Predicting the outcomes of every process for which an asymptotically accurate stationary predictor exists is impossible

Daniil Ryabko 1 Boris Ryabko 2
1 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 Institute of Computational Technologies
Abstract : The problem of prediction consists in forecasting the conditional distribution of the next outcome given the past. Assume that the source generating the data is such that there is a stationary predictor whose error converges to zero (in a certain sense). The question is whether there is a universal predictor for all such sources, that is, a predictor whose error goes to zero if any of the sources that have this property is chosen to generate the data. This question is answered in the negative, contrasting a number of previously established positive results concerning related but smaller sets of processes.
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Daniil Ryabko, Boris Ryabko. Predicting the outcomes of every process for which an asymptotically accurate stationary predictor exists is impossible. International Symposium on Information Theory, Jun 2015, Hong Kong, Hong Kong SAR China. pp.1204-1206. ⟨hal-01165876⟩

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