Question

Question 7 /10 points Grads only NaiveBayes + Conditional Likelihood As you recall, the parameters Θ- u {ểnly} for the standard NaiveBayes model are trained generatively, to optimize (log) likelihood of the training data S {[x), y0]; Σ logP (y, x) argmax (x,y)ES Of course, we often later use this NaiveBayes model for the discriminative task of predicting y given x. This suggests it might make sense to, instead, seek the parameters that optimize the log conditional likelihood OMCL argmax log Po(ylx) x,y)es Consider the sunple case where everything is binary-y E {0, 1} and x(リE {0, 1). Also, let β,-log, and A,I,-loge.ly be the logs of the corresponding θ parameters (which you may assume are all non-zero a [3 Express the value of Pe (y-1x) in terms of these Bx parameters Hint: Don't forget to compute probabilities here.../ b [6]: Write f+(x) Pey-1|x) as an explicit function of the values x. You may assume that x = (1,2:1, . . . ,xn) Hint: Observe Bcaly aB-y)for a t0,1). c 111: Quickly describe an algorithm for finding the optimal values for these parameters i.e., that optimize Equation 2. You can assume that the B,s can range freely, and not require that they correspond to as-i.e., the exp(%) values do NOT have to be in [0, 11, nor do corresponding pairs have to sum to 1

Answer 1

서 入し,