The distributional learning theory or learning of probability distribution is a framework in computational learning theory. It has been proposed from Michael Kearns, Yishay Mansour, Dana Ron, Ronitt Rubinfeld, Robert Schapire and Linda Sellie in 1994 [1] and it was inspired from the PAC-framework introduced by Leslie Valiant.[2]
In this framework the input is a number of samples drawn from a distribution that belongs to a specific class of distributions. The goal is to find an efficient algorithm that, based on these samples, determines with high probability the distribution from which the samples have been drawn. Because of its generality, this framework has been used in a large variety of different fields like machine learning, approximation algorithms, applied probability and statistics.
This article explains the basic definitions, tools and results in this framework from the theory of computation point of view.
^M. Kearns, Y. Mansour, D. Ron, R. Rubinfeld, R. Schapire, L. Sellie On the Learnability of Discrete Distributions. ACM Symposium on Theory of Computing, 1994 [1]
^L. Valiant A theory of the learnable. Communications of ACM, 1984
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