Learning General Latent-Variable Graphical Models with Predictive Belief Propagation

TL;DR

This paper introduces predictive belief propagation, a novel message-passing inference method for latent-variable graphical models, enabling a unified, efficient, and statistically consistent learning framework that outperforms existing algorithms.

Contribution

It proposes a new inference formulation and learning algorithm for latent graphical models that overcomes limitations of previous methods, unifies various models, and guarantees global optimality.

Findings

Outperforms EM and spectral algorithms in accuracy

Significantly faster computation times

Proven correctness and statistical consistency

Abstract

Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe limitations that largely restrict their applicability and affect their performance. In order to overcome these limitations, in this paper we introduce a novel formulation of message-passing inference over junction trees named predictive belief propagation, and propose a new learning and inference algorithm for general latent-variable graphical models based on this formulation. Our proposed algorithm reduces the hard parameter learning problem into a sequence of supervised learning problems, and unifies the learning of different kinds of latent graphical models into a single learning framework, which is local-optima-free and statistically consistent. We then give a proof of the correctness of our algorithm and show in experiments on both synthetic and real datasets that our algorithm significantly outperforms both the EM algorithm and the spectral algorithm while also being orders of magnitude faster to compute.