NDLI: Redundancy of the Context-Tree Weighting Method on Renewal and Markov Renewal Processes

Content Provider	IEEE Xplore Digital Library
Author	Garivier, A.
Copyright Year	1963
Abstract	The Context Tree Weighting method (CTW) is shown to be almost adaptive on the classes of renewal and Markov renewal processes. Up to logarithmic factor, ctw achieves the minimax pointwise redundancy described by I. Csiszaacuter and P. Shields in IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 2065-2072, Nov. 1996. This result not only complements previous results on the adaptivity of the Context-Tree Weighting method on the relatively small class of all finite context-tree sources (which encompasses the class of all finite order Markov sources), it shows that almost minimax redundancy can be achieved on massive classes of sources (classes that cannot be smoothly parameterized by subsets of finite-dimensional spaces). Moreover, it shows that (almost) adaptive compression can be achieved in a computationally efficient way on those massive classes. While previous adaptivity results for CTW could rely on the fact that any Markov source is a finite-context-tree source, this is no longer the case for renewal sources. In order to prove almost adaptivity of CTW over renewal sources, it is necessary to establish that CTW carefully balances estimation error and approximation error
Sponsorship	IEEE Information Theory Society
Starting Page	5579
Ending Page	5586
Page Count	8
File Size	385362
File Format	PDF
ISSN	00189448
Volume Number	52
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Minimax techniques Redundancy Source coding Estimation error Approximation error Entropy Performance analysis Context modeling Medical services source coding Adaptivity context tree weighting (CTW) method minimax redundancy renewal processes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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