  In this paper, we introduce a novel method to generate interpretable
regression function estimators. The idea is based on called data-dependent
coverings. The aim is to extract from the data a covering of the feature space
instead of a partition. The estimator predicts the empirical conditional
expectation over the cells of the partitions generated from the coverings.
Thus, such estimator has the same form as those issued from data-dependent
partitioning algorithms. We give sufficient conditions to ensure the
consistency, avoiding the sufficient condition of shrinkage of the cells that
appears in the former literature. Doing so, we reduce the number of covering
elements. We show that such coverings are interpretable and each element of the
covering is tagged as significant or insignificant. The proof of the
consistency is based on a control of the error of the empirical estimation of
conditional expectations which is interesting on its own.
