We set the output of each rule as the majority class (resp.

To explain the decision of any regression and classification model, we extend the notion ofprobabilistic sufficient explanations (P-SE).

It is a necessary feature as it appears in every Sufficient Explanations.

To explain the decision of any model, we extend the notion of probabilistic Sufficient Explanations (P-SE). For each instance, this approach selects the minimal subset of features that is sufficient to yield the same prediction with high probability, while removing other features. The crux of P-SE is to compute the conditional probability of maintaining the same prediction. Therefore, we introduce an accurate and fast estimator of this probability via random Forests for any data $(\boldsymbol{X}, Y)$ and show its efficiency through a theoretical analysis of its consistency. As a consequence, we extend the P-SE to regression problems. In addition, we deal with non-binary features, without learning the distribution of $X$ nor having the model for making predictions. Finally, we introduce local rule-based explanations for regression/classification based on the P-SE and compare our approaches w.r.t other explainable AI methods. These methods are publicly available as a Python package at \url{www.github.com/salimamoukou/acv00}.