Related papers: Non-Euclidean Sliced Optimal Transport Sampling
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…
Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance…
Selecting prototypical examples from a source distribution to represent a target data distribution is a fundamental problem in machine learning. Existing subset selection methods often rely on implicit importance scores, which can be skewed…
Empirical optimal transport (OT) plans and distances provide effective tools to compare and statistically match probability measures defined on a given ground space. Fundamental to this are distributional limit laws and we derive a central…
We introduce Guided Harmonic Path-Integral Diffusion (GH-PID), a linearly-solvable framework for guided Stochastic Optimal Transport (SOT) with a hard terminal distribution and soft, application-driven path costs. A low-dimensional guidance…
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…
In computer vision and machine learning for geographic data, out-of-domain generalization is a pervasive challenge, arising from uneven global data coverage and distribution shifts across geographic regions. Though models are frequently…
We address the convergence problem in learning the Optimal Transport (OT) map, where the OT Map refers to a map from one distribution to another while minimizing the transport cost. Semi-dual Neural OT, a widely used approach for learning…
The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization. This paper provides convergence guarantees for…
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,…
We propose a new colour transfer method with Optimal Transport (OT) to transfer the colour of a sourceimage to match the colour of a target image of the same scene that may exhibit large motion changes betweenimages. By definition OT does…
Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on…
This paper addresses the problem of estimating entropy-regularized optimal transport (EOT) maps with squared-Euclidean cost between source and target measures that are subGaussian. In the case that the target measure is compactly supported…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
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…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
We present a simple, efficient and robust approach to improve cosmological redshift measurements. The method is based on the presence of a reference sample for which a precise redshift number distribution (dN/dz) can be obtained for…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
Entropic optimal transport (EOT) presents an effective and computationally viable alternative to unregularized optimal transport (OT), offering diverse applications for large-scale data analysis. In this work, we derive novel statistical…