On delayed prediction of individual sequences

Prediction of individual sequences is investigated for cases in which the decision maker observes a delayed version of the sequence, or is forced to issue his/her predictions a number of steps in advance, with incomplete information. For nite action and observation spaces, it is shown that the prediction strategy that minimizes the worst-case regret with respect to the Bayes envelope is obtained through sub-sampling of the sequence of observations. The result extends to the case of logarithmic loss. For nite-state reference prediction strategies, the delayed nite-state predictability is de ned and related to its non-delayed counterpart. As in the non-delayed case, an e cient on-line decision algorithm, based on the incremental parsing rule, is shown to perform in the long run essentially as well as the best nite-state strategy determined in hindsight, with full knowledge of the given sequence of observations. An application to adaptive prefetching in computer memory architectures is d...

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Marcelo J. Weinberger, Erik Ordentlich
• Keywords: Delayed Nite-state Predictability, Prediction, Reference Prediction Strategies, TIT 2002