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 fascinating open directions for further research are outlined.

Furthermore, we obtain exactp-values, which are easily computed in terms of the Tulap random variable. We show that our results also apply to distribution-free hypothesis testsforcontinuous data.

Author is also affiliated with RaySearch Laboratories. Here is an incomplete list. Our proof consist of two parts. There are two cases to consider. There are two cases to consider.

Randomized smoothing is a popular certified defense against adversarial attacks.

We study causal effect estimation in a setting where the data are not i.i.d.

Recurrent Neural Networks (RNNs) are effective tools for processing sequential data.

The aforementioned references focus solely on minimising the entrywise error for imputed entries.