Related papers: Conditional Independence Testing in Hilbert Spaces…
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…
The model-X conditional randomization test (CRT) is a flexible and powerful testing procedure for the conditional independence hypothesis: X is independent of Y conditioning on Z. Though having many attractive properties, the model-X CRT…
In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…
This paper deals with the problem of nonparametric independence testing, a fundamental decision-theoretic problem that asks if two arbitrary (possibly multivariate) random variables $X,Y$ are independent or not, a question that comes up in…
Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather…
We consider testing multivariate conditional independence between a response Y and a covariate vector X given additional variables Z. We introduce the Multivariate Sufficient Statistic Conditional Randomization Test (MS-CRT), which…
It is often stated in papers tackling the task of inferring Bayesian network structures from data that there are these two distinct approaches: (i) Apply conditional independence tests when testing for the presence or otherwise of edges;…
Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…
We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is done by defining new types of kernel on an $n$…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the…
Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification,…
Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…
Statistical data is often analyzed as a contingency table, sometimes with empty cells called zeros. Such sparse tables can be due to scarse observations classified in numerous categories, as for example in genetic association studies. Thus,…
In this paper the nonparametric quantile regression model is considered in a location-scale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular…
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…
The paper considers a paired data framework and discuss the question of marginal homogeneity of bivariate high dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random…
Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the…