Atelier Apprentissage 2006–2007
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|Sequential Prediction in Stationary and Ergodic Environment|
György Ottucsák (Technical University of Budapest)
2 juillet 2007
First, a simple on-line procedure is considered for the prediction of a real-valued sequence. The algorithm is based on a combination of several simple predictors. If the sequence is a realization of an unbounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. Second, we use the above techniques for prediction of a binary-valued sequence in the setup introduced and studied by Weissman and Merhav (2001, 2004), where only side information is available for the algorithm. If the side information is also binary-valued (i.e. original sequence is corrupted by a binary sequence) and both processes are realizations of stationary and ergodic random processes then the average of the loss converges, almost surely, to the optimum. An analog result is offered for the classification of binary processes.