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We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
Lin's condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin's condition for functions of random variables have emerged. In this…
We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We…
We show that, for two non-trivial random variables X and Y under a sublinear expectation space, if X is independent from Y and Y is independent from X, then X and Y must be maximally distributed.
The present paper is a continuation of the author's previous works, in which necessary and sufficient local extrema at a stationary point of a polynomial or a power series (and thus of an analytic function) are given. It is known that for…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
We study the closure properties of the class of Bivariate Regular Variation, symbolically BRV , in standard and nonstandard cases, with respect to the randomly weighted sums. However, we take into consideration a weak dependence structure…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…
We propose an estimator of the Hilbert-Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We then get asymptotic normality of this estimator both under independence hypothesis and under the…
We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the…
Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…