TY - GEN
T1 - Universal context tree least squares prediction
AU - Singer, Andrew Carl
AU - Kozat, Suleyman S.
PY - 2006
Y1 - 2006
N2 - We investigate the problem of sequential prediction of individual sequences using a competitive algorithm approach. We have previously developed prediction algorithms that are universal with respect to the class of all linear predictors, such that the prediction algorithm competes against a continuous class of prediction algorithms, under the square error loss. In this paper, we introduce the use of a "context tree," to compete against a doubly exponential number of piecewise linear models. We use the context tree to achieve the performance of the best piecewise linear model that can choose its partition of the real line and real-valued prediction parameters, based on observing the entire sequence in advance, for the square error loss, uniformly, for any individual sequence. This performance is achieved with a prediction algorithm whose complexity is only linear in the depth of the context tree.
AB - We investigate the problem of sequential prediction of individual sequences using a competitive algorithm approach. We have previously developed prediction algorithms that are universal with respect to the class of all linear predictors, such that the prediction algorithm competes against a continuous class of prediction algorithms, under the square error loss. In this paper, we introduce the use of a "context tree," to compete against a doubly exponential number of piecewise linear models. We use the context tree to achieve the performance of the best piecewise linear model that can choose its partition of the real line and real-valued prediction parameters, based on observing the entire sequence in advance, for the square error loss, uniformly, for any individual sequence. This performance is achieved with a prediction algorithm whose complexity is only linear in the depth of the context tree.
UR - http://www.scopus.com/inward/record.url?scp=39049154885&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=39049154885&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2006.261704
DO - 10.1109/ISIT.2006.261704
M3 - Conference contribution
AN - SCOPUS:39049154885
SN - 1424405041
SN - 9781424405046
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 426
EP - 430
BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Y2 - 9 July 2006 through 14 July 2006
ER -