Decision Theoretic Foundations of Graphical Model Selection

TL;DR

This paper introduces a decision theoretic framework for learning Bayesian network structures, allowing flexible loss functions and efficient search strategies, advancing model selection methodology.

Contribution

It formulates a decision theoretic approach to graphical model selection, introducing disintegrable loss functions and an efficient bottom-up search algorithm.

Findings

Disintegrable loss functions enable flexible trade-offs in model selection.

The proposed method efficiently finds optimal structures using bottom-up search.

Framework generalizes Bayesian model selection with new loss functions.

Abstract

This paper describes a decision theoretic formulation of learning the graphical structure of a Bayesian Belief Network from data. This framework subsumes the standard Bayesian approach of choosing the model with the largest posterior probability as the solution of a decision problem with a 0-1 loss function and allows the use of more general loss functions able to trade-off the complexity of the selected model and the error of choosing an oversimplified model. A new class of loss functions, called disintegrable, is introduced, to allow the decision problem to match the decomposability of the graphical model. With this class of loss functions, the optimal solution to the decision problem can be found using an efficient bottom-up search strategy.