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Context-Tree Weighting and Maximizing : Processing Betas

The context-tree weighting method (Willems, Shtarkov, and Tjalkens [1995]) is a sequential universal source coding method that achieves the Rissanen lower bound [1984] for tree sources. The same authors also proposed context-tree maximizing, a two-pass version of the context-tree weighting method [1993]. Later Willems and Tjalkens [1998] described a method based on ratios (betas) of sequence probabilities that can be used to reduce the storage complexity of the contexttree weighting method. These betas can be applied to express a posteriori model probabilities in a recursive way (Willems, Nowbahkt-Irani, Volf [2001]). In the present paper we present new results related to betas. These results provide a new view on the relation between context-tree weighting and maximizing.