Learning Selectively Conditioned Forest Structures with Applications to DBNs and Classification

TL;DR

This paper introduces a method for efficiently learning selectively conditioned forest structures in Bayesian networks, enhancing model accuracy in temporal data and classification tasks by combining tree and limited in-degree graph structures.

Contribution

It presents a novel approach to efficiently compute MAP estimates and BMA for selectively conditioned forests, applied to Dynamic Bayesian Networks and Naive Bayes classifiers.

Findings

Improved accuracy of Dynamic Bayesian Networks with intra-timestep forests.

Selective augmented Naive Bayes classifiers outperform non-selective counterparts.

Efficient computation of MAP and BMA for SCFs in ordered variable sets.

Abstract

Dealing with uncertainty in Bayesian Network structures using maximum a posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often intractable due to the superexponential number of possible directed, acyclic graphs. When the prior is decomposable, two classes of graphs where efficient learning can take place are tree structures, and fixed-orderings with limited in-degree. We show how MAP estimates and BMA for selectively conditioned forests (SCF), a combination of these two classes, can be computed efficiently for ordered sets of variables. We apply SCFs to temporal data to learn Dynamic Bayesian Networks having an intra-timestep forest and inter-timestep limited in-degree structure, improving model accuracy over DBNs without the combination of structures. We also apply SCFs to Bayes Net classification to learn selective forest augmented Naive Bayes classifiers. We argue that the built-in feature selection of selective augmented Bayes classifiers makes them preferable to similar non-selective classifiers based on empirical evidence.