Related papers: Two-sample Statistics Based on Anisotropic Kernels
Independence analysis is an indispensable step before regression analysis to find out essential factors that influence the objects. With many applications in machine Learning, medical Learning and a variety of disciplines, statistical…
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…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
Quantifying the difference between probability distributions is crucial in machine learning. However, estimating statistical divergences from empirical samples is challenging due to unknown underlying distributions. This work proposes the…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
Covariate shifts are a common problem in predictive modeling on real-world problems. This paper proposes addressing the covariate shift problem by minimizing Maximum Mean Discrepancy (MMD) statistics between the training and test sets in…
The modelling of data on a spherical surface requires the consideration of directional probability distributions. To model asymmetrically distributed data on a three-dimensional sphere, Kent distributions are often used. The moment…
We consider the problem of change point detection for high-dimensional distributions in a location family when the dimension can be much larger than the sample size. In change point analysis, the widely used cumulative sum (CUSUM)…
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…
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…
Discrepancy measures between probability distributions are at the core of statistical inference and machine learning. In many applications, distributions of interest are supported on different spaces, and yet a meaningful correspondence…
Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
For more than $50$ years the {\it Mean Measure of Divergence} (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology…
We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…
Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proved to be of vital significance in applications since the unreliable…
Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance…
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…