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¸À¸ì¥â¥Ç¥ë¤Ï¡¤Ã±¸ìÎó¤ÎÀ¸À®³ÎΨ¤òÉÕÍ¿¤¹¤ë¥â¥Ç¥ë¤Ç¤¢¤ë¡¥Æü±ÑËÝÌõ¤Ç¤Ï¡¤ËÝÌõ¥â¥Ç¥ë¤òÍѤ¤¤ÆÀ¸À®¤µ¤ì¤¿ËÝÌõ¸õÊ䤫¤é¡¤±Ñ¸ì¤È¤·¤Æ¼«Á³¤Êʸ¤òÁª½Ð¤¹¤ë¤¿¤á¤ËÍѤ¤¤ë¡¥Åý·×ËÝÌõ¤Ç¤Ï°ìÈÌŪ¤Ë¡¤$N$-gram ¥â¥Ç¥ë¤òÍѤ¤¤ë¡¥

$N$-gram¥â¥Ç¥ë¤È¤Ï``ñ¸ìÎó $P(W_1^n) = w_1^n = w_1 , w_2 , w_3 , ... w_n $ ¤Î $i$ ÈÖÌܤÎñ¸ì $w_i$ ¤ÎÀ¸µ¯³ÎΨ $P(w_i)$ ¤ÏľÁ°¤Î($N-1$)¤Îñ¸ìÎó $w_{i-(N-1)} , w_{i-(N-2)} , w_{i-(N-3)} , ... w_{i-1} $¤Ë°Í¸¤¹¤ë''¤È¤¤¤¦²¾Àâ¤Ë´ð¤Å¤¯¥â¥Ç¥ë¤Ç¤¢¤ë¡¥ ·×»»¼°¤ò°Ê²¼¤Ë¼¨¤¹¡¥


$\displaystyle P(W^{n}_{1})$ $\textstyle =$ $\displaystyle P(w_1)¡ßP(w_2\vert w_1)¡ßP(w_3\vert w_1^2)...P(w_n\vert w_1^{n-1})$ (1)
  $\textstyle \approx$ $\displaystyle P(w_1)¡ßP(w_2\vert w_1)¡ßP(w_3\vert w_1^2)...P(w_n\vert w_{n-(N-1)}^{n-1})$ (2)
  $\textstyle =$ $\displaystyle \prod^{n}_{i=1}P(w_{i}\vert w_{i-(N-1)}^{i-1})$ (3)

¤Þ¤¿¡¤ $P(w_{i}\vert w_{n-(N-1)}^{i-1})$ ¤Ï°Ê²¼¤Î¼°¤Ç·×»»¤µ¤ì¤ë¡¥ ¤³¤³¤Ç $C(w_1^i)$ ¤Ïñ¸ìÎó $w_1^i$ ¤¬½Ð¸½¤¹¤ëÉÑÅÙ¤òɽ¤¹¡¥


$\displaystyle P(w_{i}\vert w_{i-(N-1)}^{i-1}) = \frac{C(w_{i-(N-1)}^i)}{C(w_{i-(N-1)}^{i-1})}$     (4)



2017-04-20