Relevant Explanations: Allowing Disjunctive Assignments

TL;DR

This paper introduces disjunctive assignments in relevance-based explanations for Bayesian networks, allowing variables to be assigned sets of values to address over-specification and specificity issues, and proposes algorithms for computing these generalized explanations.

Contribution

It generalizes the notion of explanations to include disjunctive assignments, improving relevance and stability in Bayesian network explanations.

Findings

GIB assignments have properties that facilitate algorithm design.

Proposed algorithms can compute GIB-MAP explanations effectively.

Disjunctive assignments help address over-specification and explanation instability.

Abstract

Relevance-based explanation is a scheme in which partial assignments to Bayesian belief network variables are explanations (abductive conclusions). We allow variables to remain unassigned in explanations as long as they are irrelevant to the explanation, where irrelevance is defined in terms of statistical independence. When multiple-valued variables exist in the system, especially when subsets of values correspond to natural types of events, the over specification problem, alleviated by independence-based explanation, resurfaces. As a solution to that, as well as for addressing the question of explanation specificity, it is desirable to collapse such a subset of values into a single value on the fly. The equivalent method, which is adopted here, is to generalize the notion of assignments to allow disjunctive assignments. We proceed to define generalized independence based explanations as maximum posterior probability independence based generalized assignments (GIB-MAPs). GIB assignments are shown to have certain properties that ease the design of algorithms for computing GIB-MAPs. One such algorithm is discussed here, as well as suggestions for how other algorithms may be adapted to compute GIB-MAPs. GIB-MAP explanations still suffer from instability, a problem which may be addressed using ?approximate? conditional independence as a condition for irrelevance.