Related papers: Adversarial Optimal Transport Through The Convolut…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
Estimating parameters from samples of an optimal probability distribution is essential in applications ranging from socio-economic modeling to biological system analysis. In these settings, the probability distribution arises as the…
Let $\pi_{0}$ and $\pi_{1}$ be two distributions on the Borel space $(\mathbb{R}^{d},\mathcal{B}(\mathbb{R}^{d}))$. Any measurable function $T:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d}$ such that $Y=T(X)\sim\pi_{1}$ if $X\sim\pi_{0}$ is…
We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the…
The paper represents an algorithm for planning safe and optimal routes for transport facilities with unrestricted movement direction that travel within areas with obstacles. Paper explains the algorithm using a ship as an example of such a…
We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of…
Given two probability densities on related data spaces, we seek a map pushing one density to the other while satisfying application-dependent constraints. For maps to have utility in a broad application space (including domain translation,…
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…
We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
This contribution presents substantial computational advancements to compare measures even with varying masses. Specifically, we utilize the nonequispaced fast Fourier transform to accelerate the radial kernel convolution in unbalanced…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in…
We frame the meta-learning of prediction procedures as a search for an optimal strategy in a two-player game. In this game, Nature selects a prior over distributions that generate labeled data consisting of features and an associated…