Learning Binary Latent Variable Models: A Tensor Eigenpair Approach

Abstract

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this problem, based on the eigenvectors of both the second order moment matrix and third order moment tensor of the observed data. We prove that under mild non-degeneracy conditions, our method consistently estimates the model parameters at the optimal parametric rate. Our tensor-based method generalizes previous orthogonal tensor decomposition approaches, where the hidden units were assumed to be either statistically independent or mutually exclusive. We illustrate the consistency of our method on simulated data and demonstrate its usefulness in learning a common model for population mixtures in genetics.

Newton Correction Methods for Computing Real Eigenpairs of Symmetric Tensors

“…The focus of this paper is on fast iterative methods to compute the real eigenpairs of symmetric tensors. These methods were recently applied by the authors and collaborators in [16] for learning a binary latent variable model by computing the eigenpairs of a third order moment tensor of the observed data.…”