$B NIST $B>e$X(B: $BI>2AJ}K!(B $BLa$k(B: $BI>2AJ}K!(B   $BL\

BLEU

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$$BLEU = BP_{BLEU} * exp(\frac{1}{N} \sum^N_{n=1} logp_n)$$ (3.23)

$BCM0h$O(B0$B!A(B1$B$G$"$j!$9b$$$[$IK]LuJ8$,@52rJ8$K6a$/!$K]Lu@:EY$,9b$$$3$H$r<($9!%(B(3.23)$B<0$N(BN$B$K$O!$0lHLE*$K(B$B$,MQ$$$i$l$k!%$^$?!$(B$B$OK]LuJ8$,@52rJ8$HHf3S$7$FC;$$>l9g$KMQ$$$k%Z%J%k%F%#78?t$G$"$k!%$3$l$O!$K]LuJ8$,@52rJ8$h$j$bC;$$>l9g$KE,9gN($,>e$,$C$F$7$^$&$3$H$r2sHr$9$k$?$a$KMQ$$$i$l$k!%(B$B$OK]LuJ8$NC18l?t$r(B$B!$@52rJ8$NC18l?t$r(B$B$H$7!$0J2<$N<0$G7W;;$5$l$k!%(B

$$BP_{BLEU} = \left \{ \begin{array}{l} 1 \ \ \ \ \ \ \ (c > r)\\ e^{1-\frac{r}{c}} \ \ \ (c \leq r) \end{array}\right.$$ (3.24)

$BK]LuJ8$NJ8;z?t$,@52rJ8$h$j$bD9$$>l9g$K$O!$(B$B$G$"$j!$(BBLEU$BCM$KBP$7$F1F6A$r5Z$\$5$J$$!%D9$$>l9g$N%Z%J%k%F%#$O8e=R$9$k!%K]LuJ8$NJ8;z?t$,@52rJ8$h$j$bC;$$>l9g$K$O!$$=$NC;$5$K1~$8$F!$(B$B$,>.$5$/$J$j!$7k2L$H$7$F(BBLEU$BCM$,>.$5$/$J$k!%$J$*!$C18l?t(B$B$H(B$B$r;;=P$9$k$H$-$NBP>]J8$,(B1$BJ8$G$O$J$/!$%3!<%Q%9A4BN$G$"$k$N$G!$3FJ8$ND9$5$N<+M3EY$,;D$5$l$F$$$k!%$^$?!$(B(3.23)$B<0$N;X?t4X?t$N(B$B$O0J2<$N<0$G7W;;$5$l$k!%(B

$$p_n = \frac{\sum_{\mbox{$BA4K]LuJ8(B}} \sum_{\mbox{$B@52rJ8(B}} \mbox{$B@5(B.. ...} {\sum_{\mbox{$B%A%(%R%s%UuJ8}(B} \sum_{\mbox{$B@52rJ8(B}} \mbox{$BA4(B {\it N}-gram\mbox{$B?t(B}}}$$ (3.25)

$B$O@52rJ8$H0lCW$9$k(BN-gram$B?t$r?t$($k$H$-$K@52rJ8$NMWAG$r=EJ#$7$F?t$($k$3$H$r2sHr$9$k$?$a$N=hM}$r9T$&!%Nc$($P!$K]LuJ8$,(B``a a a a''$B$G$"$j!$@52rJ8$,(B``This is a book''$B$G$"$k>l9g$K$3$N=hM}$r9T$o$J$1$l$P!$K]LuJ8$N(B4$B$D$N(B``a''$B$H0lCW$9$k$b$N$H$7$F!$@52rJ8$N(B``a''$B$,=EJ#$7$F?t$($i$l(B $B$H$J$k!%$3$NCM$KBP$7$F=hM}$r9T$&$3$H$G!$(B $B$H$J$k!%$^$?!$@52rJ8$KBP$7$F!$K]LuJ8$NJ}$,D9$$>l9g$K$O!$(B$B$NCM$O>.$5$/$J$k!%$D$^$j!$(BBLEU$BCM$,>.$5$/$J$k$N$G!$%Z%J%k%F%#$,(B(3.23)$B<0$K4^$^$l$F$$$k$3$H$,$o$+$k!%(B