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We study the problem of identifying a probability distribution for some givenrandomly sampled data in the limit, in the context of algorithmic learningtheory as proposed recently by Vinanyi and Chater. We show that there exists acomputable partial learner for the computable probability measures, while byBienvenu, Monin and Shen it is known that there is no computable learner forthe computable probability measures. Our main result is the characterization ofthe oracles that compute explanatory learners for the computable (continuous)probability measures as the high oracles. This provides an analogue of awell-known result of Adleman and Blum in the context of learning computableprobability distributions. We also discuss related learning notions such asbehaviorally correct learning and orther variations of explanatory learning, inthe context of learning probability distributions from data.

Algorithmic learning of probability distributions from random data in the limit