Universal filtering via prediction

Tsachy Weissman; Erik Ordentlich; Marcelo J. Weinberger; Anelia Somekh-Baruch; Neri Merhav

doi:10.1109/tit.2007.892782

Universal filtering via prediction

Tsachy Weissman, Erik Ordentlich, Marcelo J. Weinberger, Anelia Somekh-Baruch, Neri Merhav

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We consider the filtering problem, where a finite-alphabet individual sequence is corrupted by a discrete memoryless channel, and the goal is to causally estimate each sequence component based on the past and present noisy observations. We establish a correspondence between the filtering problem and the problem of prediction of individual sequences which leads to the following result: Given an arbitrary finite set of filters, there exists a filter which performs, with high probability, essentially as well as the best in the set, regardless of the underlying noiseless individual sequence. We use this relationship between the problems to derive a filter guaranteed of attaining the "finite-state filterability" of any individual sequence by leveraging results from the prediction problem.

Original language	English
Pages (from-to)	1253-1264
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	53
Issue number	4
DOIs	https://doi.org/10.1109/tit.2007.892782
State	Published - Apr 2007
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received March 6, 2006; revised September 24, 2006. This work was supported in part by the NSF CAREER and HP University Relations grants. The material in this paper was presented in part at the 37th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL September 1999, and at the 2004 Data Compression Conference (DCC’04), Snowbird, UT March 2004. Part of this work was performed while N. Merhav and T. We-sissman were visiting Hewlett-Packard Laboratories.

Funding

Manuscript received March 6, 2006; revised September 24, 2006. This work was supported in part by the NSF CAREER and HP University Relations grants. The material in this paper was presented in part at the 37th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL September 1999, and at the 2004 Data Compression Conference (DCC’04), Snowbird, UT March 2004. Part of this work was performed while N. Merhav and T. We-sissman were visiting Hewlett-Packard Laboratories.

Funders	Funder number
National Science Foundation

Keywords

Compound sequential decision problem
Discrete denoising
Expert advice
Filtering
Individual sequences
Prediction
Semistochastic setting

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10.1109/tit.2007.892782

Cite this

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note = "Funding Information: Manuscript received March 6, 2006; revised September 24, 2006. This work was supported in part by the NSF CAREER and HP University Relations grants. The material in this paper was presented in part at the 37th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL September 1999, and at the 2004 Data Compression Conference (DCC{\textquoteright}04), Snowbird, UT March 2004. Part of this work was performed while N. Merhav and T. We-sissman were visiting Hewlett-Packard Laboratories.",

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AU - Somekh-Baruch, Anelia

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KW - Expert advice

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KW - Prediction

KW - Semistochastic setting

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Universal filtering via prediction

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