  Recent work proposed $\delta$-relevant inputs (or sets) as a probabilistic
explanation for the predictions made by a classifier on a given input.
$\delta$-relevant sets are significant because they serve to relate
(model-agnostic) Anchors with (model-accurate) PI- explanations, among other
explanation approaches. Unfortunately, the computation of smallest size
$\delta$-relevant sets is complete for ${NP}^{PP}$, rendering their computation
largely infeasible in practice. This paper investigates solutions for tackling
the practical limitations of $\delta$-relevant sets. First, the paper
alternatively considers the computation of subset-minimal sets. Second, the
paper studies concrete families of classifiers, including decision trees among
others. For these cases, the paper shows that the computation of subset-minimal
$\delta$-relevant sets is in NP, and can be solved with a polynomial number of
calls to an NP oracle. The experimental evaluation compares the proposed
approach with heuristic explainers for the concrete case of the classifiers
studied in the paper, and confirms the advantage of the proposed solution over
the state of the art.
