Independence clustering (without a matrix)

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 U1,dots,Uk of S into clusters such that the clusters U1,dots,Uk 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.