Related papers: Quantifying and testing dependence to categorical …
The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new…
We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints.…
Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…
Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug…
In this paper, we are concerned with the independence test for $k$ high-dimensional sub-vectors of a normal vector, with fixed positive integer $k$. A natural high-dimensional extension of the classical sample correlation matrix, namely…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…
This paper introduces chi-square goodness-of-fit tests to check for conditional distribution model specification. The data is cross-classified according to the Rosenblatt transform of the dependent variable and the explanatory variables,…
Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…
Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed…
Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information.…
This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…
We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…
This article proposes an inferential framework for comparing predictor importance in classification problems with categorical response variables. The approach is based on the categorical Gini correlation (CGC) proposed by Dang et al.…
Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality contraints on the observed distribution. This paper derives a general formula for such…
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
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…