Related papers: Compress Then Test: Powerful Kernel Testing in Nea…
We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…
Non-parametric two-sample tests based on energy distance or maximum mean discrepancy are widely used statistical tests for comparing multivariate data from two populations. While these tests enjoy desirable statistical properties, their…
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…
We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly…
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…
We construct and analyze a neural network two-sample test to determine whether two datasets came from the same distribution (null hypothesis) or not (alternative hypothesis). We perform time-analysis on a neural tangent kernel (NTK)…
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…
Modern compression methods can summarize a target distribution $\mathbb{P}$ more succinctly than i.i.d. sampling but require access to a low-bias input sequence like a Markov chain converging quickly to $\mathbb{P}$. We introduce a new…
In this article a new family of tests is proposed for the comparison problem of the equality of distribution of two-sample under right censoring scheme. The tests are based on energy distance and kernels mean embedding, are calibrated by…
We present a comprehensive study of the commute time kernel method via the effective resistance framework analyzing the quantum complexity of the originally classical approach. Our study reveals that while there is a trade-off between…
The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…
In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…
The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially…
Change-point analysis plays a significant role in various fields to reveal discrepancies in distribution in a sequence of observations. While a number of algorithms have been proposed for high-dimensional data, kernel-based methods have not…
We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize…
We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining (normalised) MMD…
Conventional test-time adaptation (TTA) approaches typically adapt the model using only a small fraction of test samples, often those with low-entropy predictions, thereby failing to fully leverage the available information in the test…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
Randomized controlled trials (RCTs) are the gold standard for causal inference, yet practical constraints often limit the size of the concurrent control arm. Borrowing control data from previous trials offers a potential efficiency gain,…