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Independence clustering (without a matrix)

Abstract · Mar 20, 2017 12:09 ·

cs-lg cs-it math-it stat-ml

Arxiv Abstract

  • Daniil Ryabko

The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning ${U_1,\dots,U_k}$ of $S$ into clusters such that the clusters $U_1,\dots,U_k$ are mutually independent. Since mutual independence is the target, pairwise similarity measurements are of no use, and thus traditional clustering algorithms are inapplicable. The distribution of the random variables in $S$ is, in general, unknown, but a sample is available. Thus, the problem is cast in terms of time series. Two forms of sampling are considered: i.i.d.\ and stationary time series, with the main emphasis being on the latter, more general, case. A consistent, computationally tractable algorithm for each of the settings is proposed, and a number of open directions for further research are outlined.

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