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Compression-based methods for nonparametric density estimation, on-line prediction, regression and classification for time series

B. Ryabko

Published 2007 in 2008 IEEE Information Theory Workshop

ABSTRACT

We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and the real-valued ones and the following problems: estimation of the (limiting) probability P(u<sub>0</sub> <sub>hellip</sub> u<sub>s</sub>) for every s and each sequence u<sub>0</sub> hellip u<sub>s</sub> of letters from the process alphabet (or estimation of the density p(x<sub>0</sub>, <sub>hellip</sub> , x<sub>s</sub>) for real-valued time series), so-called on-line prediction, where the conditional probability P(x<sub>t+1</sub>/x<sub>1</sub>x<sub>2</sub> <sub>hellip</sub> x<sub>t</sub>) (or the conditional density p(x<sub>t+1</sub>/x<sub>1</sub>x<sub>2</sub> <sub>hellip</sub> x<sub>t</sub>)) should be estimated (in the case where x<sub>1</sub>x<sub>2</sub> hellip x<sub>t</sub> is known), regression and classification (or so-called problems with side information). We show that any universal code (or a universal data compressor) can be used as a basis for constructing asymptotically optimal methods for the above problems.

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