Related papers: Kernel Trace Distance: Quantum Statistical Metric …
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
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…
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…
This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
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,…
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…
The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…
The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…
Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore…
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…
Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…
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…
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…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency "Coulomb" matrix, used in kernel ridge regression based supervised learning. Resulting quantum machine learning models…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…