Related papers: Nearest-Neighbor Sampling Based Conditional Indepe…
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…
Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
Relational data are often represented as a square matrix, the entries of which record the relationships between pairs of objects. Many statistical methods for the analysis of such data assume some degree of similarity or dependence between…
Mutual information is a well-known tool to measure the mutual dependence between variables. In this paper, a Bayesian nonparametric estimation of mutual information is established by means of the Dirichlet process and the $k$-nearest…
The sample-based Gibbs sampler has been the dominant method for approximating joint distribution from a collection of compatible full-conditional distributions. However for conditionally specified model, mixtures of incompatible full and…
Conditional independence testing (CIT) is essential for reliable scientific discovery. It prevents spurious findings and enables controlled feature selection. Recent CIT methods have used machine learning (ML) models as surrogates of the…
Randomness or mutual independence is a fundamental assumption forming the basis of statistical inference across disciplines such as economics, finance, and management. Consequently, validating this assumption is essential for the reliable…
Modern machine learning models are highly expressive but notoriously difficult to analyze statistically. In particular, while black-box predictors can achieve strong empirical performance, they rarely provide valid hypothesis tests or…
We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type I error control and…
How can we generate samples from a conditional distribution that we never fully observe? This question arises across a broad range of applications in both modern machine learning and classical statistics, including image post-processing in…
Nearest neighbor (NN) methods are employed for drawing inferences about spatial patterns of points from two or more classes. We consider Pielou's test of niche specificity which is defined using a contingency table based on the NN…
Randomized controlled trials (RCTs) often exhibit limited inferential efficiency in estimating treatment effects due to small sample sizes. In recent years, the combination of external controls has gained increasing attention as a means of…
We introduce fully nonparametric two-sample tests for testing the null hypothesis that the samples come from the same distribution if the values are only indirectly given via current status censoring. The tests are based on the likelihood…
We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…
Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
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…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…