Related papers: New normality test in high dimension with kernel m…
We develop some theoretical results for a robust similarity measure named "generalized min-max" (GMM). This similarity has direct applications in machine learning as a positive definite kernel and can be efficiently computed via…
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…
A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice…
Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a…
We use a suitable version of the so-called "kernel trick" to devise two-sample (homogeneity) tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification related to the important practical…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
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…
Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit…
We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a new connection between neural tangent kernel (NTK) and MMD. This connection enables us to develop a computationally efficient and memory-efficient…
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…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…
This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…
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…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…