## A Binary-Classification-Based Metric between Time-Series Distributions and Its Use in Statistical and Learning Problems

*Daniil Ryabko, Jérémie Mary*; 14(Sep):2837−2856, 2013.

### Abstract

A metric between time-series distributions is proposed that can
be evaluated using binary classification methods, which were
originally developed to work on i.i.d. data. It is shown how
this metric can be used for solving statistical problems that
are seemingly unrelated to classification and concern highly
dependent time series. Specifically, the problems of time-series
clustering, homogeneity testing and the three-sample problem are
addressed. Universal consistency of the resulting algorithms is
proven under most general assumptions. The theoretical results
are illustrated with experiments on synthetic and real-world
data.

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