Related papers: Exponentially Consistent Kernel Two-Sample Tests
Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how…
Various classical machine learning models, including linear regression, kernel methods, and deep neural networks, exhibit double descent, in which the test risk peaks near the interpolation threshold and then decreases in the…
This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…
We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…
We prove that kernel density estimation on symmetric spaces of non-compact type, whose L2-risk was bounded above in previous work (Asta,2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density…
In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…
We introduce the Kernel Calibration Conditional Stein Discrepancy test (KCCSD test), a non-parametric, kernel-based test for assessing the calibration of probabilistic models with well-defined scores. In contrast to previous methods, our…
Kernel two-sample testing provides a powerful framework for distinguishing any pair of distributions based on $n$ sample points. However, existing kernel tests either run in $n^2$ time or sacrifice undue power to improve runtime. To address…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…
We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…
In analyzing high-dimensional models, sparsity of the model parameter is a common but often undesirable assumption. In this paper, we study the following two-sample testing problem: given two samples generated by two high-dimensional linear…
In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…
Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative.…
In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over…
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
In recent years, Bayesian nonparametric statistics has gathered extraordinary attention. Nonetheless, a relatively little amount of work has been expended on Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian…