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On-line learning competitive with reproducing kernel Hilbert spaces
This video was recorded at Workshop on Modelling in Classification and Statistical Learning, Eindhoven 2004. In this talk I will describe a new technique for designing competitive on-line prediction algorithms and proving loss bounds for them. The goal of such algorithms is to perform almost as well as the best decision rules in a wide benchmark class, with no assumptions made about the way the observations are generated. However, standard algorithms in this area can only deal with finite-dimensional (often countable) benchmark classes. The new technique gives similar results for decision rules ranging over infinite-dimensional function spaces. It is based on a recent game-theoretic approach to the foundations of probability and, more specifically, on recent results about defensive forecasting. Given the probabilities produced by a defensive forecasting algorithm, which are known to be well calibrated and to have good resolution in the long run, the expected loss minimization principle is used to find a suitable prediction.
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This work is licensed under a Attribution-NonCommercial-NoDerivs 3.0 United States
