Yuri Kalnishkan

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This paper compares two methods of prediction with expert advice, the Aggregating Algorithm and the Defensive Forecasting, in two different settings. The first setting is traditional, with a countable number of experts and a finite number of outcomes. Surprisingly, these two methods of fundamentally different origin lead to identical procedures. In the(More)
The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as well as any oblivious kernel predictor. The paper contains the derivation of an estimate on the performance of this(More)
In this paper the concept of asymptotic complexity of languages is introduced. This concept formalises the notion of learnability in a particular environment and generalises Lutz and Fortnow’s concepts of predictability and dimension. Then asymptotic complexities in different prediction environments are compared by describing the set of all pairs of(More)
Predictive complexity is a generalisation of Kolmogorov complexity motivated by an on-line prediction scenario. It quantifies “unpredictability” of a sequence in a particular prediction environment. This paper surveys key results on predictive complexity for games with finitely many outcomes. The issues of existence, non-existence, uniqueness, and linear(More)