We extend the concept of epsilon-entropy to include randomized density estimation methods. Based on this extension, we develop a general information theoretical inequality that measures the statistical complexity of some deterministic and randomized density estimators. Consequences of the new inequality will be presented. In particular, we show that this technique can effortlessly lead to substantial improvements of some classical results concerning the convergence of minimum description length (MDL) and Bayesian posterior distributions. Moreover, we are able to derive clean finite-sample convergence bounds that are not obtainable using previous approaches.
By: Tong Zhang
Published in: RC22980 in 2003
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