Characterizing predictable classes of processes
Daniil Ryabko
Abstract:
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discretevalued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure mu belongs to an arbitrary class C of stochastic processes. We are interested in predictors ? whose conditional probabilities converge to the 'true' muconditional probabilities if any mu { C is chosen to generate the data. We show that if such a predictor exists, then a predictor can also be obtained as a convex combination of a countably many elements of C. In other words, it can be obtained as a Bayesian predictor whose prior is concentrated on a countable set. This result is established for two very different measures of performance of prediction, one of which is very strong, namely, total variation, and the other is very weak, namely, prediction in expected average KullbackLeibler divergence.
Keywords: null
Pages: 471478
PS Link:
PDF Link: /papers/09/p471ryabko.pdf
BibTex:
@INPROCEEDINGS{Ryabko09,
AUTHOR = "Daniil Ryabko
",
TITLE = "Characterizing predictable classes of processes",
BOOKTITLE = "Proceedings of the TwentyFifth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI09)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2009",
PAGES = "471478"
}

