Relevant Explanations: Allowing Disjunctive Assignments
This work addresses explanation specificity and over-specification in Bayesian networks, which is an incremental improvement for AI reasoning and decision-making systems.
The paper tackles the over-specification problem in relevance-based explanations for Bayesian belief networks by allowing disjunctive assignments, which collapse subsets of variable values into single values to improve explanation specificity. It introduces Generalized Independence Based Maximum A Posteriori (GIB-MAP) explanations and discusses algorithms for computing them, though instability issues remain.
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.