Related papers: Stochastic Gradient Descent for Barycenters in Was…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
We define a metric in the space of positive finite positive measures that extends the 2-Wasserstein metric, i.e. its restriction to the set of probability measures is the 2-Wasserstein metric. We prove a dual and a dynamic formulation and…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the…
We study barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we establish absolute continuity of the barycenter of general measures $\Omega \in…
Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and…
We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for…
The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent progress in studying the training dynamics of the noisy gradient descent algorithm on two-layer…
The Wasserstein distance has become increasingly important in machine learning and deep learning. Despite its popularity, the Wasserstein distance is hard to approximate because of the curse of dimensionality. A recently proposed approach…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the Minimum Mutual Information property, namely the…
We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory inference, where a developing population of cells traces out a…
Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…
We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed…
Exploiting the analogy between Gaussian Distributions and Gaussian Processes' posterior, we present how the weighted Wasserstein Barycenter of Gaussian Processes (W2BGP) can be used to unify, under a common framework, different exotic…
Increasingly complex data analysis tasks motivate the study of the dependency of distributions of multivariate continuous random variables on scalar or vector predictors. Statistical regression models for distributional responses so far…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…