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¸À¸ì¥â¥Ç¥ë

¸À¸ì¥â¥Ç¥ë¤È¤Ï, ¿Í´Ö¤¬ÍѤ¤¤ë¸ÀÍդμ«Á³¤ÊʤӤò³ÎΨ¤È¤·¤Æ¥â¥Ç¥ë²½¤·¤¿¤â¤Î ¤Ç¤¢¤ê, ËÄÂç¤ÊÎ̤Îñ¸À¸ì¥Ç¡¼¥¿¤òÍѤ¤¤Æñ¸ì¤ÎÎó¤äʸ»ú¤ÎÎ󤬵¯¤³¤ë Á«°Ü³ÎΨ¤òÉÕÍ¿¤·¤¿¤â¤Î¤Ç¤¢¤ë.¸À¸ì¥â¥Ç¥ë¤Ë¤Ï°Ê²¼¤Î¤è¤¦¤Ê¤â¤Î¤¬¤¢¤ë.

$ N$ -gram(2.23)

Åý·×ËÝÌõ¤Ç¤Ï¼ç¤Ë$ N$ -gram¤òÍѤ¤¤ë. tri-gram¤Î¼°¤ò¼°2.23¤Ë¼¨¤¹.

\begin{gather*}\begin{gathered}\sum_{i=0}^{N-1} \log_2 {\frac{count(E_{i-2},E_{i-1},E_{i})}{count(E_{i-2},E_{i-1})}}\hspace{10mm}\end{gather*} (2.23)
$\displaystyle %º¸¤Ë¤º¤é¤¹¤¿¤á¤Î¥¹¥Ú¡¼¥¹
\end{gathered}$ (2.24)




$ E_{i}$ : ±Ñ¸ìñ¸ì $ N$ : ±Ñʸ¤Îñ¸ì¿ô
$ C$ : ÂÐÌõ³Ø½¬Ê¸¤ÎÉÑÅÙ  

¼ÂºÝ¤Î·×»»Îã¤ò(2.24)¤Ë¼¨¤¹.

\begin{gather*}\begin{gathered}\log_2P(I~have~a~dog.)\hspace{10mm}\end{gather*} (2.25)
$\displaystyle = \log_2 {\frac{count(I~have~a)}{count(I~have)}}\hspace{10mm}$ (2.26)
$\displaystyle + \log_2 {\frac{count(have~a~dog)}{count(have~a)}}\hspace{10mm}$ (2.27)
$\displaystyle + \log_2 {\frac{count(a~dog.)}{count(a~dog)}}\hspace{10mm}$ (2.28)
$\displaystyle = \log_2 {\frac{140}{1,007}} + \log_2 {\frac{2}{465}} + \log_2 {\frac{14}{31}}\hspace{10mm}$ (2.29)
$\displaystyle = -11.8545 \end{gathered}$ (2.30)

High order Joint Probability(2.25)

Ëܸ¦µæ¤Ç¤Ï, ¸À¸ì¥â¥Ç¥ë¤ËTri-gram¤ÎÂå¤ï¤ê¤Ë High order Joint Probability¤ò»ÈÍѤ¹¤ë. High order Joint Probability¤ò¼°2.25¤Ë¼¨¤¹.

\begin{gather*}\begin{gathered}\sum_{j=0}^{M-1}\sum_{i=0}^{N-1} count(J_{j-2},J_{j-1},J_{j},E_{i-2},E_{i-1},E_{i}) \hspace{10mm}\end{gather*} (2.31)
$\displaystyle %º¸¤Ë¤º¤é¤¹¤¿¤á¤Î¥¹¥Ú¡¼¥¹
\hspace{5mm} \times \ \log_2 \frac{cou...
..._{i})}{count(J_{j-2},J_{j-1},J_{j})count(E_{i-2},E_{i-1},E_{i})} \end{gathered}$ (2.32)


$ J_{j}$ : ÆüËܸìñ¸ì $ M$ : ÆüËܸìʸ¤Îñ¸ì¿ô
$ E_{i}$ : ±Ñ¸ìñ¸ì $ N$ : ±Ñʸ¤Îñ¸ì¿ô
$ P$ : ½Ð¸½³ÎΨ  

¼ÂºÝ¤Î·×»»Îã¤ò(2.26)¤Ë¼¨¤¹.¤Þ¤¿, ·×»»¼°¤¬Ä¹¤¯¤ËµÚ¤Ö¤¿¤á, Âè1¹à¤Î¤ß·×»»Îã¤ò¼¨¤¹.

\begin{gather*}\begin{gathered}P(¤Ö¤é¤ó¤³¤¬Íɤì¤Æ¤¤¤ë¡£~~~~The~swing~is~swinging.)\hspace{10mm}\end{gather*} (2.33)
$\displaystyle = count(¤Ö¤é¤ó¤³~¤¬~~~~The~swing) log_2 {\frac{count(¤Ö¤é¤ó¤³~¤¬~~~~The~swing)}{count(¤Ö¤é¤ó¤³~¤¬)P(The~swing)}} + ...\hspace{10mm}$ (2.34)
$\displaystyle = \frac{1}{100,000} log_2 {\frac {\frac{1}{100,000}} {\frac{2}{100,000} \frac{1}{100,000}}} + ...\hspace{10mm}$ (2.35)
$\displaystyle \end{gathered}$ (2.36)

High order Dice(2.27)

$\displaystyle \sum_{j=0}^{M-1}\sum_{i=0}^{N-1} \log_2 \frac{2 \cdot count(J_{j-...
...-2},E_{i-1},E_{i})} {count(J_{j-2},J_{j-1},J_{j})+count(E_{i-2},E_{i-1},E_{i})}$ (2.37)

¼ÂºÝ¤Î·×»»Îã¤ò(2.28)¤Ë¼¨¤¹.¤Þ¤¿, ·×»»¼°¤¬Ä¹¤¯¤ËµÚ¤Ö¤¿¤á, Âè1¹à¤Î¤ß·×»»Îã¤ò¼¨¤¹.

\begin{displaymath}\begin{split}P(¤Ö¤é¤ó¤³¤¬Íɤì¤Æ¤¤¤ë¡£~~~~The~swing~is~swingin...
...0,000}} {\frac{2}{100,000}+\frac{1}{100,000}} + ... \end{split}\end{displaymath} (2.38)

High order Log Linear(2.29)

\begin{gather*}\begin{gathered}\sum_{j=0}^{M-1}\sum_{i=0}^{N-1} \log_2 \left\{ \...
...{j-1},J_{j})}{count(E_{i-2},E_{i-1},E_{i})} \right\} \end{gathered}\end{gather*} (2.39)

¼ÂºÝ¤Î·×»»Îã¤ò(2.30)¤Ë¼¨¤¹.¤Þ¤¿, ·×»»¼°¤¬Ä¹¤¯¤ËµÚ¤Ö¤¿¤á, Âè1¹à¤Î¤ß·×»»Îã¤ò¼¨¤¹.

\begin{gather*}\begin{gathered}P(¤Ö¤é¤ó¤³¤¬Íɤì¤Æ¤¤¤ë¡£~~~~The~swing~is~swinging.)\hspace{10mm}\end{gather*} (2.40)
$\displaystyle = \log_2 \left\{ \frac{count(¤Ö¤é¤ó¤³~¤¬~~~~The~swing)}{count(¤Ö¤...
... \frac{count(The~swing~~~~¤Ö¤é¤ó¤³~¤¬)}{count(The~swing)} \right\}\hspace{10mm}$ (2.41)
$\displaystyle = \log_2 \left\{ \frac{\frac{1}{100,000}}{\frac{2}{100,000}} \rig...
...imes \left. \frac{\frac{1}{100,000}}{\frac{1}{100,000}} \right\} \end{gathered}$ (2.42)


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Next: ¥Ç¥³¡¼¥À Up: ¶ç¤Ë´ð¤Å¤¯Åý·×ËÝÌõ Previous: ¥Õ¥ì¡¼¥º¥Æ¡¼¥Ö¥ëºîÀ®Ë¡   Ìܼ¡
2020-03-11