A context tree weighting algorithm with a finite window

Abstract

Willems and colleagues proposed the context tree weighting (CTW) method. It is a method for probability estimation, by which the tree source serving the standard model for the data compression is compressed optimally in the quadratic sense with a high computational efficiency, under the condition that the parameters are unknown and the model is unknown. This article intends to apply the CTW method to the nonstationary source, which is a problem that has not been investigated. A compression algorithm with a forgetting mechanism and with a finite window (FWCTW method) is proposed. As the first step, the CTW method in general is discussed. A lemma concerning inferior probability preservation is presented, which serves as a key to the various realization problems. Using that lemma, the validity of the realization of the FWCTW method is shown. Then, for the case of a stationary memoryless source, the redundancy has asymptotic optimality in regard to the window length. The effectiveness of the application to the general constant-interval nonstationary tree source is shown by experiment. © 1999 Scripta Technica,.