Decision Theoretic Foundations of Graphical Model Selection
Paola Sebastiani, Marco Ramoni
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.
PDF Link: /papers/98/p464-sebastiani.pdf
AUTHOR = "Paola Sebastiani
and Marco Ramoni",
TITLE = "Decision Theoretic Foundations of Graphical Model Selection",
BOOKTITLE = "Proceedings of the Fourteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-98)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1998",
PAGES = "464--471"