Problem 2 - Multi-class Logistic Regression (10pts) For multi-class classification using binary logistic regression, one way is to use the One-vs-All (One-vs-Rest) as we discussed in the class. Another way is to extend the binary logistic regression to multi-class logistic regression using softmax function. Assume there are K classes, for a data sample xRn1, the predicted probability that x belongs to class k is given as (for simplicity, we don't add intercept) P(y=kx;W)=i=1Kexp(wiTx)exp(wkTx) where wkRn1 is the parameters to be learned. - (3pts) Please simplify Eq.(3) for K=2. Does the simplified one have the same format as binary logistic regression? Hint: exp(w1Tx)exp(w2Tx)=exp((w2w1)Tx) - (5pts) Assume that K=3,x=[1,2,2],w1=[1,0,1],w2=[0,1,1] and w3=[1,1,0], please calculate P(y=1x;W),P(y=2x;W), and P(y=3x;W). - (2pts) For the above example, i.e., x=[1,2,2]. Based on the calculation, which class should we classify x=[1,2,2] and why