] (tl21) at (t21.north west) {\tiny{{\color{white} \textbf{2}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (tl22) at (t22.north west) {\tiny{{\color{white} \textbf{2}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (tl23) at (t23.north west) {\tiny{{\color{white} \textbf{2}}}};
\node [anchor=north,inner sep=2pt,fill=blue!20,minimum height=1.5em,minimum width=2.5em] (t31) at ([yshift=-1em]s3.south) {you};
\node [anchor=north west,inner sep=1pt,fill=black] (tl31) at (t31.north west) {\tiny{{\color{white} \textbf{3}}}};
\node [anchor=north,inner sep=2pt,fill=orange!20,minimum height=1.5em,minimum width=3em] (t41) at ([yshift=-1em]s4.south) {$\phi$};
\node [anchor=north,inner sep=2pt,fill=orange!20,minimum height=1.5em,minimum width=3em] (t42) at ([yshift=-0.8em]t41.south) {show};
\node [anchor=north west,inner sep=1pt,fill=black] (tl41) at (t41.north west) {\tiny{{\color{white} \textbf{4}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (tl42) at (t42.north west) {\tiny{{\color{white} \textbf{4}}}};
\node [anchor=north,inner sep=2pt,fill=purple!20,minimum height=1.5em,minimum width=4.5em] (t51) at ([yshift=-1em]s5.south) {satisfy};
\node [anchor=north,inner sep=2pt,fill=purple!20,minimum height=1.5em,minimum width=4.5em] (t52) at ([yshift=-0.8em]t51.south) {satisfied};
\node [anchor=north,inner sep=2pt,fill=purple!20,minimum height=1.5em,minimum width=4.5em] (t53) at ([yshift=-0.8em]t52.south) {satisfies};
\node [anchor=north west,inner sep=1pt,fill=black] (tl51) at (t51.north west) {\tiny{{\color{white} \textbf{5}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (tl52) at (t52.north west) {\tiny{{\color{white} \textbf{5}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (tl53) at (t53.north west) {\tiny{{\color{white} \textbf{5}}}};
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{\small
{
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=1.5em,minimum width=2.5em] (ft11) at ([yshift=-1.2in]t11.west) {I'm};
\node [anchor=center,inner sep=2pt,fill=purple!20,minimum height=1.5em,minimum width=5em] (ft12) at ([xshift=6.0em]ft11.center) {satisfied};
\node [anchor=center,inner sep=2pt,fill=green!20,minimum height=1.5em,minimum width=2.5em] (ft13) at ([xshift=6.0em]ft12.center) {with};
\node [anchor=center,inner sep=2pt,fill=blue!20,minimum height=1.5em,minimum width=2.5em] (ft14) at ([xshift=5.0em]ft13.center) {you};
}
{
\node [anchor=north west,inner sep=1pt,fill=black] (ftl11) at (ft11.north west) {\tiny{{\color{white} \textbf{1}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (ftl12) at (ft12.north west) {\tiny{{\color{white} \textbf{5}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (ftl13) at (ft13.north west) {\tiny{{\color{white} \textbf{2}}}};
\node [anchor=north west,inner sep=1pt,fill=black] (ftl14) at (ft14.north west) {\tiny{{\color{white} \textbf{3}}}};
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{
\draw [->,thick] ([yshift=-0.1em]t13.south) -- ([yshift=0.1em]ft11.north);
\draw [->,thick] ([yshift=0.1em]t22.south east) ..controls +(280:3em) and +(north:3em).. ([yshift=0.1em]ft13.north);
\draw [->,thick] ([yshift=-0.1em,xshift=0.2em]t31.south west) ..controls +(south:3em) and +(north:3em).. ([yshift=0.1em,xshift=0.2em]ft14.north west);
\draw [->,thick] ([yshift=0.1em]t52.south west) ..controls +(250:4em) and +(north:4em).. ([yshift=0.1em]ft12.north);
\node [anchor=east,inner sep=1pt] (nulltranslabel) at (t42.south west) {\scriptsize{\textbf{翻空}}};
\draw [->,thick] ([yshift=0.1em]t41.south west) ..controls +(250:1em) and +(north:1em).. (nulltranslabel.north);
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\begin{scope}
{
\node [anchor=north west] (label1) at (ft11.south west) {\small{选择最佳单词翻译,调整词序,得到完美的结果}};
}
{
\draw[decorate,thick,decoration={brace,amplitude=5pt,mirror}] ([yshift=8em,xshift=-0.5em]t13.south west) -- ([xshift=-0.5em]t13.south west) node [pos=0.5,left,xshift=-0.5em,yshift=0.5em] (label2) {\footnotesize{\textbf{学习到的}}};
\node [anchor=north west] (label2part2) at ([yshift=0.3em]label2.south west) {\footnotesize{\textbf{单词翻译}}};
}
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\draw[decorate,thick,decoration={brace,amplitude=5pt,mirror}] ([yshift=-0.2em,xshift=-0.5em]t13.south west) -- ([yshift=-5em,xshift=-0.5em]t13.south west) node [pos=0.5,left,xshift=-0.5em,yshift=0.5em] (label3) {\footnotesize{\textbf{运用知识}}};
\node [anchor=north west] (label3part2) at ([yshift=0.3em]label3.south west) {\footnotesize{\textbf{生成译文}}};
}
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\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\scriptsize
\node [anchor=north west,inner sep=1pt] (entry1) at (0,0) {\tiny{\textbf{1:} 这 是 数据 $\leftrightarrow$ This is data}};
\node [anchor=north west,inner sep=1pt] (entry2) at ([yshift=0.1em]entry1.south west) {\tiny{\textbf{2:} 小心 !$\leftrightarrow$ Look out !}};
\node [anchor=north west,inner sep=1pt] (entry3) at ([yshift=0.1em]entry2.south west) {\tiny{\textbf{3:} 你 是 谁 $\leftrightarrow$ Who are you}};
\node [anchor=north west,inner sep=2pt] (entry4) at ([yshift=0.1em]entry3.south west) {...};
\node [anchor=south west] (corpuslabel) at (entry1.north west) {{\color{ublue} \textbf{双语平行数据}}};
\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (entry1) (entry2) (entry3) (entry4) (corpuslabel)] (corpus) {};
\end{pgfonlayer}
}
\node [anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east){P($t|s$)};
\node [anchor=south] (modellabel) at (P.north) {{\color{ublue} {\scriptsize \textbf{翻译模型}}}};
\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (P) (modellabel)] (model) {};
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\draw [->,very thick,ublue] ([xshift=0.2em]corpus.east) -- ([xshift=3.2em]corpus.east) node [pos=0.5, above] {\color{red}{\scriptsize{模型学习}}};
{
\draw [->,very thick,ublue] ([xshift=0.4em]model.east) -- ([xshift=3.4em]model.east) node [inner sep=0pt,pos=0.5, above,yshift=0.3em] (decodingarrow) {\color{red}{\scriptsize{穷举\&计算}}};
{\scriptsize
\node [anchor=north west,inner sep=2pt] (sentlabel) at ([xshift=5.5em,yshift=-0.3em]model.north east) {{\color{ublue} \textbf{机器翻译引擎}}};
\node [anchor=north west] (sent) at ([yshift=-0.5em]sentlabel.south west) {\textbf{对任意句子}};
\node [anchor=north west] (sentpart2) at ([yshift=0.3em]sent.south west) {\textbf{进行翻译}};
}
}
\begin{pgfonlayer}{background}
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\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (sentlabel) (sent) (sentpart2)] (segsystem) {};
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\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
{
\node [pos=0.5,left,xshift=-0.5em,yshift=2.0em] (label2) {Input: a word pair (x, y) and a sentence pair (s, t)};
\node [anchor=north west] (label2part2) at ([yshift=0.3em]label2.south west) {Output: the number of (x, y) in the (s, t)};
\node [anchor=north west] (label2part3) at ([yshift=0.3em]label2part2.south west) {{1:$count$ $\leftarrow$ 0}};
\node [anchor=north west] (label2part4) at ([yshift=0.3em]label2part3.south west) {{2:\textbf{for} $s\underline{\hbox to 0.1cm{}}word$ $\leftarrow$ $S_1$$S_{length(s)}$ \textbf{do} }};
\node [anchor=north west] (label2part5)at ([yshift=0.3em]label2part4.south west) {{3:\quad\textbf{for} $t\underline{\hbox to 0.1cm{}}word$ $\leftarrow$ $t_1$$t_{length(t)}$ \textbf{do} }};
\node [anchor=north west] (label2part6)at ([yshift=0.3em]label2part5.south west) {{4:\quad\quad\textbf{if} $s\underline{\hbox to 0.1cm{}}word$ == x \textbf{and} $t\underline{\hbox to 0.1cm{}}word$==y \textbf{then} }};
\node [anchor=north west] (label2part7) at ([yshift=0.3em]label2part6.south west) {{5:\quad\quad\quad\quad $count$ $\leftarrow$ $count$ + 1 }};
\node [anchor=north west] (label2part8) at ([yshift=0.3em]label2part7.south west) {{6:\quad\quad \textbf{end if} }};
\node [anchor=north west] (label2part9) at ([yshift=0.3em]label2part8.south west) {{7:\quad \textbf{end for} }};
\node [anchor=north west] (label2part10) at ([yshift=0.3em]label2part9.south west) {{8: \textbf{end for} }};
}
\end{scope}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\definecolor{ugreen}{rgb}{0,0.5,0}
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\node [anchor=west,draw,thick,minimum width=18.8em,minimum height=1.2em] (sent) at (0,0) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,red] (s1) at ([xshift=0.0em,yshift=-2em]sent.south west) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,ugreen] (s2) at ([xshift=2.7em]s1.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,orange] (s3) at ([xshift=2.7em]s2.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,ublue] (s4) at ([xshift=2.7em]s3.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,purple] (s5) at ([xshift=2.7em]s4.east) {};
{
\node [anchor=west,draw,thick,circle,minimum size=1.6em,red,fill=red] (t1) at ([yshift=-3.5em]s1.west) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,ugreen,fill=ugreen] (t2) at ([xshift=2.7em]t1.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,orange,fill=orange] (t3) at ([xshift=2.7em]t2.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,ublue,fill=ublue] (t4) at ([xshift=2.7em]t3.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,purple,fill=purple] (t5) at ([xshift=2.7em]t4.east) {};
}
{
\node [anchor=west,draw,thick,circle,minimum size=1.6em,red,fill=red] (ft1) at ([yshift=-3.5em]t1.west) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,ublue,fill=ublue] (ft2) at ([xshift=2.7em]ft1.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,purple,fill=purple] (ft3) at ([xshift=2.7em]ft2.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,ugreen,fill=ugreen] (ft4) at ([xshift=2.7em]ft3.east) {};
\node [anchor=west,draw,thick,circle,minimum size=1.6em,orange,fill=orange] (ft5) at ([xshift=2.7em]ft4.east) {};
}
\draw [->,thick,double] ([yshift=-0.1em]sent.south) -- ([yshift=-.8em]sent.south);
{
\draw [->,thick] ([yshift=-0.1em]s1.south) -- ([yshift=0.1em]t1.north);
\draw [->,thick] ([yshift=-0.1em]s2.south) -- ([yshift=0.1em]t2.north);
\draw [->,thick] ([yshift=-0.1em]s3.south) -- ([yshift=0.1em]t3.north);
\draw [->,thick] ([yshift=-0.1em]s4.south) -- ([yshift=0.1em]t4.north);
\draw [->,thick] ([yshift=-0.1em]s5.south) -- ([yshift=0.1em]t5.north);
}
{
\draw [->,thick] ([yshift=-0.1em]t1.south) -- ([yshift=0.1em]ft1.north);
\draw [->,thick] ([yshift=-0.1em]t2.south) -- ([yshift=0.1em]ft4.north);
\draw [->,thick] ([yshift=-0.1em]t3.south) -- ([yshift=0.1em]ft5.north);
\draw [->,thick] ([yshift=-0.1em]t4.south) -- ([yshift=0.1em]ft2.north);
\draw [->,thick] ([yshift=-0.1em]t5.south) -- ([yshift=0.1em]ft3.north);
}
{
\node [anchor=north west] (label1) at ([xshift=1.5em,yshift=0.5em]s5.east) {\textbf{分析}};
\node [anchor=north west] (label2) at ([xshift=1.5em,yshift=0.5em]t5.east) {\textbf{转换}};
\node [anchor=north west] (label3) at ([xshift=1.5em,yshift=0.5em]ft5.east) {\textbf{生成}};
}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
{
\node [pos=0.5,left,xshift=-0.5em,yshift=2.0em] (label2) {\footnotesize{{$s^1$ = 机器\quad {\color{red}翻译}\quad\quad\quad\quad 计算机\quad\quad 进行\quad {\color{red}翻译} }}};
\node [anchor=north west] (label2part2) at ([yshift=0.3em]label2.south west) {\footnotesize{{$t^1$ = machine\; {\color{red}translation}\; is\; just\; {\color{red}translation}\; by\; computer }}};
\node [anchor=north west] (label2part3) at ([yshift=0.3em]label2part2.south west) {\footnotesize{{$s^2$ = 那\quad 人工\quad {\color{red}翻译}\quad\quad ? }}};
\node [anchor=north west] (label2part4) at ([yshift=0.3em]label2part3.south west) {\footnotesize{{$t^2$ = so\; what\; is\; human\; {\color{red}translation}\;? }}};
}
\end{scope}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
{
\node [pos=0.5,left,xshift=-0.5em,yshift=2.0em] (label2) {\footnotesize{{s = 机器\quad {\color{red}翻译}\quad\quad\quad\quad 计算机\quad\quad 进行\quad {\color{red}翻译} }}};
\node [anchor=north west] (label2part2) at ([yshift=0.3em]label2.south west) {\footnotesize{{t = machine\; {\color{red}translation}\; is\; just\; {\color{red}translation}\; by\; computer }}};
}
\end{scope}
\end{tikzpicture}
%---------------------------------------------------------------------
\begin{center}
%%% outline
%-------------------------------------------------------------------------
{\footnotesize
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\begin{tikzpicture}
\begin{scope}
\node [anchor=west, font=\normalsize] (s1) at (0,0) {};
\node [anchor=west, font=\normalsize] (s2) at ([xshift=3em]s1.east) {};
\node [anchor=west, font=\normalsize] (s3) at ([xshift=5.6em]s2.east) {};
\node [anchor=west, font=\normalsize] (s4) at ([xshift=5.1em]s3.east) {感到};
\node [anchor=west, font=\normalsize] (s5) at ([xshift=3.1em]s4.east) {满意};
\end{scope}
\begin{scope}[yshift=-7em]
\node [anchor=west, font=\normalsize] (t1) at (0.4em,0) {I};
\node [anchor=west, font=\normalsize] (t2) at ([xshift=3.5em,yshift=-0.1em]t1.east) {am};
\node [anchor=west, font=\normalsize] (t3) at ([xshift=3.5em,yshift=0.1em]t2.east) {satisfied};
\node [anchor=west, font=\normalsize] (t4) at ([xshift=3.5em]t3.east) {with};
\node [anchor=west, font=\normalsize] (t5) at ([xshift=3.5em,yshift=-0.2em]t4.east) {you};
\end{scope}
{
\draw [-,very thick,ublue,dashed] (s1.south) -- (t1.north);
\draw [-,very thick,ublue,dashed] (s4.south) -- ([yshift=0.3em]t2.north);
\draw [-,very thick,ublue,dashed] (s2.south) ..controls +(south:1em) and +(north:1em).. (t4.north);
\draw [-,very thick,ublue,dashed] (s3.south) ..controls +(south:0.5em) and +(north:1.5em).. (t5.north);
\draw [-,very thick,ublue,dashed] (s5.south) -- (t3.north);
}
\end{tikzpicture}
}
%---------------------------------------------------------------------
\end{center}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
{
\node [pos=0.5,left,xshift=-0.5em,yshift=2.0em] (label2) {\footnotesize{{$t^1$ =$<$s$>$ {\color{red}machine}\; {\color{red}translation}\; is\; just\; translation\; by\; computer\; $<$/s$>$ }}};
\node [anchor=north west] (label2part2) at ([yshift=0.3em]label2.south west) {\footnotesize{{$t^2$ =$<$s$>$ how\; does\;this\; {\color{red}machine}\;work\; $?$ $<$/s$>$ }}};
\node [anchor=north west] (label2part3) at ([yshift=0.3em]label2part2.south west) {\footnotesize{{$t^3$ =$<$s$>$ we\; are\;replaced\;the\; old\; adding\; {\color{red}machine}\;with\;a\; computer\; $<$/s$>$ }}};
\node [anchor=north west] (label2part4) at ([yshift=0.3em]label2part3.south west) {\footnotesize{{$t^4$ =$<$s$>$ several\; approaches\; to\;{\color{red}machine}\;learning\; are\; used\; to\; solve\; problems\; $?$\; $<$/s$>$ }}};
}
\end{scope}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\definecolor{ugreen}{rgb}{0,0.5,0}
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\node [anchor=west,inner sep=2pt,fill=red!20,thick,minimum width=3.6em,minimum height=0.8em] (s1) at (0,0) {$\phi$};
{%第一列
\node [anchor=north west] (label1) at ([xshift=2.5em,yshift=6.3em]s1.east) {{\scriptsize \textbf{第1步}}};
\node [anchor=west,inner sep=2pt,fill=green!20,thick,minimum width=3.6em,minimum height=0.8em] (s21) at ([xshift=2.0em,yshift=3.5em]s1.east) {$w_1^1$};
\node [anchor=west,inner sep=2pt,fill=green!20,thick,minimum width=3.6em,minimum height=0.8em] (s22) at ([xshift=2.0em,yshift=0.0em]s1.east) {$w_2^1$};
\node [anchor=west] (s23) at ([xshift=3.3em,yshift=-3.2em]s1.east) {$\vdots$};
\node [anchor=west,inner sep=2pt,fill=green!20,thick,minimum width=3.6em,minimum height=0.8em] (s24) at ([xshift=2.0em,yshift=-7.0em]s1.east) {\scriptsize{$w_{m \bullet n}^1$}};
}
{
\draw [->,thick] ([yshift=0.0em]s1.east) -- ([yshift=0.0em]s21.west);
\draw [->,thick] ([yshift=0.0em]s1.east) -- ([yshift=0.0em]s22.west);
\draw [->,thick] ([yshift=0.0em]s1.east) -- ([xshift=-1.3em,yshift=-0.2em]s23.west);
\draw [->,thick] ([yshift=0.0em]s1.east) -- ([yshift=0.0em]s24.west);
}
{%第二列
\node [anchor=north west] (label2) at ([xshift=9.3em,yshift=6.3em]s1.east) {{\scriptsize \textbf{第2步}}};
\node [anchor=west,inner sep=2pt,fill=blue!20,thick,minimum width=3.6em,minimum height=0.8em] (s31) at ([xshift=8.8em,yshift=3.5em]s1.east) {$w_1^2$};
\node [anchor=west,inner sep=2pt,fill=blue!20,thick,minimum width=3.6em,minimum height=0.8em] (s32) at ([xshift=8.8em,yshift=0.0em]s1.east) {$w_2^2$};
\node [anchor=west] (s33) at ([xshift=10.1em,yshift=-3.2em]s1.east) {$\vdots$};
\node [anchor=west,inner sep=2pt,fill=blue!20,thick,minimum width=3.6em,minimum height=0.8em] (s34) at ([xshift=8.8em,yshift=-7.0em]s1.east) {\tiny{$w_{(m-1) \bullet n}^2$}};
}
{
\draw [->,thick] ([yshift=0.0em]s21.east) -- ([yshift=0.0em]s31.west);
\draw [->,thick] ([yshift=0.0em]s21.east) -- ([yshift=0.0em]s32.west);
\draw [->,thick] ([yshift=0.0em]s21.east) -- ([xshift=-1.3em,yshift=-0.2em]s33.west);
\draw [->,thick] ([yshift=0.0em]s21.east) -- ([yshift=0.0em]s34.west);
\draw [->,thick] ([yshift=0.0em]s22.east) -- ([yshift=0.0em]s31.west);
\draw [->,thick] ([yshift=0.0em]s22.east) -- ([yshift=0.0em]s32.west);
\draw [->,thick] ([yshift=0.0em]s22.east) -- ([xshift=-1.3em,yshift=-0.2em]s33.west);
\draw [->,thick] ([yshift=0.0em]s22.east) -- ([yshift=0.0em]s34.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s23.east) -- ([yshift=0.0em]s31.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s23.east) -- ([yshift=0.0em]s32.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s23.east) -- ([xshift=-1.3em,yshift=-0.3em]s33.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s23.east) -- ([yshift=0.0em]s34.west);
\draw [->,thick] ([yshift=0.0em]s24.east) -- ([yshift=0.0em]s31.west);
\draw [->,thick] ([yshift=0.0em]s24.east) -- ([yshift=0.0em]s32.west);
\draw [->,thick] ([yshift=0.0em]s24.east) -- ([xshift=-1.3em,yshift=-0.2em]s33.west);
\draw [->,thick] ([yshift=0.0em]s24.east) -- ([yshift=0.0em]s34.west);
}
{%第三列
\node [anchor=west] (s41) at ([xshift=15.6em,yshift=3.5em]s1.east) {$\cdots$};
\node [anchor=west] (s42) at ([xshift=15.6em,yshift=0.0em]s1.east) {$\cdots$};
\node [anchor=west] (s43) at ([xshift=15.6em,yshift=-3.5em]s1.east) {$\cdots$};
\node [anchor=west] (s44) at ([xshift=15.6em,yshift=-7.0em]s1.east) {$\cdots$};
\draw [->,thick] ([yshift=0.0em]s31.east) -- ([yshift=0.0em]s41.west);
\draw [->,thick] ([yshift=0.0em]s31.east) -- ([yshift=0.0em]s42.west);
\draw [->,thick] ([yshift=0.0em]s31.east) -- ([yshift=0.0em]s43.west);
\draw [->,thick] ([yshift=0.0em]s31.east) -- ([yshift=0.0em]s44.west);
\draw [->,thick] ([yshift=0.0em]s32.east) -- ([yshift=0.0em]s41.west);
\draw [->,thick] ([yshift=0.0em]s32.east) -- ([yshift=0.0em]s42.west);
\draw [->,thick] ([yshift=0.0em]s32.east) -- ([yshift=0.0em]s43.west);
\draw [->,thick] ([yshift=0.0em]s32.east) -- ([yshift=0.0em]s44.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s41.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s42.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s43.west);
\draw [->,thick] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s44.west);
\draw [->,thick] ([yshift=0.0em]s34.east) -- ([yshift=0.0em]s41.west);
\draw [->,thick] ([yshift=0.0em]s34.east) -- ([yshift=0.0em]s42.west);
\draw [->,thick] ([yshift=0.0em]s34.east) -- ([yshift=0.0em]s43.west);
\draw [->,thick] ([yshift=0.0em]s34.east) -- ([yshift=0.0em]s44.west);
}
{%第四列
\node [anchor=north west] (label3) at ([xshift=19.4em,yshift=6.3em]s1.east) {{\scriptsize \textbf{第m步}}};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s51) at ([xshift=19.0em,yshift=3.5em]s1.east) {$w_1^m$};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s52) at ([xshift=19.0em,yshift=0.0em]s1.east) {$w_2^m$};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s53) at ([xshift=19.0em,yshift=-3.5em]s1.east) {$w_{?}^{m}$};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s54) at ([xshift=19.0em,yshift=-7.0em]s1.east) {\scriptsize{$w_{1 \bullet n}^m$}};
\draw [->,thick] ([yshift=0.0em]s41.east) -- ([yshift=0.0em]s51.west);
\draw [->,thick] ([yshift=0.0em]s42.east) -- ([yshift=0.0em]s52.west);
\draw [->,thick] ([yshift=0.0em]s43.east) -- ([yshift=0.0em]s53.west);
\draw [->,thick] ([yshift=0.0em]s44.east) -- ([yshift=0.0em]s54.west);
}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\definecolor{ugreen}{rgb}{0,0.5,0}
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\node [anchor=west,inner sep=2pt,fill=red!20,thick,minimum width=3.6em,minimum height=0.8em] (s1) at (0,0) {$\phi$};
{%第一列
\node [anchor=north west] (label1) at ([xshift=2.5em,yshift=6.3em]s1.east) {{\scriptsize \textbf{第1步}}};
\node [anchor=west,inner sep=2pt,fill=green!20,thick,minimum width=3.6em,minimum height=0.8em] (s21) at ([xshift=2.0em,yshift=3.5em]s1.east) {$w_1^1$};
\node [anchor=west,inner sep=2pt,fill=green!20,thick,minimum width=3.6em,minimum height=0.8em] (s22) at ([xshift=2.0em,yshift=0.0em]s1.east) {$w_2^1$};
\node [anchor=west] (s23) at ([xshift=3.3em,yshift=-3.2em]s1.east) {$\vdots$};
\node [anchor=west,inner sep=2pt,fill=green!20,thick,minimum width=3.6em,minimum height=0.8em] (s24) at ([xshift=2.0em,yshift=-7.0em]s1.east) {\scriptsize{$w_{m \bullet n}^1$}};
}
{
\draw [->,thick,red] ([yshift=0.0em]s1.east) -- ([yshift=0.0em]s21.west);
\draw [->,thick,densely dashed] ([yshift=0.0em]s1.east) -- ([yshift=0.0em]s22.west);
\draw [->,thick,densely dashed] ([yshift=0.0em]s1.east) -- ([xshift=-1.3em,yshift=-0.2em]s23.west);
\draw [->,thick,densely dashed] ([yshift=0.0em]s1.east) -- ([yshift=0.0em]s24.west);
}
{%第二列
\node [anchor=north west] (label2) at ([xshift=9.3em,yshift=6.3em]s1.east) {{\scriptsize \textbf{第2步}}};
\node [anchor=west,inner sep=2pt,fill=blue!20,thick,minimum width=3.6em,minimum height=0.8em] (s31) at ([xshift=8.8em,yshift=3.5em]s1.east) {$w_1^2$};
\node [anchor=west,inner sep=2pt,fill=blue!20,thick,minimum width=3.6em,minimum height=0.8em] (s32) at ([xshift=8.8em,yshift=0.0em]s1.east) {$w_2^2$};
\node [anchor=west] (s33) at ([xshift=10.1em,yshift=-3.2em]s1.east) {$\vdots$};
\node [anchor=west,inner sep=2pt,fill=blue!20,thick,minimum width=3.6em,minimum height=0.8em] (s34) at ([xshift=8.8em,yshift=-7.0em]s1.east) {\tiny{$w_{(m-1) \bullet n}^2$}};
}
{
\draw [->,thick,densely dashed] ([yshift=0.0em]s21.east) -- ([yshift=0.0em]s31.west);
\draw [->,thick,densely dashed] ([yshift=0.0em]s21.east) -- ([yshift=0.0em]s32.west);
\draw [->,thick,red] ([yshift=0.0em]s21.east) -- ([xshift=-1.3em,yshift=-0.2em]s33.west);
\draw [->,thick,densely dashed] ([yshift=0.0em]s21.east) -- ([yshift=0.0em]s34.west);
}
{%第三列
\node [anchor=west] (s41) at ([xshift=15.6em,yshift=3.5em]s1.east) {$\cdots$};
\node [anchor=west] (s42) at ([xshift=15.6em,yshift=0.0em]s1.east) {$\cdots$};
\node [anchor=west] (s43) at ([xshift=15.6em,yshift=-3.5em]s1.east) {$\cdots$};
\node [anchor=west] (s44) at ([xshift=15.6em,yshift=-7.0em]s1.east) {$\cdots$};
\draw [->,thick,densely dashed] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s41.west);
\draw [->,thick,red] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s42.west);
\draw [->,thick,densely dashed] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s43.west);
\draw [->,thick,densely dashed] ([xshift=1.3em,yshift=-0.3em]s33.east) -- ([yshift=0.0em]s44.west);
}
{%第四列
\node [anchor=north west] (label3) at ([xshift=19.4em,yshift=6.3em]s1.east) {{\scriptsize \textbf{第m步}}};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s51) at ([xshift=19.0em,yshift=3.5em]s1.east) {$w_1^m$};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s52) at ([xshift=19.0em,yshift=0.0em]s1.east) {$w_2^m$};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s53) at ([xshift=19.0em,yshift=-3.5em]s1.east) {$w_{?}^{m}$};
\node [anchor=west,inner sep=2pt,fill=orange!20,thick,minimum width=3.6em,minimum height=0.8em] (s54) at ([xshift=19.0em,yshift=-7.0em]s1.east) {\scriptsize{$w_{1 \bullet n}^m$}};
\draw [->,thick,densely dashed] ([yshift=0.0em]s41.east) -- ([yshift=0.0em]s51.west);
\draw [->,thick,densely dashed] ([yshift=0.0em]s42.east) -- ([yshift=0.0em]s52.west);
\draw [->,thick,red] ([yshift=0.0em]s43.east) -- ([yshift=0.0em]s53.west);
\draw [->,thick,densely dashed] ([yshift=0.0em]s44.east) -- ([yshift=0.0em]s54.west);
}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west] (e1) at (0,0) {$g(s,t)$};
\node [anchor=west] (e2) at (e1.east) {$=$};
\node [anchor=west,inner sep=2pt,fill=red!20] (e3) at (e2.east) {$\prod\nolimits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)$};
\node [anchor=west,inner sep=1pt] (e4) at (e3.east) {$\times$};
\node [anchor=west,inner sep=3pt,fill=blue!20] (e5) at (e4.east) {$\textrm{P}_{lm}(t)$};
\node [anchor=north west,inner sep=1pt] (n1) at ([xshift=2.5em,yshift=-1em]e1.south west) {$\textrm{P}(s|t)$};
\node [anchor=north] (n1part2) at ([yshift=0.3em]n1.south) {\scriptsize{\textbf{翻译模型}}};
\node [anchor=west,inner sep=1pt] (n2) at ([xshift=2em]n1.east) {$\textrm{P}(t)$};
\node [anchor=north] (n2part2) at ([yshift=0.3em]n2.south) {\scriptsize{\textbf{语言模型}}};
\draw [->,thick] (e3.south) .. controls +(south:1em) and +(north:1em) .. (n1.north);
\draw [->,thick] (e5.south) .. controls +(south:1em) and +(70:1em) .. (n2.north);
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west] (eq1) at (0,0) {$\textrm{P}(s,a|t)=$};
\node [anchor=west,inner sep=1pt,minimum height=2.64em] (eq2) at (eq1.east) {$\textrm{P}(m|t)$};
\node [anchor=west,inner sep=1pt,minimum height=2.64em] (eq3) at ([xshift=1pt]eq2.east) {$\prod\limits_{j=1}^{m}$};
\node [anchor=west,inner sep=1pt,minimum height=2.64em] (eq4) at ([xshift=1pt]eq3.east) {$\textrm{P}(a_j|a_{1}^{j-1},s_{1}^{j-1},m,t)$};
\node [anchor=west,inner sep=1pt,minimum height=2.64em] (eq5) at ([xshift=1pt]eq4.east) {$\textrm{P}(s_j|a_{1}^{j},s_{1}^{j-1},m,t)$};
{
\node [anchor=west,inner sep=1pt,minimum height=2.64em,fill=red!20] (eq2) at (eq1.east) {$\textrm{P}(m|t)$};
}
{
\node [anchor=west,inner sep=1pt,minimum height=2.64em,fill=blue!20] (eq3) at ([xshift=1pt]eq2.east) {$\prod\limits_{j=1}^{m}$};
}
{
\node [anchor=west,inner sep=1pt,minimum height=2.64em,fill=green!20] (eq4) at ([xshift=1pt]eq3.east) {$\textrm{P}(a_j|a_{1}^{j-1},s_{1}^{j-1},m,t)$};
}
{
\node [anchor=west,inner sep=1pt,minimum height=2.64em,fill=purple!20] (eq5) at ([xshift=1pt]eq4.east) {$\textrm{P}(s_j|a_{1}^{j},s_{1}^{j-1},m,t)$};
}
{
\node [anchor=north,draw,circle,inner sep=1pt,ublue] (c1) at ([yshift=-1pt]eq2.south) {\tiny{\textbf{1}}};
}
{
\node [anchor=north,draw,circle,inner sep=1pt,ublue] (c2) at ([yshift=-1pt]eq3.south) {\tiny{\textbf{2}}};
}
{
\node [anchor=north,draw,circle,inner sep=1pt,ublue] (c3) at ([yshift=-1pt]eq4.south) {\tiny{\textbf{3}}};
}
{
\node [anchor=north,draw,circle,inner sep=1pt,ublue] (c4) at ([yshift=-1pt]eq5.south) {\tiny{\textbf{4}}};
}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\small
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {$s_1$:在};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=1em]s1.east) {$s_2$:桌子};
\node [anchor=west,inner sep=2pt] (s3) at ([xshift=1em]s2.east) {$s_3$:上};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-1.7em]s1.center) {$t_1$:on};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-1.6em]s2.center) {$t_2$:the};
\node [anchor=north,inner sep=2pt] (t3) at ([yshift=-1.6em]s3.center) {$t_3$:table};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-1.5em]t1.west) {$t_0$};
\draw [-] (s1.south) -- (t0.north);
\draw [-] (s2.south) -- (t3.north);
\draw [-] (s3.south) -- (t1.north);
}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {$s_1$:在};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=2em]s1.east) {$s_2$:桌子};
\node [anchor=west,inner sep=2pt] (s3) at ([xshift=2em]s2.east) {$s_3$:上};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-2.4em]s1.center) {$t_1$:on};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-2.4em]s2.center) {$t_2$:the};
\node [anchor=north,inner sep=2pt] (t3) at ([yshift=-2.4em]s3.center) {$t_3$:table};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-2.2em]t1.west) {$t_0$};
}
{
\draw [-,dashed,thick] (s3.south) -- (t0);
\draw [-,dashed,thick] (s3.south) -- (t1);
\draw [-,dashed,thick] (s3.south) -- (t2);
\draw [-,dashed,thick] (s3.south) -- (t3);
}
\end{tikzpicture}
%---------------------------------------------------------------------
\begin{center}
\begin{tikzpicture}
{
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {$s_1$:在};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=2em]s1.east) {$s_2$:桌子};
\node [anchor=west,inner sep=2pt] (s3) at ([xshift=2em]s2.east) {$s_3$:上};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-2.4em]s1.center) {$t_1$:on};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-2.4em]s2.center) {$t_2$:the};
\node [anchor=north,inner sep=2pt] (t3) at ([yshift=-2.4em]s3.center) {$t_3$:table};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-2.2em]t1.west) {$t_0$};
\draw [-,dashed,thick] (s1.south) -- (t0.north);
\draw [-,dashed,thick] (s2.south) -- (t3.north);
\draw [-,dashed,thick] (s3.south) -- (t1.north);
}
\draw [-,dashed,thick,red] (s2.south) -- (t3.north);
\end{tikzpicture}
\end{center}
\ No newline at end of file
\begin{tikzpicture}
\node [anchor=west] (eq1) at (0,0) {$\sum\limits_{a_1=0}^{l} ... \sum\limits_{a_m=0}^{l} \prod\limits_{j=1}^{m} f(s_j|t_{a_j})$};
\node [anchor=west] (eq1part2) at (eq1.east) {$=$};
\node [anchor=west,inner sep=2pt] (eq1part3) at (eq1part2.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$};
{
\node [anchor=west,inner sep=2pt,fill=red!20] (eq1part3) at (eq1part2.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$};
}
{
\node [anchor=west] (eq2) at ([xshift=5em,yshift=-4.5em]eq1.west) {$\textrm{P}(s|t) = \frac{\epsilon}{(l+1)^{m}} $};
\node [anchor=west,inner sep=2pt] (eq2part2) at ([xshift=-0.3em]eq2.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$};
\node [anchor=east] (eq2label) at ([xshift=-0em,yshift=0.2em]eq2.west) {\small{IBM模型1:}};
\node [anchor=west,inner sep=2pt,fill=red!20] (eq2part2) at ([xshift=-0.3em]eq2.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$};
}
{
\node [anchor=west] (eq3) at ([xshift=5em,yshift=-7.5em]eq1.west) {$\textrm{P}(s|t) = \epsilon$};
\node [anchor=west,inner sep=2pt] (eq3part2) at ([xshift=-0.3em]eq3.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} a(i|j,m,l) f(s_j|t_i)$};
\node [anchor=east] (eq3label) at ([xshift=-0em,yshift=0.2em]eq3.west) {\small{类似的,IBM模型2:}};
}
\begin{pgfonlayer}{background}
{
\node[rectangle,draw=red,inner sep=2pt] [fit = (eq2) (eq2part2) (eq2label) (eq3) (eq3part2) (eq3label)] {};
}
\end{pgfonlayer}
{
\draw [->,thick] ([xshift=-1em]eq1part3.south) .. controls +(south:1.3em) and +(north:1.3em) .. ([xshift=1em]eq2part2.north);
}
\end{tikzpicture}
\begin{tikzpicture}
\begin{scope}[scale=0.8]
\draw [-,very thick] (0,0) sin (1,1) cos (2,0) sin (3,-1) cos (4,0) sin (7,-1);
\draw [-latex,thick] (-0.5,-1.2) -- (8,-1.2);
\draw [-latex,thick] (-0.5,-1.2) -- (-0.5,1.3);
\draw [-,dashed] (1,1) -- (1,-1.2);
\node [anchor=north] at (1,-1.2) {\scriptsize{参数$x$的最优解}};
\node [anchor=center] at (1,-1.2) {$\bullet$};
\node [anchor=center] at (1,1) {$\bullet$};
\node [anchor=west] at (1.3,1) {\scriptsize{目标函数$f(x)$的最大值}};
\draw [<-] (6.5,-0.8) -- (7.0,-0.3);
\node [anchor=south west,inner sep=1pt] at (7.0,-0.3) {\scriptsize{$f(x)$}};
\end{scope}
\end{tikzpicture}
\begin{tikzpicture}
\node [anchor=west] (eq1) at (0,0) {$\hat{\theta}$};
\node [anchor=west] (eq2) at ([yshift=-0.2em]eq1.east) {=};
\node [anchor=west,inner sep=2pt] (eq3) at ([yshift=-0.0em]eq2.east) {$\argmax$};
\node [anchor=north,inner sep=1pt] (eq3part2) at ([yshift=-0.2em]eq3.south) {\scriptsize{$\theta$}};
\node [anchor=west,inner sep=2pt] (eq4) at ([xshift=0.1em]eq3.east) {$\textrm{P}_{\theta}(s|t)$};
{
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=1.35em] (eq3) at ([yshift=-0.0em]eq2.east) {$\argmax$};
\node [anchor=west,inner sep=2pt,fill=green!20] (eq4) at ([xshift=0.1em]eq3.east) {$\textrm{P}_{\theta}(s|t)$};
\node [anchor=north,draw,inner sep=3pt,fill=red!20] (eq3label) at ([yshift=-1.5em]eq3.south west) {\footnotesize{\textbf{求最优参数}}};
\node [anchor=north,draw,inner sep=3pt,fill=green!20] (eq4label) at ([yshift=-1.5em]eq4.south east) {\footnotesize{\textbf{目标函数}}};
\draw [->,thick] ([xshift=-1em]eq3.south) .. controls +(south:1em) and +(north:1em) .. (eq3label.north);
\draw [->,thick] (eq4.south) .. controls +(south:1em) and +(north:1em) .. (eq4label.north);
}
\end{tikzpicture}
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt,fill=green!20] (eq1) at (0,0) {$L(f,\lambda)$};
\node [anchor=west,inner sep=2pt] (eq2) at (eq1.east) {$=$};
\node [anchor=west,inner sep=2pt] (eq3) at (eq2.east) {$\frac{\epsilon}{(l+1)^{m}} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l}$};
\node [anchor=west,inner sep=2pt] (eq4) at (eq3.east) {\black{$f(s_j|t_{i})$}};
\node [anchor=west,inner sep=2pt] (eq5) at (eq4.east) {$-$};
\node [anchor=north west,inner sep=2pt] (eq6) at ([yshift=-6pt]eq3.south west) {$\sum_{t_y}$};
\node [anchor=west,inner sep=1pt,minimum height=1.85em] (eq7) at (eq6.east) {$\lambda_{t_y}$};
\node [anchor=west,inner sep=1pt,minimum height=1.5em] (eq8) at ([xshift=3pt]eq7.east) {$(\sum_{s_x}$};
\node [anchor=west,inner sep=1pt,minimum height=1.5em] (eq9) at (eq8.east) {\black{$f(s_x|t_y)$}};
\node [anchor=west,inner sep=1pt,minimum height=1.5em] (eq10) at (eq9.east) {$-1)$};
{
\node [anchor=west,inner sep=2pt,fill=green!20] (eq1) at (0,0) {$L(f,\lambda)$};
\node [anchor=west,inner sep=2pt] (eq2) at (eq1.east) {$=$};
\node [anchor=west,inner sep=2pt] (eq3) at (eq2.east) {$\frac{\epsilon}{(l+1)^{m}} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l}$};
\node [anchor=west,inner sep=2pt,draw,ublue,fill=blue!20] (eq4) at (eq3.east) {\black{$f(s_j|t_{i})$}};
\node [anchor=west,inner sep=2pt] (eq5) at (eq4.east) {$-$};
\node [anchor=north west,inner sep=2pt] (eq6) at ([yshift=-6pt]eq3.south west) {$\sum_{t_y}$};
\node [anchor=west,inner sep=1pt,fill=purple!20,minimum height=1.85em] (eq7) at (eq6.east) {$\lambda_{t_y}$};
\node [anchor=west,inner sep=1pt,minimum height=1.5em] (eq8) at ([xshift=3pt]eq7.east) {$(\sum_{s_x}$};
\node [anchor=west,inner sep=1pt,draw,ublue,fill=blue!20,minimum height=1.5em] (eq9) at (eq8.east) {\black{$f(s_x|t_y)$}};
\node [anchor=west,inner sep=1pt,minimum height=1.5em] (eq10) at (eq9.east) {$-1)$};
}
\begin{pgfonlayer}{background}
\node[rectangle,red,inner sep=2pt,fill=red!20] [fit = (eq3) (eq4)] (oldobj) {};
{
\node[rectangle,red,inner sep=2pt,fill=orange!20] [fit = (eq8) (eq9) (eq10)] (constraint) {};
}
\end{pgfonlayer}
\node [anchor=west,draw,fill=green!20] (label1) at ([xshift=-2em,yshift=3em]eq1.north west) {新目标函数};
\node [anchor=west,draw,fill=red!20] (label2) at ([xshift=2em]label1.east) {旧目标函数};
{
\node [anchor=west,draw,fill=blue!20] (label3) at ([xshift=2em]label2.east) {参数:词翻译概率};
\node [anchor=west,draw,fill=purple!20] (label4) at ([xshift=-4em,yshift=-2.5em]eq6.south west) {参数:拉格朗日乘数};
\node [anchor=west,draw,fill=orange!20] (label5) at ([xshift=3em]label4.east) {参数约束条件};
}
\draw [<-,thick] ([xshift=-1em]label1.south) .. controls +(south:2em) and +(north:2em) .. (eq1.north);
\draw [<-,thick] ([xshift=-1em]label2.south) .. controls +(south:1.0em) and +(north:1.0em) .. (oldobj.north);
{
\draw [<-,thick] ([xshift=0em]label3.south) .. controls +(south:6.5em) and +(north:1.5em) .. (eq9.north);
\draw [<-,thick] ([xshift=0em]label3.south) .. controls +(south:1.5em) and +(north:1.5em) .. (eq4.north);
\draw [<-,thick] ([xshift=-2em]label4.north) .. controls +(north:1.5em) and +(south:1.5em) .. (eq7.south);
\draw [<-,thick] ([xshift=0em]label5.north) .. controls +(north:1.5em) and +(south:1.5em) .. (constraint.south);
}
\end{tikzpicture}
\begin{tikzpicture}
\node[anchor=west,inner sep=2pt] (eq11) at (0,0) {\large{$\frac{\partial \big[ \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i) \big]}{\partial f(s_u|t_v)}$}};
\node[anchor=west,inner sep=2pt] (eq12) at ([yshift=-9pt]eq11.east) {=};
\node[anchor=west,inner sep=2pt,fill=red!20] (eq13) at ([yshift=2pt]eq12.east) {\large{$\frac{\partial \big[ \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i) \big]}{\partial \big[ \sum\limits_{i=0}^{l}f(s_u|t_i) \big]}$}};
\node[anchor=west,inner sep=2pt] (eq14) at ([yshift=-1pt]eq13.east) {$\cdot$};
\node[anchor=west,inner sep=2pt,fill=blue!20,minimum height=4em] (eq15) at ([yshift=8pt]eq14.east) {\large{$\frac{\partial \big[ \sum\limits_{i=0}^{l}f(s_u|t_i) \big]}{\partial f(s_u|t_v)}$}};
\node[anchor=south,inner sep=1pt] (label1) at ([yshift=1pt]eq13.north) {\footnotesize{$\partial g(z)/\partial z$}};
\node[anchor=south,inner sep=1pt] (label2) at ([yshift=1pt]eq15.north) {\footnotesize{$\partial z/\partial f$}};
\node[anchor=north west,inner sep=2pt] (eq21) at (eq13.south west) {$\frac{\sum\limits_{j=1}^{m} \delta(s_j,s_u)}{\sum\limits_{i=0}^{l}f(s_u|t_i)} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i) \cdot \sum\limits_{i=0}^{l} \delta(t_i,t_v)$};
\node[anchor=east,inner sep=2pt] (eq20) at (eq21.west) {=};
\end{tikzpicture}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\large
\node [anchor=west,minimum height=3em,inner sep=2pt] (eq11) at (0,0) {max};
\node [anchor=west,inner sep=2pt] (eq12) at ([xshift=2pt]eq11.east) {$\Big( \frac{\epsilon}{(l+1)^{m}} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l}$};
\node [anchor=west,inner sep=2pt] (eq13) at (eq12.east) {$f(s_j|t_i)$};
\node [anchor=west,inner sep=2pt] (eq14) at ([yshift=0.2em]eq13.east) {$\Big)$};
\node [anchor=north west,minimum height=1.8em,inner sep=2pt] (eq21) at ([yshift=-0.5em]eq11.south west) {s.t.};
\node [anchor=west] (eq22) at ([xshift=0.5em,yshift=-0.1em]eq21.east) {\normalsize{for each word $t_y$}:};
\node [anchor=west] (eq23) at ([xshift=0.1em,yshift=-0.0em]eq22.east) {$\sum_{s_x} f(s_x|t_y) = 1$};
{
\node [anchor=west,minimum height=3em,inner sep=2pt,fill=green!20] (eq11) at (0,0) {max};
\node [anchor=west,draw,thin,ublue,inner sep=2pt,fill=blue!20] (eq13) at (eq12.east) {\black{$f(s_j|t_i)$}};
\node [anchor=north west,minimum height=1.8em,inner sep=2pt,fill=purple!20] (eq21) at ([yshift=-0.5em]eq11.south west) {s.t.};
\node [anchor=west,fill=orange!20] (eq23) at ([xshift=0.1em,yshift=-0.0em]eq22.east) {$\sum_{s_x} f(s_x|t_y) = 1$};
}
\begin{pgfonlayer}{background}
{
\node[rectangle,red,inner sep=0pt,fill=red!20] [fit = (eq12) (eq13) (eq14)] (eq1full) (eq1obj) {};
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\end{pgfonlayer}
}
{
\node [anchor=west,draw,fill=green!20] (label1) at ([xshift=-2em,yshift=3em]eq11.north west) {最大化函数};
\node [anchor=west,draw,fill=red!20] (label2) at ([xshift=4em]label1.east) {目标函数};
\node [anchor=west,draw,fill=blue!20] (label3) at ([xshift=4em]label2.east) {参数};
\node [anchor=west,draw,fill=purple!20] (label4) at ([xshift=-2em,yshift=-2.5em]eq21.south west) {subject to=满足...约束};
\node [anchor=west,draw,fill=orange!20] (label5) at ([xshift=3em]label4.east) {翻译概率归一化约束条件};
\draw [<-,thick] ([xshift=-2em]label1.south) .. controls +(south:2em) and +(north:2em) .. (eq11.north);
\draw [<-,thick] ([xshift=-0em]label2.south) .. controls +(south:1.7em) and +(north:1.7em) .. (eq1obj.north);
\draw [<-,thick] ([xshift=-0em]label3.south) .. controls +(south:2.5em) and +(north:2.5em) .. (eq13.north);
\draw [<-,thick] ([xshift=2em]label4.north) .. controls +(north:1.5em) and +(south:1.5em) .. (eq21.south);
\draw [<-,thick] ([xshift=0em]label5.north) .. controls +(north:1.0em) and +(south:1.0em) .. (eq23.south);
}
\end{tikzpicture}
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt,fill=green!20] (eq1) at (0,0) {$L(f,\lambda)$};
\node [anchor=west,inner sep=2pt] (eq2) at (eq1.east) {$=$};
\node [anchor=west,inner sep=2pt] (eq3) at (eq2.east) {$\frac{\epsilon}{(l+1)^{m}} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l}$};
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\node [anchor=west,inner sep=2pt] (eq5) at (eq4.east) {$-$};
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{
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{
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{
\node [anchor=west,draw,fill=blue!20] (label3) at ([xshift=2em]label2.east) {参数:词翻译概率};
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\draw [<-,thick] ([xshift=0em]label5.north) .. controls +(north:1.5em) and +(south:1.5em) .. (constraint.south);
}
\end{tikzpicture}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\scriptsize
\node [anchor=north west,inner sep=1pt] (entry1) at (0,0) {\tiny{\textbf{1:} 这 是 数据 $\leftrightarrow$ This is data}};
\node [anchor=north west,inner sep=1pt] (entry2) at ([yshift=0.1em]entry1.south west) {\tiny{\textbf{2:} 小心 !$\leftrightarrow$ Look out !}};
\node [anchor=north west,inner sep=1pt] (entry3) at ([yshift=0.1em]entry2.south west) {\tiny{\textbf{3:} 你 是 谁 $\leftrightarrow$ Who are you}};
\node [anchor=north west,inner sep=2pt] (entry4) at ([yshift=0.1em]entry3.south west) {...};
\node [anchor=south west] (corpuslabel) at (entry1.north west) {{\color{ublue} \textbf{双语平行数据}}};
\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (entry1) (entry2) (entry3) (entry4) (corpuslabel)] (corpus) {};
\end{pgfonlayer}
}
\node [anchor=west,ugreen] (P) at ([xshift=4em,yshift=-0.7em]corpus.east){P($t|s$)};
\node [anchor=south] (modellabel) at (P.north) {{\color{ublue} {\scriptsize \textbf{翻译模型}}}};
\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (P) (modellabel)] (model) {};
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{\scriptsize
\node [anchor=north west,inner sep=2pt] (sentlabel) at ([xshift=5.5em,yshift=-0.3em]model.north east) {{\color{ublue} \textbf{机器翻译引擎}}};
\node [anchor=north west] (sent) at ([yshift=-0.5em]sentlabel.south west) {\textbf{对任意句子}};
\node [anchor=north west] (sentpart2) at ([yshift=0.3em]sent.south west) {\textbf{进行翻译}};
}
\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (sentlabel) (sent) (sentpart2)] (segsystem) {};
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\node[rectangle,fill=white,fill opacity=0.85,inner sep=0pt] [fit = (segsystem) (decodingarrow)] (segsystem2) {};
\node[rectangle,fill=white,fill opacity=0.85,inner sep=0pt] [fit = (corpus) (trainingarrow)] (corpus2) {};
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=3em] (eq1) at (0,0) {$f(s_u|t_v)$};
\node [anchor=west,inner sep=2pt] (eq2) at ([xshift=-2pt]eq1.east) {$=$};
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\node [anchor=west,inner sep=2pt] (eq4) at ([xshift=-2pt]eq3.east) {$\frac{\epsilon}{(l+1)^{m}}$};
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=3em] (eq5) at ([xshift=-2pt]eq4.east) {\footnotesize{$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i)$}};
\node [anchor=west,inner sep=2pt] (eq6) at ([xshift=-2pt]eq5.east) {\footnotesize{$\sum\limits_{j=1}^{m} \delta(s_j,s_u) \sum\limits_{i=0}^{l} \delta(t_i,t_v)$}};
\node [anchor=west,inner sep=2pt,fill=red!20,minimum height=3em] (eq7) at ([xshift=-2pt,yshift=-0pt]eq6.east) {$\frac{f(s_u|t_v)}{\sum_{i=0}^{l}f(s_u|t_i)}$};
\node [anchor=south west,inner sep=2pt] (label1) at ([yshift=1em]eq1.north west) {\footnotesize{\textbf{新的参数值}}};
\node [anchor=south east,inner sep=2pt] (label2) at ([yshift=1em,xshift=-5em]eq7.north east) {\footnotesize{\textbf{旧的参数值}}};
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\draw [<-,thick] ([xshift=-0.5em]label2.south) .. controls +(240:1em) and +(north:1em) .. ([xshift=1em]eq5.north);
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt,minimum height=2em] (eq1) at (0,0) {$f(s_u|t_v)$};
\node [anchor=west,inner sep=2pt] (eq2) at ([xshift=-2pt]eq1.east) {$=$};
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\node [anchor=west,inner sep=2pt,minimum height=3.0em] (eq5) at ([xshift=1pt]eq4.east) {\footnotesize{$\sum\limits_{j=1}^{m} \delta(s_j,s_u) \sum\limits_{i=0}^{l} \delta(t_i,t_v)$}};
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{
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\node [anchor=west,inner sep=2pt,fill=green!20,minimum height=3.0em] (eq6) at ([xshift=1pt]eq5.east) {$\frac{f(s_u|t_v)}{\sum_{i=0}^{l}f(s_u|t_i)}$};
}
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\node [anchor=south west,inner sep=2pt] (label1) at (eq4.north west) {\textbf{\scriptsize{翻译概率$\textrm{P}(s|t)$}}};
}
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\node [anchor=south west,inner sep=2pt] (label2) at (eq5.north west) {\textbf{\scriptsize{配对的总次数}}};
\node [anchor=south west,inner sep=2pt] (label2part2) at ([yshift=-3pt]label2.north west) {\textbf{\scriptsize{$(s_u,t_v)$在句对$(s,t)$}}};
}
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\node [anchor=south west,inner sep=2pt] (label3) at (eq6.north west) {\textbf{\scriptsize{有的$t_i$的相对值}}};
\node [anchor=south west,inner sep=2pt] (label4) at ([yshift=-3pt]label3.north west) {\textbf{\scriptsize{$f(s_u|t_v)$对于所}}};
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{
\node [anchor=east,rotate=90] (neweq1) at ([yshift=-0em]eq4.south) {=};
\node [anchor=north,inner sep=1pt] (neweq1full) at (neweq1.west) {\large{$\textrm{P}(s|t)$}};
}
{
\draw[decorate,thick,decoration={brace,amplitude=5pt,mirror}] ([yshift=-0.2em]eq5.south west) -- ([yshift=-0.2em]eq6.south east) node [pos=0.4,below,xshift=-0.0em,yshift=-0.3em] (expcount1) {\footnotesize{\textbf{'$t_v$翻译为$s_u$'这个事件}}};
\node [anchor=north west] (expcount2) at ([yshift=0.5em]expcount1.south west) {\footnotesize{\textbf{出现次数的期望的估计}}};
\node [anchor=north west] (expcount3) at ([yshift=0.5em]expcount2.south west) {\footnotesize{\textbf{称之为期望频次expected count}}};
}
\end{tikzpicture}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=west,inner sep=2pt] (eq1) at (0,0) {$f(s_u|t_v)$};
\node [anchor=west] (eq2) at (eq1.east) {$=$\ };
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\node [anchor=south west] (eq3) at ([xshift=1em]eq2.east) {$\sum_{i=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[i]},t^{[i]})$};
\node [anchor=north west] (eq4) at (eq2.east) {$\sum_{s_u} \sum_{i=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[i]},t^{[i]})$};
{
\node [anchor=south] (label1) at ([yshift=-6em,xshift=3em]eq1.north west) {利用这个公式计算};
\node [anchor=north west] (label1part2) at ([yshift=0.3em]label1.south west) {新的$f(s_u|t_v)$};
}
{
\node [anchor=west] (label2) at ([xshift=5em]label1.east) {用当前的$f(s_u|t_v)$};
\node [anchor=north west] (label2part2) at ([yshift=0.3em]label2.south west) {计算期望频次$c_{\mathbb{E}}(\cdot)$};
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\node[rectangle,draw,ublue,inner sep=0] [fit = (label2) (label2part2)] (clabel) {};
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{
\draw [->,thick] (eq1.south) ..controls +(south:1.5em) and +(north:1.5em).. (flabel.north);
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\draw [->,thick] ([yshift=1em]flabel.east) -- ([yshift=1em]clabel.west);
\draw [<-,thick] ([yshift=-1em]flabel.east) -- ([yshift=-1em]clabel.west) node [pos=0.5,above,yshift=0.3em] {\footnotesize{\textbf{反复执行}}};
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\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\definecolor{ugreen}{rgb}{0,0.5,0}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [anchor=north west] (line1) at (0,0) {\textbf{IBM模型1的训练(EM算法)}};
\node [anchor=north west] (line2) at ([yshift=-0.3em]line1.south west) {输入: 平行语料${(s^{[1]},t^{[1]}),...,(s^{[N]},t^{[N]})}$};
\node [anchor=north west] (line3) at ([yshift=-0.1em]line2.south west) {输出: 参数$f(\cdot|\cdot)$的最优值};
\node [anchor=north west] (line4) at ([yshift=-0.1em]line3.south west) {1: \textbf{Function} \textsc{TrainItWithEM}($\{(s^{[1]},t^{[1]}),...,(s^{[N]},t^{[N]})\}$) };
\node [anchor=north west] (line5) at ([yshift=-0.1em]line4.south west) {2: \ \ Initialize $f(\cdot|\cdot)$ \hspace{5em} $\rhd$ 比如给$f(\cdot|\cdot)$一个均匀分布};
\node [anchor=north west] (line6) at ([yshift=-0.1em]line5.south west) {3: \ \ Loop until $f(\cdot|\cdot)$ converges};
\node [anchor=north west] (line7) at ([yshift=-0.1em]line6.south west) {4: \ \ \ \ \textbf{foreach} $k = 1$ to $N$ \textbf{do}};
\node [anchor=north west] (line8) at ([yshift=-0.1em]line7.south west) {5: \ \ \ \ \ \ \ \footnotesize{$c_{\mathbb{E}}(s_u|t_v;s^{[k]},t^{[k]}) = \sum\limits_{j=1}^{|s^{[k]}|} \delta(s_j,s_u) \sum\limits_{i=0}^{|t^{[k]}|} \delta(t_i,t_v) \cdot \frac{f(s_u|t_v)}{\sum_{i=0}^{l}f(s_u|t_i)}$}\normalsize{}};
\node [anchor=north west] (line9) at ([yshift=-0.1em]line8.south west) {6: \ \ \ \ \textbf{foreach} $t_v$ appears at least one of $\{t^{[1]},...,t^{[N]}\}$ \textbf{do}};
\node [anchor=north west] (line10) at ([yshift=-0.1em]line9.south west) {7: \ \ \ \ \ \ \ $\lambda_{t_v}^{'} = \sum_{s_u} \sum_{k=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[k]},t^{[k]})$};
\node [anchor=north west] (line11) at ([yshift=-0.1em]line10.south west) {8: \ \ \ \ \ \ \ \textbf{foreach} $s_u$ appears at least one of $\{s^{[1]},...,s^{[N]}\}$ \textbf{do}};
\node [anchor=north west] (line12) at ([yshift=-0.1em]line11.south west) {9: \ \ \ \ \ \ \ \ \ $f(s_u|t_v) = \sum_{k=1}^{N} c_{\mathbb{E}}(s_u|t_v;s^{[k]},t^{[k]}) \cdot (\lambda_{t_v}^{'})^{-1}$};
\node [anchor=north west] (line13) at ([yshift=-0.1em]line12.south west) {10: \ \textbf{return} $f(\cdot|\cdot)$};
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\end{tikzpicture}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
{
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
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{
\node [anchor=south east,inner sep=0pt] (p) at (t0.north west) {\small{{\color{ugreen} P(}}};
\node [anchor=south west,inner sep=0pt] (p2) at ([yshift=0.2em]t2.north east) {\small{{\color{ugreen} )}}};
\node [anchor=west] (eq) at ([xshift=0.7em]p2.east) {\small{+}};
}
}
\end{scope}
\begin{scope}[xshift=3in,yshift=-0.6in]
{
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=0.4em]s1.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-1.4em]s1.center) {thank};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-1.6em]s2.center) {you};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-0.2em,yshift=-0.05em]t1.west) {$t_0$};
\draw [-] (s1.south) -- ([yshift=-0.2em]t1.north);
\draw [-] (s2.south) -- (t2.north);
{
\node [anchor=south east,inner sep=0pt] (p) at (t0.north west) {\small{{\color{ugreen} P(}}};
\node [anchor=south west,inner sep=0pt] (p2) at ([yshift=0.2em]t2.north east) {\small{{\color{ugreen} )}}};
\node [anchor=west] (eq) at ([xshift=0.7em]p2.east) {\small{+}};
}
}
\end{scope}
\begin{scope}[yshift=-1.2in]
{
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=0.4em]s1.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-1.4em]s1.center) {thank};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-1.6em]s2.center) {you};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-0.2em,yshift=-0.05em]t1.west) {$t_0$};
\draw [-] (s1.south) -- (t2.north);
\draw [-] (s2.south) -- (t0.north);
{
\node [anchor=south east,inner sep=0pt] (p) at (t0.north west) {\small{{\color{ugreen} P(}}};
\node [anchor=south west,inner sep=0pt] (p2) at ([yshift=0.2em]t2.north east) {\small{{\color{ugreen} )}}};
\node [anchor=west] (eq) at ([xshift=0.7em]p2.east) {\small{+}};
}
}
\end{scope}
\begin{scope}[xshift=1.5in,yshift=-1.2in]
{
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=0.4em]s1.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-1.4em]s1.center) {thank};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-1.6em]s2.center) {you};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-0.2em,yshift=-0.05em]t1.west) {$t_0$};
\draw [-] (s1.south) -- (t2.north);
\draw [-] (s2.south) -- (t1.north);
{
\node [anchor=south east,inner sep=0pt] (p) at (t0.north west) {\small{{\color{ugreen} P(}}};
\node [anchor=south west,inner sep=0pt] (p2) at ([yshift=0.2em]t2.north east) {\small{{\color{ugreen} )}}};
\node [anchor=west] (eq) at ([xshift=0.7em]p2.east) {\small{+}};
}
}
\end{scope}
\begin{scope}[xshift=3in,yshift=-1.2in]
{
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=0.4em]s1.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-1.4em]s1.center) {thank};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-1.6em]s2.center) {you};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-0.2em,yshift=-0.05em]t1.west) {$t_0$};
\draw [-] (s1.south) -- (t2.north);
\draw [-] (s2.south) -- (t2.north);
{
\node [anchor=south east,inner sep=0pt] (p) at (t0.north west) {\small{{\color{ugreen} P(}}};
\node [anchor=south west,inner sep=0pt] (p2) at ([yshift=0.2em]t2.north east) {\small{{\color{ugreen} )}}};
\node [anchor=west] (eq) at ([xshift=0.7em]p2.east) {\normalsize{= \ P($s|t$)}};
}
}
\end{scope}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\small
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=1em]s1.east) {桌子};
\node [anchor=west,inner sep=2pt] (s3) at ([xshift=1em]s2.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-1.7em]s1.center) {on};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-1.5em]s2.center) {the};
\node [anchor=north,inner sep=2pt] (t3) at ([yshift=-1.5em]s3.center) {table};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-1.5em]t1.west) {$t_0$};
\draw [-] (s1.south) -- (t0.north);
\draw [-] (s2.south) -- (t3.north);
\draw [-] (s3.south) .. controls +(south:1em) and +(north:1em) .. (t1.north);
}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
{\small
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=2em]s1.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-2.2em]s1.center) {thank};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-2.45em]s2.center) {you};
\draw [-] (s1.south) -- ([yshift=-0.2em]t1.north);
\draw [-] (s2.south) -- (t2.north);
\node [anchor=center,draw=ublue,circle,thick,fill=white,inner sep=1pt,circular drop shadow={shadow xshift=0.1em,shadow yshift=-0.1em}] (mark) at ([xshift=0.8em,yshift=-0.7em]s2.south east) {{\color{ugreen} \tiny{\textbf{Yes}}}};
}
\end{scope}
\begin{scope}[xshift=1.8in]
{\small
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=2em]s1.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-2.2em]s1.center) {thank};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-2.45em]s2.center) {you};
\draw [-] (s1.south) -- ([yshift=-0.2em]t1.north);
\draw [-] (s1.south) -- (t2.north);
\node [anchor=center,draw=ublue,circle,thick,fill=white,inner sep=1.5pt,circular drop shadow={shadow xshift=0.1em,shadow yshift=-0.1em}] (mark) at ([xshift=0.8em,yshift=-0.7em]s2.south east) {{\color{red} \tiny{\textbf{No}}}};
}
\end{scope}
\begin{scope}[xshift=3.6in]
{\small
\node [anchor=west,inner sep=2pt] (s1) at (0,0) {谢谢};
\node [anchor=west,inner sep=2pt] (s2) at ([xshift=2em]s1.east) {};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-2.2em]s1.center) {thank};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-2.45em]s2.center) {you};
\draw [-] (s1.south) -- ([yshift=-0.2em]t1.north);
\draw [-] (s2.south) -- ([yshift=-0.2em]t1.north);
\node [anchor=center,draw=ublue,circle,thick,fill=white,inner sep=1pt,circular drop shadow={shadow xshift=0.1em,shadow yshift=-0.1em}] (mark) at ([xshift=0.8em,yshift=-0.7em]s2.south east) {{\color{ugreen} \tiny{\textbf{Yes}}}};
}
\end{scope}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\node [draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s1) at (0,0) {\black{$s$}};
\node [draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t) at ([xshift=1in]s1.east) {\black{$\hat{t}$}};
\draw [->,thick,] (s1.north east) .. controls +(north east:1em) and +(north west:1em).. (t.north west) node[pos=0.5,below] {\tiny{正确翻译}};
\node [draw,red,fill=red!10,thick,anchor=center,circle,inner sep=3.5pt] (s) at ([xshift=13em,yshift=0em]s1.east) {\black{$s$}};
\node [draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t1) at ([xshift=1in]s.east) {\black{$t_1$}};
\node [draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t2) at ([xshift=3em,yshift=2em]t1.north east) {\black{$t_2$}};
\node [draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t3) at ([xshift=1em,yshift=4em]t1.north east) {\black{$t_3$}};
\node [draw,ublue,fill=blue!10,thick,anchor=center,circle,inner sep=2pt] (t4) at ([xshift=3em,yshift=-1.5em]t1.north east) {\black{$t_4$}};
\node [draw,dashed,ublue,fill=blue!10,thick,anchor=center,circle,minimum size=18pt] (t5) at ([xshift=3em]t3.east) {};
\node [draw,dashed,ublue,fill=blue!10,thick,anchor=center,circle,minimum size=18pt] (t6) at ([xshift=3em]t2.east) {};
\node [draw,dashed,ublue,fill=blue!10,thick,anchor=center,circle,minimum size=18pt] (t7) at ([xshift=3em]t4.east) {};
\draw [->,thick,] (s.north east) .. controls +(north east:1em) and +(north west:1em).. (t1.north west) node[pos=0.5,below] {\tiny{P ($t_1|s$)=0.1}};
\draw [->,thick,] (s.60) .. controls +(50:4em) and +(west:1em).. (t2.west) node[pos=0.5,below] {\tiny{P($t_2|s$)=0.2}};
\draw [->,thick,] (s.north) .. controls +(70:4em) and +(west:1em).. (t3.west) node[pos=0.5,above,xshift=-1em] {\tiny{P($t_3|s$)=0.3}};
\draw [->,thick,] (s.south east) .. controls +(300:3em) and +(south west:1em).. (t4.south west) node[pos=0.5,below] {\tiny{P($t_4|s$)=0.1}};
\node [anchor=center] (foot1) at ([xshift=3.8em,yshift=-3em]s1.south) {\footnotesize{人的翻译候选空间}};
\node [anchor=center] (foot2) at ([xshift=7em,yshift=-3em]s.south) {\footnotesize{机器的翻译候选空间}};
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
\node [anchor=west] (s1) at (0,0) {$s$ = 在\ \ 桌子\ \ };
\node [anchor=west] (t1) at ([yshift=-2em]s1.west) {$t$ = on\ \ the\ \ table};
\draw [->,double,thick,ublue] ([yshift=0.2em]s1.south) -- ([yshift=-0.8em]s1.south);
\end{scope}
\begin{scope}[xshift=1.5in]
\node [anchor=west] (s2) at (0,0) {$s$ = 在\ \ 桌子\ \ };
\node [anchor=west] (t2) at ([yshift=-2em]s2.west) {$t'$ = table \ on\ \ the};
\draw [->,double,thick,ublue] ([yshift=0.2em]s2.south) -- ([yshift=-0.8em]s2.south);
\end{scope}
\node [anchor=north] (score11) at ([yshift=-2.0em]s1.south) {$\textrm{P}(s|t)$};
\node [anchor=north] (score12) at ([yshift=-2.0em]s2.south) {$\textrm{P}(s|t')$};
\node [anchor=west] (comp1) at ([xshift=2.3em]score11.east) {\large{$\mathbf{=}$}};
\node [anchor=east] (label1) at ([xshift=-1em,yshift=0.1em]score11.west) {\textbf{IBM模型1:}};
{
\node [anchor=north] (score21) at ([yshift=0.2em]score11.south) {$\textrm{P}(s|t)$};
\node [anchor=north] (score22) at ([yshift=0.2em]score12.south) {$\textrm{P}(s|t')$};
\node [anchor=west] (comp2) at ([xshift=2.3em]score21.east) {\large{$\mathbf{>}$}};
\node [anchor=east] (label2) at ([xshift=-1em,yshift=0.1em]score21.west) {\textbf{理想:}};
}
\end{tikzpicture}
%---------------------------------------------------------------------
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\definecolor{ugreen}{rgb}{0,0.5,0}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\footnotesize
\node [anchor=west] (mid) at (0,0) {$\alpha(1,0)\alpha(2,0) + \alpha(1,0)\alpha(2,1) + \alpha(1,0)\alpha(2,2) +$};
\node [anchor=west] (mid2) at ([yshift=-2em]mid.west) {$\alpha(1,1)\alpha(2,0) + \alpha(1,1)\alpha(2,1) + \alpha(1,1)\alpha(2,2)+$};
\node [anchor=west] (mid3) at ([yshift=-2em]mid2.west) {$\alpha(1,2)\alpha(2,0) + \alpha(1,2)\alpha(2,1) + \alpha(1,2)\alpha(2,2)$};
}
\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (mid) (mid2) (mid3)] (exampleeq) {};
\end{pgfonlayer}
{\footnotesize
{
\node [anchor=north] (eq1) at ([xshift=2em,yshift=-2em]exampleeq.south west) {$\sum\limits_{y_1=0}^{2} \sum\limits_{y_2=0}^{2} \alpha(1,y_1)\alpha(2,y_2)$};
\node [anchor=west] (eq1part2) at ([xshift=-1em,yshift=-3em]eq1.west) {$=$};
\node [anchor=west] (eq1part3) at ([xshift=-0.5em]eq1part2.east) {$\sum\limits_{y_1=0}^{2} \sum\limits_{y_2=0}^{2} \prod\limits_{x=1}^{2} $};
\node [anchor=west,inner sep=2pt] (eq1part4) at ([xshift=-0.3em]eq1part3.east) {$\alpha(x,y_x)$};
}
{
\node [anchor=north] (eq2) at ([xshift=-2em,yshift=-2em]exampleeq.south east) {$(\alpha(1,0)+\alpha(1,1)+\alpha(1,2))\cdot$};
\node [anchor=west] (eq2part2) at ([yshift=-1.5em]eq2.west) {$(\alpha(2,0)+\alpha(2,1)+\alpha(2,2))$};
\node [anchor=west] (eq2part3) at ([xshift=2.1in]eq1part2.east){$=$};
\node [anchor=west] (eq2part4) at ([xshift=-0.5em]eq2part3.east){$\prod\limits_{x=1}^{2} \sum\limits_{y=0}^{2}$};
\node [anchor=west,inner sep=2pt] (eq2part5) at ([xshift=-0.3em]eq2part4.east){$\alpha(x,y)$};
}
}
\begin{pgfonlayer}{background}
{
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (eq1) (eq1part2) (eq1part3)] (eq1full) {};
}
{
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (eq2) (eq2part2) (eq2part3) (eq2part4)] (eq2full) {};
}
\end{pgfonlayer}
{
\draw [->,thick] ([xshift=-3em]exampleeq.south) .. controls +(south:1.5em) and +(north:1.5em) .. (eq1full.north);
}
{
\draw [->,thick] ([xshift=3em]exampleeq.south) .. controls +(south:1.5em) and +(north:1.5em) .. (eq2full.north);
}
{
\node [anchor=west] at ([xshift=0.7em]eq1full.east) {\LARGE{\textbf{=}}};
}
{
{\large
\node [anchor=west] (feq) at ([xshift=3em,yshift=-3em]eq1full.south west) {$\sum\limits_{a_1=0}^{l} ... \sum\limits_{a_m=0}^{l} \prod\limits_{j=1}^{m}$};
\node [anchor=west,inner sep=2pt,fill=blue!20] (feqpart2) at ([xshift=-0.3em]feq.east) {$f(s_j|t_{a_j})$};
\node [anchor=west,inner sep=1pt] (feqpart3) at (feqpart2.east) {=};
\node [anchor=west] (feqpart4) at (feqpart3.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l}$};
\node [anchor=west,inner sep=2pt,fill=blue!20] (feqpart5) at ([xshift=-0.3em]feqpart4.east) {$f(s_j|t_i)$};
}
\draw [->,thick] (eq1part4.south) .. controls +(south:2.5em) and +(north:2.5em) .. (feqpart2.north);
\draw [->,thick] (eq2part5.south) .. controls +(south:1.5em) and +(north:1.5em) .. (feqpart5.north);
\node [anchor=west,inner sep=2pt,fill=blue!20] (eq1part4) at ([xshift=-0.3em]eq1part3.east) {\footnotesize{$\alpha(x,y_x)$}};
\node [anchor=west,inner sep=2pt,fill=blue!20] (eq2part5) at ([xshift=-0.3em]eq2part4.east){\footnotesize{$\alpha(x,y)$}};
}
\end{tikzpicture}
%%% outline
%-------------------------------------------------------------------------
\begin{tabular}{| l | l |}
\hline
& {\footnotesize{$\prod\limits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)$} } \\ \hline
\begin{tikzpicture}
\begin{scope}
{\footnotesize
\begin{scope}
\node [anchor=west] (s1) at (0,0) {$_1$};
\node [anchor=west] (s2) at ([xshift=2.2em]s1.east) {$_2$};
\node [anchor=west] (s3) at ([xshift=3.2em]s2.east) {$_3$};
\node [anchor=west] (s4) at ([xshift=3.6em]s3.east) {感到$_4$};
\node [anchor=west] (s5) at ([xshift=1.9em]s4.east) {满意$_5$};
\node [anchor=east] (s) at (s1.west) {$s=$};
\end{scope}
\begin{scope}[yshift=-3.6em]
\node [anchor=west] (t1) at (0.35em,0) {I$_1$};
\node [anchor=west] (t2) at ([xshift=2.3em,yshift=-0.1em]t1.east) {am$_2$};
\node [anchor=west] (t3) at ([xshift=2.3em,yshift=0.1em]t2.east) {satisfied$_3$};
\node [anchor=west] (t4) at ([xshift=2.3em]t3.east) {with$_4$};
\node [anchor=west] (t5) at ([xshift=2.3em,yshift=-0.2em]t4.east) {you$_5$};
\node [anchor=east] (t) at (t1.west) {$t'=$};
\end{scope}
\draw [-,thick,ublue,dashed] (s1.south) -- (t1.north);
\draw [-,thick,ublue,dashed] (s4.south) -- ([yshift=0.3em]t2.north);
\draw [-,thick,ublue,dashed] (s2.south) ..controls +(south:1em) and +(north:1em).. (t4.north);
\draw [-,thick,ublue,dashed] (s3.south) ..controls +(south:0.5em) and +(north:1.5em).. (t5.north);
\draw [-,thick,ublue,dashed] (s5.south) -- (t3.north);
}
\end{scope}
\end{tikzpicture}
& {\tikz{\node[minimum height=3.2em]{\small{0.0023}};}} \\
\begin{tikzpicture}
\begin{scope}
{\footnotesize
\begin{scope}
\node [anchor=west] (s1) at (0,0) {$_1$};
\node [anchor=west] (s2) at ([xshift=2.5em]s1.east) {$_2$};
\node [anchor=west] (s3) at ([xshift=2.5em]s2.east) {$_3$};
\node [anchor=west] (s4) at ([xshift=2.5em]s3.east) {感到$_4$};
\node [anchor=west] (s5) at ([xshift=2.5em]s4.east) {满意$_5$};
\node [anchor=east] (s) at (s1.west) {$s=$};
\end{scope}
\begin{scope}[yshift=-3.6em]
\node [anchor=center] (t1) at ([yshift=-1.6em]s1.south) {I$_1$};
\node [anchor=center] (t2) at ([yshift=-1.6em]s2.south) {with$_2$};
\node [anchor=center] (t3) at ([yshift=-1.7em]s3.south) {you$_3$};
\node [anchor=center] (t4) at ([yshift=-1.7em]s4.south) {am$_4$};
\node [anchor=center] (t5) at ([yshift=-1.6em]s5.south) {satisfied$_5$};
\node [anchor=center] (t) at ([xshift=-1.3em]t1.west) {$t''=$};
\end{scope}
\draw [-,thick,ublue,dashed] (s1.south) -- (t1.north);
\draw [-,thick,ublue,dashed] (s2.south) -- (t2.north);
\draw [-,thick,ublue,dashed] (s3.south) -- (t3.north);
\draw [-,thick,ublue,dashed] (s4.south) -- (t4.north);
\draw [-,thick,ublue,dashed] (s5.south) -- (t5.north);
}
\end{scope}
\end{tikzpicture}
&{\tikz{\node[minimum height=3.2em]{\small{0.0023}};}}\\
\hline
\end{tabular}
%---------------------------------------------------------------------
\begin{tikzpicture}
{
\node [anchor=north west,inner sep=2pt,align=left] (line1) at (0,0) {\textrm{\textbf{Function} \textsc{WordDecoding}($s$)}};
\node [anchor=north west,inner sep=2pt,align=left] (line2) at ([yshift=-1pt]line1.south west) {\textrm{1: $\pi = $\textsc{GetTransOptions}($s$)}};
\node [anchor=north west,inner sep=2pt,align=left] (line3) at ([yshift=-1pt]line2.south west) {\textrm{2: $best = \phi$}};
\node [anchor=north west,inner sep=2pt,align=left] (line4) at ([yshift=-1pt]line3.south west) {\textrm{3: \textbf{for} $i$ in $[1,m]$ \textbf{do}}};
\node [anchor=north west,inner sep=2pt,align=left] (line5) at ([yshift=-1pt]line4.south west) {\textrm{4: \hspace{1em} $h = \phi$}};
\node [anchor=north west,inner sep=2pt,align=left] (line6) at ([yshift=-1pt]line5.south west) {\textrm{5: \hspace{1em} \textbf{foreach} $j$ in $[1,m]$ \textbf{do}}};
\node [anchor=north west,inner sep=2pt,align=left] (line7) at ([yshift=-1pt]line6.south west) {\textrm{6: \hspace{2em} \textbf{if} $used[j]=$ \textbf{true} \textbf{then}}};
\node [anchor=north west,inner sep=2pt,align=left] (line8) at ([yshift=-1pt]line7.south west) {\textrm{7: \hspace{3em} $h = h \cup \textrm{\textsc{Join}}(best,\pi[j])$}};
\node [anchor=north west,inner sep=2pt,align=left] (line9) at ([yshift=-1pt]line8.south west) {\textrm{8: \hspace{1em} $best = \textrm{\textsc{PruneForTop1}}(h)$}};
\node [anchor=north west,inner sep=2pt,align=left] (line10) at ([yshift=-1pt]line9.south west) {\textrm{9: \hspace{1em} $used[best.j] = \textrm{\textsc{\textbf{true}}}$}};
\node [anchor=north west,inner sep=2pt,align=left] (line11) at ([yshift=-1pt]line10.south west) {\textrm{10: \textbf{return} $best.translatoin$}};
\node [anchor=south west,inner sep=2pt,align=left] (head1) at ([yshift=1pt]line1.north west) {输出: 找的最佳译文};
\node [anchor=south west,inner sep=2pt,align=left] (head2) at ([yshift=1pt]head1.north west) {输入: 源语句子$s=s_1...s_m$};
}
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\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (head2) (line8) (line11)] (algorithm) {};
%% highlights
%\begin{pgfonlayer}{background}
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}
%\end{pgfonlayer}
\end{pgfonlayer}
{
%% remark 1
\begin{scope}
{
\node [anchor=north west,align=left] (remark1) at ([xshift=0.4in]algorithm.north east) {获取每个单词\\的翻译候选};
\node [anchor=west,draw,thick,circle,minimum size=0.3em,inner sep=2.1pt,red] (s1) at ([yshift=-0.7em,xshift=0.5em]remark1.north east){1};
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\node [anchor=center,draw,thick,circle,minimum size=0.3em,inner sep=2pt,red,fill=red] (t1) at ([yshift=-1.7em]s1.center) {{\color{white} $n$}};
\node [anchor=center,draw,thick,circle,minimum size=0.3em,inner sep=2pt,ugreen,fill=ugreen] (t2) at ([yshift=-1.7em]s2.center) {{\color{white} $n$}};
\node [anchor=center,draw,thick,circle,minimum size=0.3em,inner sep=2pt,orange,fill=orange] (t3) at ([yshift=-1.7em]s3.center) {{\color{white} $n$}};
\node [anchor=center,draw,thick,circle,minimum size=0.3em,inner sep=2pt,ublue,fill=ublue] (t4) at ([yshift=-1.7em]s4.center) {{\color{white} $n$}};
\node [anchor=center,draw,thick,circle,minimum size=0.3em,inner sep=2pt,purple,fill=purple] (t5) at ([yshift=-1.7em]s5.center) {{\color{white} $n$}};
\draw [->,thick] ([yshift=-0.1em]s1.south) -- ([yshift=0.1em]t1.north);
\draw [->,thick] ([yshift=-0.1em]s2.south) -- ([yshift=0.1em]t2.north);
\draw [->,thick] ([yshift=-0.1em]s3.south) -- ([yshift=0.1em]t3.north);
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{
\node[rectangle,draw,inner sep=0.2em,fill=blue!10] [fit = (remark1) (t5)] (remark1label) {};
}
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}
\end{scope}
%% end of remark 1
%% remark 2
\begin{scope}
{
\node [anchor=north west,draw,inner sep=2pt,fill=blue!10] (remark2) at ([xshift=-0.2em,yshift=-1em]remark1.south west) {$best$用于保存当前最好的翻译结果};
}
\end{scope}
%% end of remark 2
\node [anchor=north west] (remark4) at ([xshift=21.8em,yshift=-0.6em]line7.east) {};
%% remark 3
\begin{scope}
{
\node [anchor=north west,draw,inner sep=2pt,fill=blue!10] (remark3) at ([yshift=-0.5em]remark2.south west) {$h$用于保存每步生成的所有译文候选};
}
\end{scope}
%% end of remark 3
{
\draw [->,thick] (line2highlight.east) ..controls +(east:1em) and +(west:1em).. (remark1label.west);
}
{
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\draw [->,thick] (line5highlight.east) ..controls +(east:1em) and +(west:1em).. ([yshift=0.3em]remark3.south west);
}
}
\end{tikzpicture}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{
\node [anchor=north west,inner sep=2pt,align=left] (line1) at (0,0) {\textrm{\textbf{Function} \textsc{WordDecoding}($s$)}};
\node [anchor=north west,inner sep=2pt,align=left] (line2) at ([yshift=-1pt]line1.south west) {\textrm{1: $\pi = $\textsc{GetTransOptions}($s$)}};
\node [anchor=north west,inner sep=2pt,align=left] (line3) at ([yshift=-1pt]line2.south west) {\textrm{2: $best = \phi$}};
\node [anchor=north west,inner sep=2pt,align=left] (line4) at ([yshift=-1pt]line3.south west) {\textrm{3: \textbf{for} $i$ in $[1,m]$ \textbf{do}}};
\node [anchor=north west,inner sep=2pt,align=left] (line5) at ([yshift=-1pt]line4.south west) {\textrm{4: \hspace{1em} $h = \phi$}};
\node [anchor=north west,inner sep=2pt,align=left] (line6) at ([yshift=-1pt]line5.south west) {\textrm{5: \hspace{1em} \textbf{foreach} $j$ in $[1,m]$ \textbf{do}}};
\node [anchor=north west,inner sep=2pt,align=left] (line7) at ([yshift=-1pt]line6.south west) {\textrm{6: \hspace{2em} \textbf{if} $used[j]=$ \textbf{true} \textbf{then}}};
\node [anchor=north west,inner sep=2pt,align=left] (line8) at ([yshift=-1pt]line7.south west) {\textrm{7: \hspace{3em} $h = h \cup \textrm{\textsc{Join}}(best,\pi[j])$}};
\node [anchor=north west,inner sep=2pt,align=left] (line9) at ([yshift=-1pt]line8.south west) {\textrm{8: \hspace{1em} $best = \textrm{\textsc{PruneForTop1}}(h)$}};
\node [anchor=north west,inner sep=2pt,align=left] (line10) at ([yshift=-1pt]line9.south west) {\textrm{9: \hspace{1em} $used[best.j] = \textrm{\textsc{\textbf{true}}}$}};
\node [anchor=north west,inner sep=2pt,align=left] (line11) at ([yshift=-1pt]line10.south west) {\textrm{10: \textbf{return} $best.translatoin$}};
\node [anchor=south west,inner sep=2pt,align=left] (head1) at ([yshift=1pt]line1.north west) {输出: 找的最佳译文};
\node [anchor=south west,inner sep=2pt,align=left] (head2) at ([yshift=1pt]head1.north west) {输入: 源语句子$s=s_1...s_m$};
}
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\node[rectangle,draw=ublue,thick,inner sep=0.2em,fill=white,drop shadow,minimum height=1.6cm] [fit = (head2) (line8) (line11)] (algorithm) {};
%% highlights
%\begin{pgfonlayer}{background}
{
\node[anchor=west,fill=blue!20,minimum height=0.16in,minimum width=2.21in] (line2highlight) at (line2.west) {};
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%\end{pgfonlayer}
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{
%% remark 1
\begin{scope}
{
\node [anchor=north west,align=left] (remark1) at ([xshift=0.4in]algorithm.north east) {获取每个单词\\的翻译候选};
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\node [anchor=center,draw,thick,circle,minimum size=0.3em,inner sep=2pt,red,fill=red] (t1) at ([yshift=-1.7em]s1.center) {{\color{white} $n$}};
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\node[rectangle,draw,inner sep=0.2em,fill=blue!10] [fit = (remark1) (t5)] (remark1label) {};
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\end{scope}
%% end of remark 1
%% remark 2
\begin{scope}
{
\node [anchor=north west,draw,inner sep=2pt,fill=blue!10] (remark2) at ([xshift=-0.2em,yshift=-1em]remark1.south west) {$best$用于保存当前最好的翻译结果};
}
\end{scope}
%% end of remark 2
%% remark 3
\begin{scope}
{
\node [anchor=north west,draw,inner sep=2pt,fill=blue!10] (remark3) at ([yshift=-0.5em]remark2.south west) {$h$用于保存每步生成的所有译文候选};
}
\end{scope}
%% end of remark 3
%% remark 4
\begin{scope}
{
\node [anchor=north west,inner sep=2pt,align=left] (remark4) at ([xshift=0.25em,yshift=-0.6em]remark3.south west) {\textsc{Join}($a,b$) 返回\\$a$$b$ 的所有组合};
{
\node [anchor=north west,inner sep=1pt,align=center,draw] (a1) at ([yshift=-0.2em]remark4.north east) {a1\\a2};
\node [anchor=west] (join) at (a1.east) {$\times$};
\node [anchor=north west,inner sep=1pt,align=center,draw] (b1) at ([xshift=1.5em]a1.north east) {b1\\b2};
\node [anchor=west] (join) at (b1.east) {$=$};
\node [anchor=north west,inner sep=1pt,align=center,draw] (result) at ([xshift=1.5em]b1.north east) {a1b1 a1b2\\a2b1 a2b2};
}
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{
\node[rectangle,draw,inner sep=2pt,fill=blue!10] [fit = (remark4) (result)] (remark4label) {};
}
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}
\end{scope}
%% end of remark 4
%% remark 5
\begin{scope}
{
\node [anchor=north west,align=left] (remark5) at ([xshift=0.0em,yshift=-1.3em]remark4.south west) {\textsc{PruneForTop1}\\保留得分最高的结果};
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\draw [-] ([yshift=-0.1em,xshift=-0.2em]s1.south west) -- ([yshift=-0.1em,xshift=3em]s1.south east);
\node [anchor=west] (top1) at ([xshift=0.1em]s1.east) {\color{red}{$\gets$ top1}};
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\node[rectangle,draw,inner sep=0.2em,fill=blue!10] [fit = (remark5) (s3) (top1)] (remark5label) {};
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}
\end{scope}
% end of remark 5
%% remark 6
\begin{scope}
{
\node [anchor=north west,align=left] (remark6) at ([xshift=0.0em,yshift=-1.3em]remark5.south west) {记录已经翻译过\\的源语单词};
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% end of remark 6
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%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
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\node [anchor=east] at (s.west) {\scriptsize{信宿}};
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\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tabular}{| l | l |}
\hline
& {\footnotesize{$\prod\limits_{(j,i) \in \hat{A}} \textrm{P}(s_j,t_i)$} \color{red}{{\footnotesize{$\times\textrm{P}_{lm}(t)$}}}} \\ \hline
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{\footnotesize
\begin{scope}
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& {\tikz{\node[minimum height=3.2em]{\small{0.0023}{\color{red}\small{$\times$0.0107}}};}} \\
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\begin{scope}
{\footnotesize
\begin{scope}
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&{ \tikz{\node[minimum height=3em]{\small{0.0023}{\color{red}\small{$\times$0.0009}}};}}\\
\hline
\end{tabular}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\small
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%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
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{
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\node [anchor=west,inner sep=2pt] (s2) at ([xshift=2em]s1.east) {$s_2$:桌子};
\node [anchor=west,inner sep=2pt] (s3) at ([xshift=2em]s2.east) {$s_3$:上};
\node [anchor=north,inner sep=2pt] (t1) at ([yshift=-2.4em]s1.center) {$t_1$:on};
\node [anchor=north,inner sep=2pt] (t2) at ([yshift=-2.4em]s2.center) {$t_2$:the};
\node [anchor=north,inner sep=2pt] (t3) at ([yshift=-2.4em]s3.center) {$t_3$:table};
\node [anchor=east,inner sep=2pt] (t0) at ([xshift=-2.2em]t1.west) {$t_0$};
\draw [-,dashed,thick] (s1.south) -- (t0.north);
\draw [-,dashed,thick] (s2.south) -- (t3.north);
\draw [-,dashed,thick] (s3.south) -- (t1.north);
}
\begin{pgfonlayer}{background}
{
\path [fill=red!20] (s2.north west) -- (s2.south west) -- (t3.north west) -- (t3.south west) -- (t3.south east) -- (t3.north east) -- (s2.south east) -- (s2.north east) -- (s2.north west);
}
\end{pgfonlayer}
\end{tikzpicture}
%---------------------------------------------------------------------
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
\begin{scope}
\node [anchor=west] (s1) at (0,0) {$_1$};
\node [anchor=west] (s2) at ([xshift=3em]s1.east) {$_2$};
\node [anchor=west] (s3) at ([xshift=4.6em]s2.east) {$_3$};
\node [anchor=west] (s4) at ([xshift=5.1em]s3.east) {感到$_4$};
\node [anchor=west] (s5) at ([xshift=3.1em]s4.east) {满意$_5$};
\node [anchor=east] (s) at (s1.west) {$s=$};
\end{scope}
\begin{scope}[yshift=-7.0em]
\node [anchor=west] (t1) at (0.4em,0) {I$_1$};
\node [anchor=west] (t2) at ([xshift=3.5em,yshift=-0.1em]t1.east) {am$_2$};
\node [anchor=west] (t3) at ([xshift=3.5em,yshift=0.1em]t2.east) {satisfied$_3$};
\node [anchor=west] (t4) at ([xshift=3.5em]t3.east) {with$_4$};
\node [anchor=west] (t5) at ([xshift=3.5em,yshift=-0.2em]t4.east) {you$_5$};
\node [anchor=east] (t) at ([xshift=-0.3em]t1.west) {$t=$};
\end{scope}
\draw [-,thick,ublue,dashed] (s1.south) -- (t1.north);
\draw [-,thick,ublue,dashed] (s4.south) -- ([yshift=0.3em]t2.north);
\draw [-,thick,ublue,dashed] (s2.south) ..controls +(south:1em) and +(north:1em).. (t4.north);
\draw [-,thick,ublue,dashed] (s3.south) ..controls +(south:0.5em) and +(north:1.5em).. (t5.north);
\draw [-,thick,ublue,dashed] (s5.south) -- (t3.north);
\end{tikzpicture}
%---------------------------------------------------------------------
\def\CTeXPreproc{Created by ctex v0.2.13, don't edit!}
\documentclass[cjk,t,compress,12pt]{standalone}
%\documentclass{article}
%\usepackage{beamerarticle}
\usepackage{pstricks}
\usepackage{etex}
\usepackage{eso-pic,graphicx}
\usepackage{fancybox}
\usepackage{amsmath,amssymb}
\usepackage{setspace}
\usepackage{xcolor}
\usepackage{CJK}
\usepackage{tikz}
\usepackage{tikz-qtree}
\usepackage{hyperref}
\usetikzlibrary{arrows,decorations.pathreplacing}
\usetikzlibrary{shadows} % LATEX and plain TEX when using Tik Z
\usepgflibrary{arrows} % LATEX and plain TEX and pure pgf
\usetikzlibrary{arrows} % LATEX and plain TEX when using Tik Z
\usetikzlibrary{decorations}
\usetikzlibrary{arrows,shapes}
\usetikzlibrary{decorations.text}
\usetikzlibrary{positioning,fit,calc}
\usetikzlibrary{mindmap,backgrounds} % mind map
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\definecolor{ublue}{rgb}{0.152,0.250,0.545}
\definecolor{ugreen}{rgb}{0,0.5,0}
\begin{document}
\begin{CJK}{UTF8}{you}
%%% outline
%-------------------------------------------------------------------------
\begin{tikzpicture}
{\footnotesize
\node [anchor=west] (mid) at (0,0) {$\alpha(1,0)\alpha(2,0) + \alpha(1,0)\alpha(2,1) + \alpha(1,0)\alpha(2,2) +$};
\node [anchor=west] (mid2) at ([yshift=-2em]mid.west) {$\alpha(1,1)\alpha(2,0) + \alpha(1,1)\alpha(2,1) + \alpha(1,1)\alpha(2,2)+$};
\node [anchor=west] (mid3) at ([yshift=-2em]mid2.west) {$\alpha(1,2)\alpha(2,0) + \alpha(1,2)\alpha(2,1) + \alpha(1,2)\alpha(2,2)$};
}
\begin{pgfonlayer}{background}
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (mid) (mid2) (mid3)] (exampleeq) {};
\end{pgfonlayer}
{\footnotesize
{
\node [anchor=north] (eq1) at ([xshift=2em,yshift=-2em]exampleeq.south west) {$\sum\limits_{y_1=0}^{2} \sum\limits_{y_2=0}^{2} \alpha(1,y_1)\alpha(2,y_2)$};
\node [anchor=west] (eq1part2) at ([xshift=-1em,yshift=-3em]eq1.west) {$=$};
\node [anchor=west] (eq1part3) at ([xshift=-0.5em]eq1part2.east) {$\sum\limits_{y_1=0}^{2} \sum\limits_{y_2=0}^{2} \prod\limits_{x=1}^{2} $};
\node [anchor=west,inner sep=2pt] (eq1part4) at ([xshift=-0.3em]eq1part3.east) {$\alpha(x,y_x)$};
}
{
\node [anchor=north] (eq2) at ([xshift=-2em,yshift=-2em]exampleeq.south east) {$(\alpha(1,0)+\alpha(1,1)+\alpha(1,2))\cdot$};
\node [anchor=west] (eq2part2) at ([yshift=-1.5em]eq2.west) {$(\alpha(2,0)+\alpha(2,1)+\alpha(2,2))$};
\node [anchor=west] (eq2part3) at ([xshift=2.1in]eq1part2.east){$=$};
\node [anchor=west] (eq2part4) at ([xshift=-0.5em]eq2part3.east){$\prod\limits_{x=1}^{2} \sum\limits_{y=0}^{2}$};
\node [anchor=west,inner sep=2pt] (eq2part5) at ([xshift=-0.3em]eq2part4.east){$\alpha(x,y)$};
}
}
\begin{pgfonlayer}{background}
{
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (eq1) (eq1part2) (eq1part3)] (eq1full) {};
}
{
\node[rectangle,draw=ublue,red,inner sep=0.1em,fill=white] [fit = (eq2) (eq2part2) (eq2part3) (eq2part4)] (eq2full) {};
}
\end{pgfonlayer}
{
\draw [->,thick] ([xshift=-3em]exampleeq.south) .. controls +(south:1.5em) and +(north:1.5em) .. (eq1full.north);
}
{
\draw [->,thick] ([xshift=3em]exampleeq.south) .. controls +(south:1.5em) and +(north:1.5em) .. (eq2full.north);
}
{
\node [anchor=west] at ([xshift=0.7em]eq1full.east) {\LARGE{\textbf{=}}};
}
{
{\large
\node [anchor=west] (feq) at ([xshift=3em,yshift=-3em]eq1full.south west) {$\sum\limits_{a_1=0}^{l} ... \sum\limits_{a_m=0}^{l} \prod\limits_{j=1}^{m}$};
\node [anchor=west,inner sep=2pt,fill=blue!20] (feqpart2) at ([xshift=-0.3em]feq.east) {$f(s_j|t_{a_j})$};
\node [anchor=west,inner sep=1pt] (feqpart3) at (feqpart2.east) {=};
\node [anchor=west] (feqpart4) at (feqpart3.east) {$\prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l}$};
\node [anchor=west,inner sep=2pt,fill=blue!20] (feqpart5) at ([xshift=-0.3em]feqpart4.east) {$f(s_j|t_i)$};
}
\draw [->,thick] (eq1part4.south) .. controls +(south:2.5em) and +(north:2.5em) .. (feqpart2.north);
\draw [->,thick] (eq2part5.south) .. controls +(south:1.5em) and +(north:1.5em) .. (feqpart5.north);
\node [anchor=west,inner sep=2pt,fill=blue!20] (eq1part4) at ([xshift=-0.3em]eq1part3.east) {\footnotesize{$\alpha(x,y_x)$}};
\node [anchor=west,inner sep=2pt,fill=blue!20] (eq2part5) at ([xshift=-0.3em]eq2part4.east){\footnotesize{$\alpha(x,y)$}};
}
\end{tikzpicture}
%---------------------------------------------------------------------
\end{CJK}
\end{document}
......@@ -68,3 +68,155 @@
year={1993},
publisher={Springer}
}
@article{rabiner1989tutorial,
title={A tutorial on hidden Markov models and selected applications in speech recognition},
author={Rabiner, Lawrence R},
journal={Proceedings of the IEEE},
volume={77},
number={2},
pages={257--286},
year={1989},
publisher={Ieee}
}
@article{rabiner1986introduction,
title={An introduction to hidden Markov models},
author={Rabiner, Lawrence and Juang, B},
journal={ieee assp magazine},
volume={3},
number={1},
pages={4--16},
year={1986},
publisher={IEEE}
}
@article{parsing2009speech,
title={Speech and language processing},
author={Parsing, Constituency},
year={2009}
}
@article{ney1994structuring,
title={On structuring probabilistic dependences in stochastic language modelling},
author={Ney, Hermann and Essen, Ute and Kneser, Reinhard},
journal={Computer Speech \& Language},
volume={8},
number={1},
pages={1--38},
year={1994}
}
@article{chen1999empirical,
title={An empirical study of smoothing techniques for language modeling},
author={Chen, Stanley F and Goodman, Joshua},
journal={Computer Speech \& Language},
volume={13},
number={4},
pages={359--394},
year={1999},
publisher={Elsevier}
}
@book{茆诗松2011概率论与数理统计教程,
title={概率论与数理统计教程: 第二版},
author={茆诗松 and 程依明 and 濮晓龙 and 平装 and 查看清 and 单书目},
year={2011},
publisher={北京: 高等教育出版社}
}
@book{kolmogorov2018foundations,
title={Foundations of the theory of probability: Second English Edition},
author={Kolmogorov, Andre Nikolaevich and Bharucha-Reid, Albert T},
year={2018},
publisher={Courier Dover Publications}
}
@article{brown1993mathematics,
title={The mathematics of statistical machine translation: Parameter estimation},
author={Brown, Peter F and Pietra, Vincent J Della and Pietra, Stephen A Della and Mercer, Robert L},
journal={Computational linguistics},
volume={19},
number={2},
pages={263--311},
year={1993},
publisher={MIT Press}
}
@article{shannon1949communication,
title={Communication theory of secrecy systems},
author={Shannon, Claude E},
journal={Bell system technical journal},
volume={28},
number={4},
pages={656--715},
year={1949},
publisher={Wiley Online Library}
}
@article{brown1990statistical,
title={A statistical approach to machine translation},
author={Brown, Peter F and Cocke, John and Della Pietra, Stephen A and Della Pietra, Vincent J and Jelinek, Frederick and Lafferty, John and Mercer, Robert L and Roossin, Paul S},
journal={Computational linguistics},
volume={16},
number={2},
pages={79--85},
year={1990}
}
@book{刘克2004实用马尔可夫决策过程,
title={实用马尔可夫决策过程},
author={刘克},
volume={3},
year={2004},
publisher={清华大学出版社有限公司}
}
@book{resnick1992adventures,
title={Adventures in stochastic processes},
author={Resnick, Sidney I},
year={1992},
publisher={Springer Science \& Business Media}
}
@article{good1953population,
title={The population frequencies of species and the estimation of population parameters},
author={Good, Irving J},
journal={Biometrika},
volume={40},
number={3-4},
pages={237--264},
year={1953},
publisher={Oxford University Press}
}
@article{gale1995good,
title={Good-turing frequency estimation without tears},
author={Gale, William A and Sampson, Geoffrey},
journal={Journal of quantitative linguistics},
volume={2},
number={3},
pages={217--237},
year={1995},
publisher={Taylor \& Francis}
}
@inproceedings{kneser1995improved,
title={Improved backing-off for m-gram language modeling},
author={Kneser, Reinhard and Ney, Hermann},
booktitle={1995 International Conference on Acoustics, Speech, and Signal Processing},
volume={1},
pages={181--184},
year={1995},
organization={IEEE}
}
@article{chen1999empirical,
title={An empirical study of smoothing techniques for language modeling},
author={Chen, Stanley F and Goodman, Joshua},
journal={Computer Speech \& Language},
volume={13},
number={4},
pages={359--394},
year={1999},
publisher={Elsevier}
}
\ No newline at end of file
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