相关论文: Wasserstein medians: robustness, PDE characterizat…
The efficiency of a Markov sampler based on the underdamped Langevin diffusion is studied for high dimensional targets with convex and smooth potentials. We consider a classical second-order integrator which requires only one gradient…
The Wasserstein barycenter problem is to compute the average of $m$ given probability measures, which has been widely studied in many different areas; however, real-world data sets are often noisy and huge, which impedes its applications in…
In this paper we develop an intrinsic formalism to study the topology, smooth structure, and Riemannian geometry of the Wasserstein space of a closed Riemannian manifold. Our formalism allows for a new characterisation of the Weak topology…
We study a general formulation of regularized Wasserstein barycenters that enjoys favorable regularity, approximation, stability and (grid-free) optimization properties. This barycenter is defined as the unique probability measure that…
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…
The sliced Wasserstein barycenter (SWB) is a widely acknowledged method for efficiently generalizing the averaging operation within probability measure spaces. However, achieving marginal fairness SWB, ensuring approximately equal distances…
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…
Wasserstein distortion is a one-parameter family of distortion measures that was recently proposed to unify fidelity and realism constraints. After establishing continuity results for Wasserstein in the extreme cases of pure fidelity and…
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…
Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics. However, it is unknown whether Wasserstein barycenters can be computed in polynomial…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
Let $M$ be a connected compact Riemannian manifold possibly with a boundary, let $V\in C^2(M)$ such that $\mu(\d x):=\e^{V(x)}\d x$ is a probability measure, where $\d x$ is the volume measure, and let $L=\Delta+\nabla V$. The exact…
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions.…
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…
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…
Let $X_t$ be the (reflecting) diffusion process generated by $L:=\Delta+\nabla V$ on a complete connected Riemannian manifold $M$ possibly with a boundary $\partial M$, where $V\in C^1(M)$ such that $\mu(d x):= e^{V(x)}d x$ is a probability…
A new least squares mean of positive definite matrices for the divergence associated with the sandwiched quasi-relative entropy has been introduced. It generalizes the well-known Wasserstein mean for covariance matrices of Gaussian…
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…
We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability…