Update Rules for Parameter Estimation in Bayesian Networks

TL;DR

This paper introduces a unified framework for parameter estimation in Bayesian networks that integrates online and batch learning methods, including new update schemes like parameterized EM, with improved convergence properties.

Contribution

It presents a novel unified framework that encompasses existing and new parameter estimation algorithms for Bayesian networks, bridging online and batch learning approaches.

Findings

Parameterized EM converges faster than standard EM.

The framework unifies gradient projection, EM, and online learning methods.

Empirical and theoretical results support the effectiveness of the new schemes.

Abstract

This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for parameter estimation that encompasses both on-line learning, where the model is continuously adapted to new data cases as they arrive, and the more traditional batch learning, where a pre-accumulated set of samples is used in a one-time model selection process. In the batch case, our framework encompasses both the gradient projection algorithm and the EM algorithm for Bayesian networks. The framework also leads to new on-line and batch parameter update schemes, including a parameterized version of EM. We provide both empirical and theoretical results indicating that parameterized EM allows faster convergence to the maximum likelihood parameters than does standard EM.