Learning Binary Latent Variable Models: A Tensor Eigenpair Approach

TL;DR

This paper introduces a spectral tensor eigenpair method for learning binary latent variable models, achieving consistent parameter estimation even with noise, and generalizing previous tensor decomposition techniques.

Contribution

The paper presents a novel tensor eigenpair approach that extends orthogonal tensor decomposition to more general binary latent variable models with noise.

Findings

Consistent estimation of model parameters under mild conditions

Generalizes previous tensor decomposition methods

Effective in genetic population mixture modeling

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.