Related papers: Non-geodesically-convex optimization in the Wasser…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different…
In this article, we formulate topology optimization problems concerning the mass distribution as minimization problems for functionals on the Wasserstein space. We relax optimization problems regarding non-convex objective functions on the…
We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…
In this paper, we consider the problem of learning high-dimensional tensor regression problems with low-rank structure. One of the core challenges associated with learning high-dimensional models is computation since the underlying…
Planning under process and measurement uncertainties is a challenging problem. In its most general form it can be modeled as a Partially Observed Markov Decision Process (POMDP) problem. However POMDPs are generally difficult to solve when…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
We consider the geometry of the space of Borel measures endowed with a distance that is defined by generalizing the dynamical formulation of the Wasserstein distance to concave, nonlinear mobilities. We investigate the energy landscape of…
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
The article proposes an exact approach to find the global solution of a nonconvex semivectorial bilevel optimization problem, where the objective functions at each level are pseudoconvex, and the constraints are quasiconvex. Due to its…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…
The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…