Related papers: On Ranking-based Tests of Independence
This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…
This paper provides a nonparametric test for the identity of two multivariate continuous distribution functions (d.f.'s) when they differ in locations. The test uses Wilcoxon rank-sum statistics on distances between observations for each of…
We extend the use of Classification Without Labels for anomaly detection with a hypothesis test designed to exclude the background-only hypothesis. By testing for statistical independence of the two discriminating dataset regions, we are…
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…
It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
The Y-test is a useful tool for detecting missing confounders in the context of a multivariate regression.However, it is rarely used in practice since it requires identifying multiple conditionally independent instruments, which is often…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
Chatterjee (2021)'s ingenious approach to estimating a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the unusual property of being…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the…
ROC analyses are considered under a variety of assumptions concerning the distributions of a measurement $X$ in two populations. These include the binormal model as well as nonparametric models where little is assumed about the form of…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
We propose a new method named the Conditional Randomization Rank Test (CRRT) for testing conditional independence of a response variable Y and a covariate variable X, conditional on the rest of the covariates Z. The new method generalizes…
We study a stylized multiple testing problem where the test statistics are independent and assumed to have the same distribution under their respective null hypotheses. We first show that, in the normal means model where the test statistics…
Conditional independence testing (CIT) is a common task in machine learning, e.g., for variable selection, and a main component of constraint-based causal discovery. While most current CIT approaches assume that all variables are numerical…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
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…
We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…
Due to the lack of a canonical ordering in ${\mathbb R}^d$ for $d>1$, defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a…