On the existence of the maximum likelihood estimate and convergence rate under gradient descent for multi-class logistic regression

arXiv:2012.04576v5 Announce Type: replace
Abstract: We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The notion of data separability is not needed, which is in contrast to the classical set up of multi-class logistic regression in which each data sample belongs to one class. We also provide a general and constructive estimate …

abstract arxiv class convergence cs.lg dataset every gradient likelihood logistic logistic regression math.st maximum positive probability rate regression sample show stat.th type