On the Robustness of Most Probable Explanations

TL;DR

This paper investigates the robustness of Most Probable Explanations in Bayesian networks, providing a novel procedure to determine how much network parameter variation can occur without altering the MPE, with computational efficiency tied to network size and complexity.

Contribution

It introduces the first method to compute parameter change bounds that preserve the MPE in Bayesian networks, enhancing understanding of model stability.

Findings

Provides a polynomial-time procedure for robustness analysis

Quantifies parameter change limits that keep the MPE unchanged

Advances understanding of Bayesian network stability under parameter variations

Abstract

In Bayesian networks, a Most Probable Explanation (MPE) is a complete variable instantiation with a highest probability given the current evidence. In this paper, we discuss the problem of finding robustness conditions of the MPE under single parameter changes. Specifically, we ask the question: How much change in a single network parameter can we afford to apply while keeping the MPE unchanged? We will describe a procedure, which is the first of its kind, that computes this answer for each parameter in the Bayesian network variable in time O(n exp(w)), where n is the number of network variables and w is its treewidth.