PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Tracking the best quantizer
Andras Gyorgy, Tamas Linder and Gábor Lugosi
IEEE Transactions on Information Theory 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. A randomized 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 se- quence 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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3926
Deposited By:Gábor Lugosi
Deposited On:25 February 2008