Related papers: Conditional Dependence via U-Statistics Pruning

This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation…

We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…

We introduce two novel non-parametric statistical hypothesis tests. The first test, called the relative test of dependency, enables us to determine whether one source variable is significantly more dependent on a first target variable or a…

Distance covariance is a measure of dependence between two random variables that take values in two, in general different, metric spaces, see Sz\'ekely, Rizzo and Bakirov (2007) and Lyons (2013). It is known that the distance covariance,…

A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…

Statistical inference can be computationally prohibitive in ultrahigh-dimensional linear models. Correlation-based variable screening, in which one leverages marginal correlations for removal of irrelevant variables from the model prior to…

It is important to draw causal inference from observational studies, which, however, becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. We…

Causal influence measures for machine learnt classifiers shed light on the reasons behind classification, and aid in identifying influential input features and revealing their biases. However, such analyses involve evaluating the classifier…

For multivariate data, dependence beyond pair-wise can be important. This is true, for example, in using functional MRI (fMRI) data to investigate brain functional connectivity. When one has more than a few variables, however, the number of…

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…

Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally…

A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…

Experimental and observational studies often lead to spurious association between the outcome and independent variables describing the intervention, because of confounding to third-party factors. Even in randomized clinical trials,…

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…

Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…

Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…

We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…

Independence screening methods such as the two sample $t$-test and the marginal correlation based ranking are among the most widely used techniques for variable selection in ultrahigh dimensional data sets. In this short note, simple…

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…

The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…