The questio

I was asked to estimate theta_(0,1) by maximizing the log-likelihood. I want to introduce Lagrange multipliers and the Lagrange function. I am totally lost at this point. Can you help me how to formulate the function in order to solve the problem.

Recall that the Naive Bayes classifier assumes the probability of an input depends on its input feature. The feature for each sample is defined as a) = [x]", 12',...,']], i = 1, ...,m and the class of the ith sample is y"). In our case the length of the input vector is d = 15, which is equal to the number of words in the vocabulary V. Each entry ," is equal to the number of times word V, occurs in the i-th message. 2. (15 points) In the Naive Bayes model, assuming the keywords are independent of each other (this is a simplification), the likelihood of a sentence with its feature vector a given a class c is given by d P(xly = c) = II c, k' c = {0,1} k=1 where 0