相关论文: Low-Rank Optimal Transport through Factor Relaxati…
In this article we revisit the weak optimal transport (WOT) problem, introduced by Gozlan, Roberto, Samson and Tetali (2017). We work on the real line, with barycentric cost functions, and as our first result give the following…
Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios,…
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
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.…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets -- tasks ubiquitous in data science and machine learning. Because…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…
The ability to align points across two related yet incomparable point clouds (e.g. living in different spaces) plays an important role in machine learning. The Gromov-Wasserstein (GW) framework provides an increasingly popular answer to…
The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability…
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…
Computationally solving multi-marginal optimal transport (MOT) with squared Euclidean costs for $N$ discrete probability measures has recently attracted considerable attention, in part because of the correspondence of its solutions with…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…
Selecting input features of top relevance has become a popular method for building self-explaining models. In this work, we extend this selective rationalization approach to text matching, where the goal is to jointly select and align text…
Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which…
Speculative sampling reduces the latency of autoregressive decoding for target model LLMs without sacrificing inference quality, by using a cheap draft model to suggest a candidate token and a verification criterion to accept or resample…
We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…
The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attention and played essential roles in many modern applications.…
Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured. In this paper,…