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Competitive online statistics
 International Statistical Review
, 1999
"... A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive online algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid’s prequential sta ..."
Abstract

Cited by 63 (10 self)
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A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive online 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 online statistics”, it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive online 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. Keywords: Bayes’s rule, competitive online algorithms, linear regression, prequential statistics, worstcase analysis.
MachineLearning Applications of Algorithmic Randomness
 In Proceedings of the Sixteenth International Conference on Machine Learning
, 1999
"... Most machine learning algorithms share the following drawback: they only output bare predictions but not the confidence in those predictions. In the 1960s algorithmic information theory supplied universal measures of confidence but these are, unfortunately, noncomputable. In this paper we com ..."
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Cited by 23 (13 self)
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Most machine learning algorithms share the following drawback: they only output bare predictions but not the confidence in those predictions. In the 1960s algorithmic information theory supplied universal measures of confidence but these are, unfortunately, noncomputable. In this paper we combine the ideas of algorithmic information theory with the theory of Support Vector machines to obtain practicable approximations to universal measures of confidence. We show that in some standard problems of pattern recognition our approximations work well. 1 INTRODUCTION Two important differences of most modern methods of machine learning (such as statistical learning theory, see Vapnik [21], 1998, or PAC theory) from classical statistical methods are that: ffl machine learning methods produce bare predictions, without estimating confidence in those predictions (unlike, eg, prediction of future observations in traditional statistics (Guttman [5], 1970)); ffl many machine learning ...
Algorithmic Information Theory and Machine Learning
, 2000
"... this paper we only consider the context of concept learning : Let X be a set called the instance space. A concept is a subset of X . Usually concepts are identied with their indicating function (by abuse of notations c(x) = 1 x 2 c) A concept class is a set C 2 ..."
Abstract
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this paper we only consider the context of concept learning : Let X be a set called the instance space. A concept is a subset of X . Usually concepts are identied with their indicating function (by abuse of notations c(x) = 1 x 2 c) A concept class is a set C 2