Data-Derived Universal Compression

Abstract: 

In universal estimation problems where the underlying model class is too complex to admit estimators with convergence rates that can be uniformly bounded over each probability distribution in the model class, it is conventional to settle for estimators with convergence guarantees that are model-dependent, i.e. pointwise consistent estimators. This viewpoint has the serious drawback that estimator performance is a function of the unknown model, and is therefore unknown. Even if an estimator is pointwise consistent, how well it is doing at any given time may not be clear, no matter what the sample size of the observations. Departing from the classical uniform/pointwise consistency dichotomy that leads to this impasse, a new analysis framework is explored by studying rich model classes that may only admit pointwise consistency guarantees, yet all the information about the unknown model driving the observations that is needed to gauge estimator accuracy can be inferred from the sample at hand. We call this framework data-derived estimation. This talk will discuss in detail how to analyze the problem of lossless compression of data in this novel data-derived framework.

(Joint work with Narayana Prasad Santhanam and Wojtek Szpankowski)

Speaker Bio: 

Venkat Anantharam is on the faculty of the EECS department at U. C. Berkeley, where he has been since 1994. Prior to this he was on the faculty of the School of EE at Cornell University, from 1986 to 1994. He received his Ph.D. in EE from U. C. Berkeley in 1986. He is a winner of the prize paper award of the IEEE Information theory society and the Stephen O. Rice prize paper award of the IEEE Communications society as well as several conference best paper awards. He is a Fellow of the IEEE.

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