IPF for Discrete Chain Factor Graphs

Iterative Proportional Fitting (IPF), com­ bined with EM, is commonly used as an al­ gorithm for likelihood maximization in undi­ rected graphical models. In this paper, we present two iterative algorithms that gener­ alize 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 graph­ ical 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.