Antos, András and Györfi, László and György, András (2005) Individual convergence rates in empirical vector quantizer design. IEEE TRANSACTIONS ON INFORMATION THEORY, 51 (11). pp. 4013-4022.

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Abstract

We consider the rate of convergence of the expected distortion redundancy of empirically optimal vector quantizers. Earlier results show that the mean-squared distortion of an empirically optimal quantizer designed from n independent and identically distributed source samples converges uniformly to the optimum at a rate of O(1 / \sqrt{n}), and that this rate is sharp in the minimax sense. We prove that for any fixed distribution supported on a given finite set the convergence rate is O(1/n) (faster than the minimax lower bound), where the corresponding constant depends on the source distribution. For more general source distributions we provide conditions implying a little bit worse O(log n/n) rate of convergence. Although these conditions, in general, are hard to verify, we show that sources with continuous densities satisfying certain regularity properties (similar to the ones in [Pol82b] that were used to prove a central limit theorem for the code points of the empirically optimal quantizers) are included in the scope of this result. In particular, scalar distributions with strictly log-concave densities with bounded support (such as the truncated Gaussian distribution) satisfy these conditions.

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:	https://eprints.sztaki.hu/id/eprint/4031

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