Related papers: Learning Generative Models with Sinkhorn Divergenc…
To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
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…
This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach…
Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
Physics phenomena are often described by ordinary and/or partial differential equations (ODEs/PDEs), and solved analytically or numerically. Unfortunately, many real-world systems are described only approximately with missing or unknown…
Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…
Learning meaningful representations of complex objects that can be seen through multiple ($k\geq 3$) views or modalities is a core task in machine learning. Existing methods use losses originally intended for paired views, and extend them…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a…
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…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…
Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…
Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$…
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…