2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134018This correspondence studies an estimator of the conditional support of a distribution underlying a set of i.i.d. observations. The relation with mutual information is shown via an extension of Fano's theorem in combination with a generalization bound based on a compression argument. Extensions to estimating the conditional quantile interval, and statistical guarantees on the minimal convex hull are given.Information TheoryMachine Learningtext