Decision Theoretic Foundations of Graphical Model Selection
This work addresses the challenge of model selection in graphical models for researchers and practitioners in machine learning, offering a more flexible and computationally efficient approach, though it appears incremental as it builds upon existing Bayesian methods.
The paper tackles the problem of learning graphical structures in Bayesian Belief Networks by introducing a decision theoretic framework that generalizes the standard Bayesian approach, allowing for more flexible loss functions that balance model complexity and error, and proposes a new class of disintegrable loss functions enabling efficient bottom-up search for optimal solutions.
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.