IPF for Discrete Chain Factor Graphs

TL;DR

This paper introduces two generalized iterative algorithms based on IPF for likelihood maximization in a broad class of discrete graphical models, including chain graphs and Bayesian networks, with closed-form iteration steps.

Contribution

The paper presents two novel IPF-based algorithms that extend likelihood maximization techniques to a wider range of discrete graphical models with closed-form updates.

Findings

Algorithms are competitive with state-of-the-art methods.

Applicable to various models including chain graphs and sigmoid belief networks.

Closed-form iteration steps simplify computations.

Abstract

Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define as a wide class of discrete variable models including undirected graphical models and Bayesian networks, but also chain graphs and sigmoid belief networks. The second one is for conditional likelihood maximization in standard undirected models and Bayesian networks. In both algorithms, the iteration steps are expressed in closed form. Numerical simulations show that the algorithms are competitive with state of the art methods.