Relevant Explanations: Allowing Disjunctive Assignments

Relevance-based explanation is a scheme in which partial assignments to Bayesian belief network variables are explanations ( abduc­ tive conclusions). We allow variables to re­ main unassigned in explanations as long as they are irrelevant to the explanation, where irrelevance is defined in terms of statistical in­ dependence. When multiple-valued variables exist in the system, especially when subsets of values correspond to natural types of events, the overspecification problem, alleviated by independence-based explanation, resurfaces. As a solution to that, as well as for address­ ing the question of explanation specificity, it is desirable to collapse such a subset of val­ ues into a single value on the fly. The equiv­ alent method, which is adopted here, is to generalize the notion of assignments to allow disjunctive assignments. We proceed to define generalized indepen­ dence based explanations as maximum poste­ rior probability independence based general­ ized assignments (GIB-MAPs). GIB assign­ ments are shown to have certain properties that ease the deJ>ign of algorithms for com­ puting GIB-MAPs. One such algorithm is discussed here, as well as suggestions for how other algorithms may be adapted to com­ pute GIB-MAPs. GIB-MAP explanations still suffer from instability, a problem which may be addressed using "approximate" con­ ditional independence as a condition for ir­ relevance.