Competitive On-line Statistics |
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Authors: | Volodya Vovk |
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Institution: | Computer Learning Research Centre, Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK. E-mail:. |
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Abstract: | A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive on-line algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid's prequential statistics). In this approach, which we call "competitive on-line statistics", it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive on-line statistical procedures are guaranteed to hold (and not just hold with high probability or on the average). This paper reviews some results in this area; the new material in it includes the proofs for the performance of the Aggregating Algorithm in the problem of linear regression with square loss. |
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Keywords: | Bayes's rule Competitive on-line algorithms Linear regression Prequential statistics Worst-case analysis |
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