Relevant Explanations: Allowing Disjunctive Assignments
  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.
