# On sequence predictions for arbitrary measures

## Date

2007

## Authors

Ryabko, Daniil

Hutter, Marcus

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## Publisher

Institute of Electrical and Electronics Engineers (IEEE Inc)

## Abstract

Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences. Consider the question when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain sense), if one of the measures is chosen to generate the sequence. This question may be considered a refinement of the problem of sequence prediction in its most general formulation: for a given class of probability measures, does there exist a measure which predicts all of the measures in the class? To address this problem, we find some conditions on local absolute continuity which are sufficient for prediction and generalize several different notions that are known to be sufficient for prediction. We also formulate some open questions to outline a direction for finding the conditions on classes of measures for which prediction is possible.

## Description

## Keywords

Keywords: Probability measures; Sequence prediction; Cybernetics; Forecasting; Information theory; Random processes; Technical presentations; Risk assessment

## Citation

## Collections

## Source

Proceedings of IEEE International Symposium on Information Theory (ISIT 2007)

## Type

Conference paper

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## License Rights

## DOI

10.1109/ISIT.2007.4557570

## Restricted until

2037-12-31