Constrained Approximate Maximum Entropy Learning of Markov Random Fields

TL;DR

This paper introduces a novel approximate maximum entropy learning method for Markov random fields that improves parameter estimation by combining dual optimization with Bethe approximation, outperforming traditional inference methods.

Contribution

It presents a new framework for MRF learning that incorporates parameter sharing, regularization, and conditional training, unifying and extending previous approaches like piecewise training.

Findings

Algorithms outperform loopy belief propagation and piecewise training.

Framework enables analysis of relaxation trade-offs in entropy and constraints.

Demonstrated effectiveness on real-world network data.

Abstract

Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning - maximizing entropy with moment matching constraints - and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piecewise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints.