Related papers: On the Hardness of Conditional Independence Testin…
Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting,…
Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference…
Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure…
Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…
We propose a conditional independence (CI) test based on a new measure, the \emph{spectral generalized covariance measure} (SGCM). The SGCM is constructed by expressing the squared norm of the conditional cross-covariance operator in…
Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic…
Many relations of scientific interest are nonlinear, and even in linear systems distributions are often non-Gaussian, for example in fMRI BOLD data. A class of search procedures for causal relations in high dimensional data relies on sample…
Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…
We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine…
Determining conditional independence (CI) relationships between random variables is a fundamental yet challenging task in machine learning and statistics, especially in high-dimensional settings. Existing generative model-based CI testing…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of conditional dependence between two random variables $Y$ and $Z$ given a third variable $X$, all taking values in general topological spaces.…
We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
The standard constraint-based paradigm for causal discovery with incomplete data -- impute first, test second -- is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching…
Despite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analyzing a…
Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, $X$ and $Y$, are conditionally…
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…