Related papers: Normalizing flows as approximations of optimal tra…
We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
We establish that Polchinski's equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This provides a compelling information-theoretic formulation of the…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…
This paper focuses on an AC optimal power flow (OPF) problem for distribution feeders equipped with controllable distributed energy resources (DERs). We consider a solution method that is based on a continuous approximation of the projected…
We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of…
We investigate the optimal transport (OT) problem over networks, wherein supply and demand are conceptualized as temporal marginals governing departure rates of particles from source nodes and arrival rates at sink nodes. This setting…
We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $\mu$ and $\nu$. Our work is motivated by the specific setting of Monge-Kantorovich quantiles where…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…
In this paper we consider generalized flow problems where there is an $m$-edge $n$-node directed graph $G = (V,E)$ and each edge $e \in E$ has a loss factor $\gamma_e >0$ governing whether the flow is increased or decreased as it crosses…
There are well-established connections between combinatorial optimization, optimal transport theory and Hydrodynamics, through the linear assignment problem in combinatorics, the Monge-Kantorovich problem in optimal transport theory and the…
Diffusion is a fundamental graph procedure and has been a basic building block in a wide range of theoretical and empirical applications such as graph partitioning and semi-supervised learning on graphs. In this paper, we study…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…
Beckmann's problem in optimal transport minimizes the total squared flux in a continuous transport problem from a source to a target distribution. In this article, the regularity theory for solutions to Beckmann's problem in optimal…
Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…