Learning Binary Latent Variable Models: A Tensor Eigenpair Approach
This work addresses a computational bottleneck for applications like population genetics, offering a more general approach than prior methods that assumed independence or mutual exclusivity of hidden units.
The paper tackles the challenging problem of learning latent variable models with hidden binary units in noisy settings by proposing a novel spectral method using second and third order moments. The method consistently estimates model parameters at the optimal parametric rate under mild conditions and is validated on simulated data and a genetics application.
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.