# Sequential Local Learning for Latent Graphical Models

## TL;DR

This paper introduces a sequential local learning framework for latent graphical models, expanding the class of models that can be effectively learned by leveraging marginalization and conditioning techniques.

## Contribution

It proposes a novel sequential learning approach that enlarges the class of latent GMs solvable by method of moments, including complex loopy models.

## Key findings

- Enlarged the class of learnable latent GMs
- Successfully applied to convolutional and random regular models
- Achieved broader applicability over existing methods

## Abstract

Learning parameters of latent graphical models (GM) is inherently much harder than that of no-latent ones since the latent variables make the corresponding log-likelihood non-concave. Nevertheless, expectation-maximization schemes are popularly used in practice, but they are typically stuck in local optima. In the recent years, the method of moments have provided a refreshing angle for resolving the non-convex issue, but it is applicable to a quite limited class of latent GMs. In this paper, we aim for enhancing its power via enlarging such a class of latent GMs. To this end, we introduce two novel concepts, coined marginalization and conditioning, which can reduce the problem of learning a larger GM to that of a smaller one. More importantly, they lead to a sequential learning framework that repeatedly increases the learning portion of given latent GM, and thus covers a significantly broader and more complicated class of loopy latent GMs which include convolutional and random regular models.