Related papers: Neural Monge Map estimation and its applications
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a…
Standard representational similarity methods align each layer of a network to its best match in another independently, producing asymmetric results, lacking a global alignment score, and struggling with networks of different depths. These…
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the…
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…
Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However,…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
A remarkable connection between optimal design and Monge transport was initiated in the years 1997 in the context of the minimal elastic compliance problem and where the euclidean metric cost was naturally involved. In this paper we present…
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…
A simple procedure to map two probability measures in $\mathbb{R}^d$ is the so-called \emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the…
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Connections to geometry, inequalities, and…
We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
We investigate the approximation of Monge--Kantorovich problems on general compact metric spaces, showing that optimal values, plans and maps can be effectively approximated via a fully discrete method. First we approximate optimal values…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…
We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory. The generative map from the latent space to the data space…