Maximum entropy discrimination factor analyzers

Devising generative models that allow for inferring low dimensional latent feature representations of high-dimensional observations is a significant problem in statistical machine learning. Factor analysis (FA) is a well-established linear latent variable scheme addressing this problem by modeling the covariances between the elements of multivariate observations under a set of linear assumptions. FA is closely related to principal components analysis (PCA), and might be considered as a generalization of both PCA and its probabilistic version, PPCA. Recently, the invention of Gaussian process latent variable models (GP-LVMs) has given rise to a whole new family of latent variable modeling schemes that generalize FA under a nonparametric Bayesian inference framework. In this work, we examine generalization of FA models under a different Bayesian inference perspective. Specifically, we propose a large-margin formulation of FA under the maximum entropy discrimination (MED) framework. The MED framework integrates the large-margin principle with Bayesian posterior inference in an elegant and computationally efficient fashion, allowing to leverage existing high-performance solvers for convex optimization problems. We devise efficient mean-field inference algorithms for our model, and exhibit its advantages by evaluating it in a number of diverse application scenarios, dealing with high-dimensional data classification and reconstruction.