C.A. Micchelli, W.L. Miranker
Journal of the ACM
We examine the sequential prediction of individual sequences under the square error loss using a competitive algorithm framework. Previous work has described a first-order algorithm that competes against a doubly exponential number of piecewise linear models. Using context trees, this firstorder algorithm achieves the performance of the best piecewise linear first-order model that can choose its prediction parameters observing the entire sequence in advance, uniformly, for any individual sequence, with a complexity only linear in the depth of the context tree. In this paper, we extend these results to a sequential predictor of order p > 1, that asymptotically performs as well as the best piecewise linear pth-order model. © 2006 IEEE.
C.A. Micchelli, W.L. Miranker
Journal of the ACM
Saurabh Paul, Christos Boutsidis, et al.
JMLR
Joxan Jaffar
Journal of the ACM
Kenneth L. Clarkson, Elad Hazan, et al.
Journal of the ACM