Universal piecewise linear prediction via context trees

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Universal piecewise linear prediction via context trees (2006)

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by Suleyman S. Kozat , Andrew C. Singer , Senior Member , Georg Christoph Zeitler

Venue:	IEEE Transactions on Signal Processing, p. Accepted
Citations:	10 - 8 self

BibTeX

@ARTICLE{Kozat06universalpiecewise,
    author = {Suleyman S. Kozat and Andrew C. Singer and Senior Member and Georg Christoph Zeitler},
    title = {Universal piecewise linear prediction via context trees},
    journal = {IEEE Transactions on Signal Processing, p. Accepted},
    year = {2006}
}

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Abstract

Abstract—This paper considers the problem of piecewise linear prediction from a competitive algorithm approach. In prior work, prediction algorithms have been developed that are “universal” with respect to the class of all linear predictors, such that they perform nearly as well, in terms of total squared prediction error, as the best linear predictor that is able to observe the entire sequence in advance. In this paper, we introduce the use of a “context tree, ” to compete against a doubly exponential number of piecewise linear (affine) models. We use the context tree to achieve the total squared prediction error performance of the best piecewise linear model that can choose both its partitioning of the regressor space and its real-valued prediction parameters within each region of the partition, based on observing the entire sequence in advance, uniformly, for every bounded individual sequence. This performance is achieved with a prediction algorithm whose complexity is only linear in the depth of the context tree per prediction. Upper bounds on the regret with respect to the best piecewise linear predictor are given for both the scalar and higher order case, and lower bounds on the regret are given for the scalar case. An explicit algorithmic description and examples demonstrating the performance of the algorithm are given. Index Terms—Context tree, piecewise linear, prediction, universal. I.

Keyphrases

context tree universal piecewise linear prediction prediction algorithm linear predictor entire sequence piecewise linear regressor space scalar case competitive algorithm approach order case piecewise linear predictor explicit algorithmic description piecewise linear prediction individual sequence real-valued prediction parameter prediction error performance total squared prediction error index term context tree piecewise linear model doubly exponential number prior work

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