Universal hypothesis testing in the learning-limited regime

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Universal hypothesis testing in the learning-limited regime


Creation Date: Jun 13, 2010

Published In: Jun 2010

Paper Type: Conference Paper

Book Title: Proc. of IEEE International Symposium on Information Theory

Address: Austin, TX, USA


Given training sequences generated by two distinct, but unknown distributions sharing a common alphabet, we seek a classifier that can correctly decide whether a third test sequence is generated by the first or second distribution using only the training data. To model `limited learning' we allow the alphabet size to grow and therefore probability distributions to change with the blocklength. We prove that a natural choice, namely a generalized likelihood ratio test, is universally consistent (has a probability of error tending to zero with the blocklength for all underlying distributions) when the alphabet size is sub-linear in the blocklength, but inconsistent for linear alphabet growth. For up-to quadratic alphabet growth, in a regime where all probabilities are of the same order, we prove the universally consistency of a new test and show there are no such tests when the alphabet grows quadratically or faster.

IEEE Explore link: http://dx.doi.org/10.1109/ISIT.2010.5513583

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