Related papers: regMMD: An R package for parametric estimation and…
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,…
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…
Maximum mean discrepancy (MMD) has been widely adopted in domain adaptation to measure the discrepancy between the source and target domain distributions. Many existing domain adaptation approaches are based on the joint MMD, which is…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
In the missing data literature, the Maximum Likelihood Estimator (MLE) is celebrated for its ignorability property under missing at random (MAR) data. However, its sensitivity to misspecification of the (complete) data model, even under…
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects…
Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…
We consider the maximum mean discrepancy ($\mathrm{MMD}$) GAN problem and propose a parametric kernelized gradient flow that mimics the min-max game in gradient regularized $\mathrm{MMD}$ GAN. We show that this flow provides a descent…
We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…
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…
Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data. Such mismatches are…
The Maximum Mean Discrepancy (MMD) has found numerous applications in statistics and machine learning, most recently as a penalty in the Wasserstein Auto-Encoder (WAE). In this paper we compute closed-form expressions for estimating the…
This work focuses on per-video unsupervised action segmentation, which is of interest to applications where storing large datasets is either not possible, or nor permitted. We propose to segment videos by learning in deep kernel space, to…
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…
An adaptive bandwidth selection procedure for the mixture kernel in the maximum mean discrepancy (MMD) for fitting generative moment matching networks (GMMNs) is introduced, and its ability to improve the learning of copula random number…
Over the last decade, an approach that has gained a lot of popularity to tackle nonparametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of…
Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does…