Related papers: Variational Transport: A Convergent Particle-Based…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
We consider problems of minimizing functionals $\mathcal{F}$ of probability measures on the Euclidean space. To propose an accelerated gradient descent algorithm for such problems, we consider gradient flow of transport maps that give…
Joint distribution matching (JDM) problem, which aims to learn bidirectional mappings to match joint distributions of two domains, occurs in many machine learning and computer vision applications. This problem, however, is very difficult…
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…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…
How should researchers select experimental sites when the deployment population differs from observed data? I formulate the problem of experimental site selection as an optimal transport problem, developing methods to minimize downstream…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
Computing the empirical Wasserstein distance in the Wasserstein-distance-based independence test is an optimal transport (OT) problem with a special structure. This observation inspires us to study a special type of OT problem and propose a…
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…
Let $M$ be a complete connected Riemannian manifold. For $n \geq 0$, we endow the Wasserstein space $P^{(n)}_2(M) = P_2(\ldots P_2(M)\ldots)$, equipped with the Wasserstein distance $W_2$, with a variational structure that generalizes the…
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…
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…
Worst-case generation plays a critical role in evaluating robustness and stress-testing systems under distribution shifts, in applications ranging from machine learning models to power grids and medical prediction systems. We develop a…
We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
This paper is concerned with the theoretical and computational development of a new class of nonlinear filtering algorithms called the optimal transport particle filters (OTPF). The algorithm is based on a recently introduced variational…
The problem of optimization on Stiefel manifold, i.e., minimizing functions of (not necessarily square) matrices that satisfy orthogonality constraints, has been extensively studied. Yet, a new approach is proposed based on, for the first…
We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…