Independence clustering (without a matrix)

TL;DR

This paper introduces a novel approach to independence clustering for random variables, focusing on stationary time series, with algorithms that are both consistent and computationally feasible, addressing a gap in traditional clustering methods.

Contribution

It proposes the first consistent, computationally tractable algorithms for independence clustering in stationary time series, a setting where mutual independence is the key criterion.

Findings

Algorithms are proven to be consistent in both i.i.d. and stationary time series settings.

The approach effectively identifies the finest partition into mutually independent clusters.

Open research directions for further development are outlined.

Abstract

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.