Cesa-Bianchi Nicolò, Lugosi Gábor. Prediction, Learning, and Games

Cambridge University Press, 2006. — 403 p. — ISBN13: 978-0-511-19178-7 ; 978-0-521-84108-5 ; ISBN10: 0-511-19178-2 ; 0-521-84108-9.This important text and reference for researchers and students in machine learning, game theory, statistics, and information theory offer a comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, the prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. A repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts' framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections.