Related papers: Projected Wasserstein gradient descent for high-di…
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…
Wasserstein gradient flows (WGFs) describe the evolution of probability distributions in Wasserstein space as steepest descent dynamics for a free energy functional. Computing the full path from an arbitrary initial distribution to…
We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of…
Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over…
Wasserstein gradient flow (WGF) is a common method to perform optimization over the space of probability measures. While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does…
This paper considers reconstructing a spectrally sparse signal from a small number of randomly observed time-domain samples. The signal of interest is a linear combination of complex sinusoids at $R$ distinct frequencies. The frequencies…
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…
We provide a numerical analysis and computation of neural network projected schemes for approximating one dimensional Wasserstein gradient flows. We approximate the Lagrangian mapping functions of gradient flows by the class of two-layer…
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…
We study policy gradient methods for continuous-action, entropy-regularized reinforcement learning through the lens of Wasserstein geometry. Starting from a Wasserstein proximal update, we derive Wasserstein Proximal Policy Gradient (WPPG)…
Minimizing functionals in the space of probability distributions can be done with Wasserstein gradient flows. To solve them numerically, a possible approach is to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to the…
Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In…
Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…
We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the…
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…