Related papers: Optimally-Transported Generalized Method of Moment…
The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
The Gromov-Wasserstein (GW) framework adapts ideas from optimal transport to allow for the comparison of probability distributions defined on different metric spaces. Scalable computation of GW distances and associated matchings on graphs…
Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
In the context of first-order algorithms subject to random gradient noise, we study the trade-offs between the convergence rate (which quantifies how fast the initial conditions are forgotten) and the "risk" of suboptimality, i.e.…
We propose a constrained generalized method of moments (GMM) estimator with some equilibrium uniqueness conditions for estimating the conduct parameter in a log-linear model with homogeneous goods markets. Monte Carlo simulations…
We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in…
We take a Hamiltonian-based perspective to generalize Nesterov's accelerated gradient descent and Polyak's heavy ball method to a broad class of momentum methods in the setting of (possibly) constrained minimization in Euclidean and…
This paper deals with the problem of quantifying the impact of model misspecification when computing general expected values of interest. The methodology that we propose is applicable in great generality, in particular, we provide examples…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
Optimal transport provides a robust framework for comparing probability distributions. Its effectiveness is significantly influenced by the choice of the underlying ground metric. Traditionally, the ground metric has either been (i)…
The optimal mass transportation was introduced by Monge some 200 years ago and is, today, the source of large number of results in analysis, geometry and convexity. Here I investigate a new, surprising link between optimal transformations…
We study the optimal transport (OT) problem for measures supported on a graph metric space. Recently, Le et al. (2022) leverage the graph structure and propose a variant of OT, namely Sobolev transport (ST), which yields a closed-form…
Training data are usually limited or heterogeneous in many chemical and biological applications. Existing machine learning models for chemistry and materials science fail to consider generalizing beyond training domains. In this article, we…
This paper proposes a Multimarginal Optimal Transport ($MOT$) approach for simultaneously comparing $k\geq 2$ measures supported on finite subsets of $\mathbb{R}^d$, $d \geq 1$. We derive asymptotic distributions of the optimal value of the…
A new data-enabled control technique for uncertain linear time-invariant systems, recently conceived by Coulson et\ al., builds upon the direct optimization of controllers over input/output pairs drawn from a large dataset. We adopt an…