PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Tracking the Best Quantizer
Andras Gyorgy, Tamas Linder and Gábor Lugosi
IEEE Transactions on Information Theory Volume 54, Number 4, pp. 1604-1625, 2008.


An algorithm is presented for online prediction that allows to track the best expert efficiently even when the number of experts is exponentially large, provided that the set of experts has a certain additive structure. As an example, we work out the case where each expert is represented by a path in a directed graph and the loss of each expert is the sum of the weights over the edges in the path. These results are then used to construct universal limited delay schemes for lossy coding of individual sequences. In particular, we consider the problem of tracking the best scalar quantizer that is adaptively matched to the source sequence with piecewise different behavior.Arandomized algorithm is presented which can perform, on any source sequence, asymptotically as well as the best scalar quantization algorithm that is matched to the sequence and is allowed to change the employed quantizer for a given number of times. The complexity of the algorithm is quadratic in the sequence length, but at the price of some deterioration in performance, the complexity can be made linear. Analogous results are obtained for sequential multiresolution and multiple description scalar quantization of individual sequences.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:4847
Deposited By:Andras Gyorgy
Deposited On:24 March 2009