The energy of data is the value of a real function of distances between data in metric spaces.
The name energy derives from Newton's gravitational potential energy, which is also a …

Is it possible to define a coefficient of correlation which is (a) as simple as the classical
coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently …

Even though vast amounts of genome-wide gene expression data have become available in
plants, it remains a challenge to effectively mine this information for the discovery of genes …

How should one quantify the strength of association between two random variables without
bias for relationships of a specific form? Despite its conceptual simplicity, this notion of …

Optimal transport maps between two probability distributions $\mu $ and $\nu $ on $\R^ d $
have found extensive applications in both machine learning and statistics. In practice, these …

In this article, we propose a general framework for distribution-free nonparametric testing in
multi-dimensions, based on a notion of multivariate ranks defined using the theory of …

This article introduces a machine for sampling approximate model-X knockoffs for arbitrary
and unspecified data distributions using deep generative models. The main idea is to …

We demonstrate that a popular class of non-parametric mutual information (MI) estimators
based on k-nearest-neighbor graphs requires number of samples that scales exponentially …

One major task in molecular biology is to understand the dependency among genes to
model gene regulatory networks. Pearson's correlation is the most common method used to …

This article investigates the problem of testing independence of two random vectors of
general dimensions. For this, we give for the first time a distribution-free consistent test. Our …