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UNIVERSAL PIECEWISE LINEAR REGRESSION OF INDIVIDUAL SEQUENCES: LOWER BOUND
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@MISC{Kozat_universalpiecewise,
author = {Suleyman S. Kozat and Andrew C. Singer and Georg C. Zeitler},
title = {UNIVERSAL PIECEWISE LINEAR REGRESSION OF INDIVIDUAL SEQUENCES: LOWER BOUND},
year = {}
}
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Abstract
We consider universal piecewise linear regression of real valued bounded sequences under the squared loss function. In this setting, we present a lower bound on the regret of a universal sequential piecewise linear regressor compared to the best piecewise linear regressor that has access to the entire sequence in advance. This lower bound are tight with the corresponding upper bounds, suggesting a min-max optimality of the sequential regressor, for every individual bounded sequence. Index Terms — Regression, piecewise linear, universal 1.
