The Context-Tree Weighting Method: Basic Properties

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The Context-Tree Weighting Method: Basic Properties (1995)

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by Frans M. J. Willems , Yuri M. Shtarkov , Tjalling J. Tjalkens

Venue:	IEEE Trans. Inform. Theory
Citations:	230 - 18 self

BibTeX

@ARTICLE{Willems95thecontext-tree,
    author = {Frans M. J. Willems and Yuri M. Shtarkov and Tjalling J. Tjalkens},
    title = {The Context-Tree Weighting Method: Basic Properties},
    journal = {IEEE Trans. Inform. Theory},
    year = {1995},
    volume = {41},
    pages = {653--664}
}

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Abstract

We describe a sequential universal data compression procedure for binary tree sources that performs the "double mixture." Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding distribution for tree sources with an unknown model and unknown parameters. Computational and storage complexity of the proposed procedure are both linear in the source sequence length. We derive a natural upper bound on the cumulative redundancy of our method for individual sequences. The three terms in this bound can be identified as coding, parameter, and model redundancy. The bound holds for all source sequence lengths, not only for asymptotically large lengths. The analysis that leads to this bound is based on standard techniques and turns out to be extremely simple. Our upper bound on the redundancy shows that the proposed context-tree weighting procedure is optimal in the sense that it achieves the Rissanen (1984) lower bound.

Keyphrases

context-tree weighting method basic property source sequence length natural upper bound coding distribution memory tree source sequential universal data compression procedure unknown parameter tree source cumulative redundancy binary tree source context tree storage complexity model redundancy efficient recursive way desirable coding distribution standard technique unknown model individual sequence method weight context-tree weighting procedure large length upper bound double mixture

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