Exploration of a Variety of Monte Carlo Methods in the Context of Logistic Classification when N < P

Abstract :

An investigation into the performance of a variety of Monte Carlo methods in regards to the classification problem of hand-written digits (0-9) using a dimension-reduced version of the MNIST dataset. We achieve a 65% prediction accuracy—baseline of 44% using Gaussian discriminant analysis—with a training set smaller than the number of parameters estimated, thus overcoming a widespread learning condition requiring n > p.