In lecture we saw a method for language modeling called linear interpolation, where the trigram estimate q(t, I wi-2, tri-1 ) s defined as Here X1, A2, 3 are weights for the trigram, bigram, and unigram estimates, and qML stands for the maximum- likelihood estimate One way to optimize the values (again, as seen in lecture), is to use a set of validation data, in the following way. Say the validation data consists of n sentences, S1, S2,.., Sn Define c'(wi, w2, ws) to be the number of times the trigram w1 , w2, w3 is seen in the validation sentences. Then the values are chosen to maximize the following function: e'(w,2 )log q(ws, lw, w2) Question: show that choosing values that maximize L(Ai, Az, 3) is equivalent to choosing values that minimize the perplexity of the language model on the validation data. In lecture we saw a method for language modeling called linear interpolation, where the trigram estimate q(t, I wi-2, tri-1 ) s defined as Here X1, A2, 3 are weights for the trigram, bigram, and unigram estimates, and qML stands for the maximum- likelihood estimate One way to optimize the values (again, as seen in lecture), is to use a set of validation data, in the following way. Say the validation data consists of n sentences, S1, S2,.., Sn Define c'(wi, w2, ws) to be the number of times the trigram w1 , w2, w3 is seen in the validation sentences. Then the values are chosen to maximize the following function: e'(w,2 )log q(ws, lw, w2) Question: show that choosing values that maximize L(Ai, Az, 3) is equivalent to choosing values that minimize the perplexity of the language model on the validation data