Robust inference of trees

Abstract. This paper is concerned with the reliable inference of optimal treeapproximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between random variables by the index called mutual information. In this paper reliability is achieved by Walley's imprecise Dirichlet model, which generalizes Bayesian learning with Dirichlet priors. Adopting the imprecise Dirichlet model results in posterior interval expectation for mutual information, and in a set of plausible trees consistent with the data. Reliable inference about the actual tree is achieved by focusing on the substructure common to all the plausible trees. We develop an exact algorithm that infers the substructure in time O(m4 ), m being the number of random variables. The new algorithm is applied to a set of data sampled from a known distribution. The method is shown to reliably infer edges of the actual tree even when the d...

• Type: Journal
• Year: 2005
• Where: AMAI
• Authors: Marco Zaffalon, Marcus Hutter
• Keywords: AMAI 2005, Artificial Intelligence, Imprecise Dirichlet Model, Mutual Information, Reliable Inference