This paper is an attempt to bridge the conceptual gaps between researchers working on the
two widely used approaches based on positive definite kernels: Bayesian learning or …

Abstract The Hilbert–Schmidt independence criterion (HSIC) was originally designed to
measure the statistical dependence of the distribution-based Hilbert space embedding in …

Learning a causal directed acyclic graph from data is a challenging task that involves
solving a combinatorial problem for which the solution is not always identifiable. A new line …

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 …

In many fields, such as environmental risk assessment, agronomic system behavior,
aerospace engineering, and nuclear safety, mathematical models turned into computer code …

Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional
independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently …

We investigate the problem of testing whether d possibly multivariate random variables,
which may or may not be continuous, are jointly (or mutually) independent. Our method …

In kernel methods, the median heuristic has been widely used as a way of setting the
bandwidth of RBF kernels. While its empirical performances make it a safe choice under …

We propose a series of computationally efficient, nonparametric tests for the two-sample,
independence and goodness-of-fit problems, using the Maximum Mean Discrepancy …

We identify situations in which conditioning on text can address confounding in
observational studies. We argue that a matching approach is particularly well‐suited to this …