Institute of Fundamental Technological Research
Polish Academy of Sciences

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Dariusz Kalociński, PhD

University of Warsaw (PL)

Supervision of doctoral theses
1.  2020-10-15
co-supervisor
Steifer Tomasz Computable prediction of infinite binary sequences with zero one loss 

Recent publications
1.  Kalociński D., Steifer T., On unstable and unoptimal prediction, MATHEMATICAL LOGIC QUARTERLY, ISSN: 1521-3870, DOI: 10.1002/malq.201800085, Vol.65, No.2, pp.218-227, 2019

Abstract:
We consider the notion of prediction functions (or predictors) studied before in the context of randomness and stochasticity by Ko, and later by Ambos‐Spies and others. Predictor is a total computable function which tries to predict bits of some infinite binary sequence. The prediction error is defined as the limit of the number of incorrect answers divided by the number of answers given so far. We discuss indefiniteness of prediction errors for weak 1‐generics and show that this phenomenon affects certain c.e. sequences as well. On the other hand, a notion of optimal predictor is considered. It is shown that there is a sequence for which increasingly better predictors exist but for which no predictor is optimal.

Affiliations:
Kalociński D. - University of Warsaw (PL)
Steifer T. - IPPT PAN

Conference papers
1.  Kalociński D., Steifer T., An Almost Perfectly Predictable Process with No Optimal Predictor, IEEE-ISIT, IEEE International Symposium on Information Theory, 2019-07-07/07-12, Paryż (FR), DOI: 10.1109/ISIT.2019.8849587, pp.2504-2508, 2019

Abstract:
A novel kind of a negative result is presented for the problem of computable prediction. A non-stationary binary stochastic process is constructed for which almost surely no effective method of prediction achieves the infimum of prediction errors defined as the normalized Hamming distance between the sequence of predictions and the realization of the process. Yet it is shown that this process may be effectively predicted almost surely up to an arbitrarily small error since the infimum of prediction errors is zero.

Affiliations:
Kalociński D. - University of Warsaw (PL)
Steifer T. - IPPT PAN

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