Related papers: Two-sample Test with Kernel Projected Wasserstein …
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…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
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…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…
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…
The two-sample homogeneity testing problem is fundamental in statistics and becomes particularly challenging in high dimensions, where classical tests can suffer substantial power loss. We develop a learning-assisted procedure based on the…
We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
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…
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…
Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…
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…
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…
Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing under $L_1$-distance. However, when the support is very large or even continuous,…