Related papers: Pearson Chi-squared Conditional Randomization Test
We present the $U$-Statistic Permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson's chi-squared test of independence, or the $G$-test, are typically used for this task, but…
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of…
Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally…
This paper revisits the Pearson Chi-squared independence test. After presenting the underlying theory with modern notations and showing new way of deriving the proof, we describe an innovative and intuitive graphical presentation of this…
The model-X conditional randomization test is a generic framework for conditional independence testing, unlocking new possibilities to discover features that are conditionally associated with a response of interest while controlling type-I…
In many scientific problems, researchers try to relate a response variable $Y$ to a set of potential explanatory variables $X = (X_1,\dots,X_p)$, and start by trying to identify variables that contribute to this relationship. In statistical…
We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…
Conditional independence (CI) testing is a fundamental and challenging task in modern statistics and machine learning. Many modern methods for CI testing rely on powerful supervised learning methods to learn regression functions or Bayes…
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 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…
We demonstrate how to test for conditional independence of two variables with categorical data using Poisson log-linear models. The size of the conditioning set of variables can vary from 0 (simple independence) up to many variables. We…
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 consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test…
Testing the significance of a variable or group of variables $X$ for predicting a response $Y$, given additional covariates $Z$, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test…