Related papers: Controlling Wasserstein Distances by Kernel Norms …
In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…
As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate,…
We study quantum neural networks where the generated function is the expectation value of the sum of single-qubit observables across all qubits. In [Girardi \emph{et al.}, arXiv:2402.08726], it is proven that the probability distributions…
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…
Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…
The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
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,…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the optimal transport and machine learning literature, due to…
This paper presents a novel feature selection method leveraging the Wasserstein distance to improve feature selection in machine learning. Unlike traditional methods based on correlation or Kullback-Leibler (KL) divergence, our approach…
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…
Clustering is a data analysis method for extracting knowledge by discovering groups of data called clusters. Among these methods, state-of-the-art density-based clustering methods have proven to be effective for arbitrary-shaped clusters.…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a…
We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the…
Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between such metric measure spaces is theGromov-Wasserstein (GW)…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…