1. Property of quadratically regularized multinomial logistic regression. Multiclass logistic re- gression has the form p(ylac) = exp(d by) Ec_1 exp($TOc) An interesting observation is that if all O is added by a common vector 0, it does not affect the posterior probability of any of the data samples, i.e., p(y|ac) = exp(d by) exp($ (By + 0) ) Lo=1 exp(dec) Ex- exp($(0c + 0)) This also means that the unregularized version of multinomial logistic regression does not have a unique solution. Now consider the quadratically regularized multinomial logistic regression n k k minimize log n [exp(dec) ) - $0yi ) + Elec112. i=1 c=1 Show that at the optimum we have _~_10cj = 0 for all j = 1, ..., m. This shows that the shift ambiguity is removed by the quadratic regularization. What does it mean when k = 2