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- Yuri Kalnishkan, Michael V. Vyugin
- COLT
- 2005

This paper resolves the problem of predicting as well as the best expert up to an additive term of the order o(n), where n is the length of a sequence of letters from a finite alphabet. We call the games that permit this weakly mixable and give a geometrical characterisation of the class of weakly mixable games. Weak mixability turns out to be equivalent to… (More)

- Alexey V. Chernov, Yuri Kalnishkan, Fedor Zhdanov, Vladimir Vovk
- Theor. Comput. Sci.
- 2008

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)

- Yuri Kalnishkan, Vladimir Vovk, Michael V. Vyugin
- COLT
- 2007

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)

- Yuri Kalnishkan
- 2014

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)

- Yuri Kalnishkan
- COLT
- 1999

In this paper we consider and compare different types of predictive complexity, which bounds the ability of any algorithm to predict elements of a sequence. Particular types of predictive complexity are specified by loss functions we use to measure the deviations between predictions and actual outcomes. We consider the logarithmic and square loss functions.… (More)

- Steven Busuttil, Yuri Kalnishkan
- ALT
- 2007

This paper deals with the problem of making predictions in the online mode of learning where the dependence of the outcome yt on the signal xt can change with time. The Aggregating Algorithm (AA) is a technique that optimally merges experts from a pool, so that the resulting strategy suffers a cumulative loss that is almost as good as that of the best… (More)

- Steven Busuttil, Yuri Kalnishkan
- ECML
- 2007

Consider the online regression problem where the dependence of the outcome yt on the signal xt changes with time. Standard regression techniques, like Ridge Regression, do not perform well in tasks of this type. We propose two methods to handle this problem: WeCKAAR, a simple modification of an existing regression technique, and KAARCh, an application of… (More)

- Fedor Zhdanov, Yuri Kalnishkan
- ALT
- 2010

This paper derives an identity connecting the square loss of ridge regression in on-line mode with the loss of the retrospectively best regressor. Some corollaries about the properties of the cumulative loss of on-line ridge regression are also obtained.