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

2015/09/25 by Daniil Ryabko, Ryabko, Daniil, Boris Ryabko +1
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistics Theory (math.ST) #cs.IT #math.IT #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1509.07776

appears in the proceedings of ISIT 2015, pp. 1204-1206, Hong Kong

arxiv created 2015/09/25 · arxiv updated 2015/09/28

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 ergodic 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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