Related papers: Computational-Statistical Trade-off in Kernel Two-…
The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…
Bayes factors are widely computed by Monte Carlo, yet heavy-tailed sampling distributions can make numerical validation unreliable. The Turing--Good identities provide exact moment equalities for powers of a Bayes factor (a density ratio).…
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…
Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…
Permutation tests are a popular choice for distinguishing distributions and testing independence, due to their exact, finite-sample control of false positives and their minimax optimality when paired with U-statistics. However, standard…
In MT evaluation, pairwise comparisons are conducted to identify the better system. In conducting the comparison, the experimenter must allocate a budget to collect Direct Assessment (DA) judgments. We provide a cost effective way to spend…
Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
Clustered effects are often encountered in multiple hypothesis testing of spatial signals. In this paper, we propose a new method, termed \textit{two-dimensional spatial multiple testing} (2d-SMT) procedure, to control the false discovery…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed through reproducing-kernel maximum mean discrepancy (MMD) penalties, and develop a computational…
In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift…
We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However,…
Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the…
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)…
This paper considers the change point detection problem under dependent samples. In particular, we provide performance guarantees for the MMD-CUSUM test under exponentially $\alpha$, $\beta$, and fast $\phi$-mixing processes, which…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…