Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
The minimax distortion redundancy in noisy source coding
IEEE Transactions on Information Theory
Communicating Probability Distributions
IEEE Transactions on Information Theory
Achievable Rates for Pattern Recognition
IEEE Transactions on Information Theory
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The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d, training sample from their joint distribution. Allowable predictors are constrained to lie in some specified class, and the goal is to approach asymptotically the performance of the best predictor in the class. We consider two settings in which the learning agent only has access to rate-limited descriptions of the training data, and present information-theoretic bounds on the predictor performance achievable in the presence of these communication constraints. Our proofs do not assume any separation structure between compression and learning and rely on a new class of operational criteria specifically tailored to joint design of encoders and learning algorithms in rate-constrained settings.