相关论文: Practical Kernel Tests of Conditional Independence

This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…

Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive…

In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…

Identifying relationships among stochastic processes is a core objective in many fields, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear…

This paper is concerned with the problem of conditional independence testing for discrete data. In recent years, researchers have shed new light on this fundamental problem, emphasizing finite-sample optimality. The non-asymptotic viewpoint…

We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…

Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous…

We propose a nonparametric test of independence, termed optHSIC, between a covariate and a right-censored lifetime. Because the presence of censoring creates a challenge in applying the standard permutation-based testing approaches, we use…

Reasoning based on causality, instead of association has been considered as a key ingredient towards real machine intelligence. However, it is a challenging task to infer causal relationship/structure among variables. In recent years, an…

The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…

We propose a series of computationally efficient nonparametric tests for the two-sample, independence, and goodness-of-fit problems, using the Maximum Mean Discrepancy (MMD), Hilbert Schmidt Independence Criterion (HSIC), and Kernel Stein…

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…

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…

We consider the problem of conditional independence testing: given a response Y and covariates (X,Z), we test the null hypothesis that Y is independent of X given Z. The conditional randomization test (CRT) was recently proposed as a way to…

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…

Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernel-based specification test of a…

Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…

This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…

Notions of counterfactual invariance (CI) have proven essential for predictors that are fair, robust, and generalizable in the real world. We propose graphical criteria that yield a sufficient condition for a predictor to be…