相关论文: How many moments does MMD compare?

Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…

This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. More precisely, we prove that, on a locally compact, non-compact, Hausdorff space, the MMD…

The classical Mercer's theorem claims that a continuous positive definite kernel $K({\mathbf x}, {\mathbf y})$ on a compact set can be represented as $\sum_{i=1}^\infty \lambda_i\phi_i({\mathbf x})\phi_i({\mathbf y})$ where…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…

Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…

Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…

Negative distance kernels $K(x,y) := - \|x-y\|$ were used in the definition of maximum mean discrepancies (MMDs) in statistics and lead to favorable numerical results in various applications. In particular, so-called slicing techniques for…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean…

Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…

While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

We establish quantitative rates of convergence for the empirical estimation of probability measures by means of the Maximum Mean Discrepancy (MMD) with power kernel $K_q(x,y) = -|x-y|^q$, $q \in (0,2)$. The resulting discrepancy is the…

Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…

Distance metrics are central to machine learning, yet distances between ensembles of quantum states remain poorly understood due to fundamental quantum measurement constraints. We introduce a hierarchy of integral probability metrics,…

Comparing conditional distributions is a fundamental challenge in statistics and machine learning, with applications across a wide range of domains. While proposed methods for measuring discrepancies using kernel embeddings of distributions…

We find probability error bounds for approximations of functions $f$ in a separable reproducing kernel Hilbert space $\mathcal{H}$ with reproducing kernel $K$ on a base space $X$, firstly in terms of finite linear combinations of functions…

This paper studies random operator-valued positive definite (p.d.) kernels and their connection to moment dilations. A class of random p.d. kernels is introduced in which the positivity requirement is imposed only in expectation, extending…

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental…