Related papers: Differentially Private Wasserstein Barycenters
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
We introduce a weak notion of barycenter of a probability measure $\mu$ on a metric measure space $(X, d, {\bf m})$, with the metric $d$ and reference measure ${\bf m}$. Under the assumption that optimal transport plans are given by…
We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a d-dimensional Euclidean space. This work is motivated by applications in bioinformatics…
Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of…
Bayesian optimization is a powerful tool for fine-tuning the hyper-parameters of a wide variety of machine learning models. The success of machine learning has led practitioners in diverse real-world settings to learn classifiers for…
We consider synthesis and analysis of probability measures using the entropy-regularized Wasserstein-2 cost and its unbiased version, the Sinkhorn divergence. The synthesis problem consists of computing the barycenter, with respect to these…
We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well…
Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary…
Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Differential privacy is a recent notion of privacy for statistical databases that provides rigorous, meaningful confidentiality guarantees, even in the presence of an attacker with access to arbitrary side information. We show that for a…
Differential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their…
Differential privacy (DP) is a class of mathematical standards for assessing the privacy provided by a data-release mechanism. This work concerns two important flavors of DP that are related yet conceptually distinct: pure…
In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation…
Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive…
We introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or treelike structure with a particular direction of orientation. Our…