Improved minimax bounds on the test and training distortion of empirically designed vector quantizers

Antos, András (2005) Improved minimax bounds on the test and training distortion of empirically designed vector quantizers. IEEE TRANSACTIONS ON INFORMATION THEORY, 51 (11). pp. 4022-4032.

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Abstract

It is shown by earlier results that the minimax expected (test) distortion redundancy of empirical vector quantizers with three or more levels designed from n independent and identically distributed data points is at least Omega(1 / sqrt{n}) for the class of distributions on a bounded set. In this paper, a much simpler construction and proof for this are given with much better constants. There are similar bounds for the training distortion of the empirical optimal vector quantizer with three or more levels. These rates, however, do not hold for a one-level quantizer. Here the two-level quantizer case is clarified, showing that it already shares the behavior of the general case. Given that the minimax bounds are proved using a construction that involves discrete distributions, one suspects that for the class of distributions with uniformly bounded continuous densities, the expected distortion redundancy might decrease as o(1 / sqrt{n}) uniformly. It is shown as well that this is not so, proving that the lower bound for the expected test distortion remains true for these subclasses.

Item Type: Article
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions: Informatics Laboratory
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:18
Last Modified: 11 Dec 2012 15:18
URI: http://eprints.sztaki.hu/id/eprint/4032

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