Related papers: An Optimal Transport-Based Generative Model for Ba…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map.…
We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…
The static optimal transport $(\mathrm{OT})$ problem between Gaussians seeks to recover an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been well studied and applied to a wide variety of tasks. Here we…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
Optimal transport (OT) has recently been shown as a promising criterion for unsupervised restoration when no explicit prior model is available. Despite its theoretical appeal, OT still significantly falls short of supervised methods on…
Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of…
Score-based diffusion models have significantly advanced high-dimensional data generation across various domains, by learning a denoising oracle (or score) from datasets. From a Bayesian perspective, they offer a realistic modeling of data…
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…
Single-cell RNA sequencing provides insights into gene expression at single-cell resolution, yet inferring temporal processes from these static snapshot measurements remains a fundamental challenge. Current approaches utilizing neural…
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…
We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the target. Our approach is an infinite-dimensional Newton…
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…
We investigate the use of entropy-regularized optimal transport (EOT) cost in developing generative models to learn implicit distributions. Two generative models are proposed. One uses EOT cost directly in an one-shot optimization problem…
We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…
Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between…
Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
We introduce a general framework for testing statistical hypotheses for probability measures supported on finite spaces, which is based on optimal transport (OT). These tests are inspired by the analysis of variance (ANOVA) and its…
The field of deep generative modeling is dominated by generative adversarial networks (GANs). However, the training of GANs often lacks stability, fails to converge, and suffers from model collapse. It takes an assortment of tricks to solve…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…