Commit d1c4df30 by xiaotong

minor updates of section 2

parent f1db191d
...@@ -783,7 +783,8 @@ N & = & \sum_{r=0}^{\infty}{r^{*}n_r} \nonumber \\ ...@@ -783,7 +783,8 @@ N & = & \sum_{r=0}^{\infty}{r^{*}n_r} \nonumber \\
也就是说,$N$仍然为这个整个样本分布最初的计数。样本中所有事件的概率之和为: 也就是说,$N$仍然为这个整个样本分布最初的计数。样本中所有事件的概率之和为:
\begin{eqnarray} \begin{eqnarray}
\textrm{P}(r>0) & = & \sum_{r>0}{\textrm{P}_r} \nonumber \\ \textrm{P}(r>0) & = & \sum_{r>0}{\textrm{P}_r} \nonumber \\
& = & 1 - \frac{n_1}{N} < 1 & = & 1 - \frac{n_1}{N} \nonumber \\
& < & 1
\label{eq:2.4-11} \label{eq:2.4-11}
\end{eqnarray} \end{eqnarray}
...@@ -882,7 +883,7 @@ c_{\textrm{KN}}(\cdot) & = & \begin{cases} \textrm{count}(\cdot)\quad\quad \text ...@@ -882,7 +883,7 @@ c_{\textrm{KN}}(\cdot) & = & \begin{cases} \textrm{count}(\cdot)\quad\quad \text
\end{eqnarray} \end{eqnarray}
\noindent 其中catcount$(\cdot)$表示的是基于某个单个词作为第$n$个词的$n$-gram的种类数目。 \noindent 其中catcount$(\cdot)$表示的是基于某个单个词作为第$n$个词的$n$-gram的种类数目。
\parinterval Kneser-Ney平滑是很多语言模型工具的基础\cite{wang-etal-2018-niutrans}\cite{heafield-2011-kenlm}\cite{stolcke2002srilm}。还有很多基于此为基础衍生出来的算法,有兴趣的读者可以通过参考文献自行了解\cite{parsing2009speech}\cite{ney1994structuring}\cite{chen1999empirical} \parinterval Kneser-Ney平滑是很多语言模型工具的基础\cite{wang-etal-2018-niutrans}\cite{heafield-2011-kenlm}\cite{stolcke2002srilm}。还有很多以此为基础衍生出来的算法,感兴趣的读者可以通过参考文献自行了解\cite{parsing2009speech}\cite{ney1994structuring}\cite{chen1999empirical}
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\section{句法分析(短语结构分析)}\index{Chapter2.5} \section{句法分析(短语结构分析)}\index{Chapter2.5}
...@@ -948,7 +949,6 @@ c_{\textrm{KN}}(\cdot) & = & \begin{cases} \textrm{count}(\cdot)\quad\quad \text ...@@ -948,7 +949,6 @@ c_{\textrm{KN}}(\cdot) & = & \begin{cases} \textrm{count}(\cdot)\quad\quad \text
一个上下文无关文法可以被视为一个系统$G=<N,\Sigma,R,S>$,其中 一个上下文无关文法可以被视为一个系统$G=<N,\Sigma,R,S>$,其中
\begin{itemize} \begin{itemize}
\item
\item $N$为一个非终结符集合 \item $N$为一个非终结符集合
\item $\Sigma$为一个终结符集合 \item $\Sigma$为一个终结符集合
\item $R$为一个规则(产生式)集合,每条规则 $r \in R$的形式为$X \to Y_1Y_2...Y_n$,其中$X \in N$, $Y_i \in N \cup \Sigma$ \item $R$为一个规则(产生式)集合,每条规则 $r \in R$的形式为$X \to Y_1Y_2...Y_n$,其中$X \in N$, $Y_i \in N \cup \Sigma$
...@@ -1016,7 +1016,6 @@ s_0 \overset{r_1}{\Rightarrow} s_1 \overset{r_2}{\Rightarrow} s_2 \overset{r_3}{ ...@@ -1016,7 +1016,6 @@ s_0 \overset{r_1}{\Rightarrow} s_1 \overset{r_2}{\Rightarrow} s_2 \overset{r_3}{
\begin{itemize} \begin{itemize}
\item
\item $\forall i \in [0,n], s_i \in (N\cup\Sigma)^*$ \hspace{3.5em} $\lhd$ $s_i$为合法的字符串 \item $\forall i \in [0,n], s_i \in (N\cup\Sigma)^*$ \hspace{3.5em} $\lhd$ $s_i$为合法的字符串
\item $\forall j \in [1,n], r_j \in R$ \hspace{6.3em} $\lhd$ $r_j$$G$的规则 \item $\forall j \in [1,n], r_j \in R$ \hspace{6.3em} $\lhd$ $r_j$$G$的规则
\item $s_0 \in S$ \hspace{10.9em} $\lhd$ $s_0$为起始非终结符 \item $s_0 \in S$ \hspace{10.9em} $\lhd$ $s_0$为起始非终结符
...@@ -1092,7 +1091,6 @@ s_0 \overset{r_1}{\Rightarrow} s_1 \overset{r_2}{\Rightarrow} s_2 \overset{r_3}{ ...@@ -1092,7 +1091,6 @@ s_0 \overset{r_1}{\Rightarrow} s_1 \overset{r_2}{\Rightarrow} s_2 \overset{r_3}{
一个概率上下文无关文法可以被视为一个系统$G=<N,\Sigma,R,S>$,其中 一个概率上下文无关文法可以被视为一个系统$G=<N,\Sigma,R,S>$,其中
\begin{itemize} \begin{itemize}
\item
\item $N$为一个非终结符集合 \item $N$为一个非终结符集合
\item $\Sigma$为一个终结符集合 \item $\Sigma$为一个终结符集合
\item $R$为一个规则(产生式)集合,每条规则 $r \in R$的形式为$p:X \to Y_1Y_2...Y_n$,其中$X \in N$, $Y_i \in N \cup \Sigma$,每个$r$都对应一个概率$p$,表示其生成的可能性。 \item $R$为一个规则(产生式)集合,每条规则 $r \in R$的形式为$p:X \to Y_1Y_2...Y_n$,其中$X \in N$, $Y_i \in N \cup \Sigma$,每个$r$都对应一个概率$p$,表示其生成的可能性。
......
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\indexentry{Chapter1.4|hyperpage}{22} \indexentry{Chapter1.4|hyperpage}{18}
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\contentsline {subsubsection}{标量、向量和矩阵}{211}{section*.222} \contentsline {subsubsection}{标量、向量和矩阵}{207}{section*.222}
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\contentsline {subsubsection}{单层神经网络$\rightarrow $多层神经网络}{222}{section*.246} \contentsline {subsubsection}{单层神经网络$\rightarrow $多层神经网络}{218}{section*.246}
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...@@ -112,13 +112,13 @@ ...@@ -112,13 +112,13 @@
% CHAPTERS % CHAPTERS
%---------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------
%\include{Chapter1/chapter1} \include{Chapter1/chapter1}
\include{Chapter2/chapter2} \include{Chapter2/chapter2}
%\include{Chapter3/chapter3} \include{Chapter3/chapter3}
%\include{Chapter4/chapter4} \include{Chapter4/chapter4}
%\include{Chapter5/chapter5} \include{Chapter5/chapter5}
%\include{Chapter6/chapter6} \include{Chapter6/chapter6}
%\include{ChapterAppend/chapterappend} \include{ChapterAppend/chapterappend}
......
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