Related papers: Sound Field Estimation Using Optimal Transport Bar…
In this work, we consider the problem of jointly estimating a set of room impulse responses (RIRs) corresponding to closely spaced microphones. The accurate estimation of RIRs is crucial in acoustic applications such as speech enhancement,…
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability…
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,…
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the…
Time-frequency representations, such as the short-time Fourier transform (STFT), are fundamental tools for analyzing non-stationary signals. However, their ability to achieve sharp localization in both time and frequency is inherently…
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 optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying…
We demonstrate the effectiveness of one of the many multi-tracer analyses enabled by Optimal Transport (OT) reconstruction. Leveraging a semi-discrete OT algorithm, we determine the displacements between initial and observed positions of…
Optimal transport theory has recently reemerged as a vastly resourceful field of mathematics with elegant applications across physics and computer science. Harnessing methods from geometry processing, we report on the efficient…
A framework is proposed that addresses both conditional density estimation and latent variable discovery. The objective function maximizes explanation of variability in the data, achieved through the optimal transport barycenter generalized…
Several fields in science, from genomics to neuroimaging, require monitoring populations (measures) that evolve with time. These complex datasets, describing dynamics with both time and spatial components, pose new challenges for data…
Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…
A weighted, semi-discrete, fast optimal transport (OT) algorithm for reconstructing the Lagrangian positions of proto-halos from their evolved Eulerian positions is presented. The algorithm makes use of a mass estimate of the biased tracers…
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…
Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches…
Few-Shot Remote Sensing Scene Classification (FS-RSSC) presents the challenge of classifying remote sensing images with limited labeled samples. Existing methods typically emphasize single-modal feature learning, neglecting the potential…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…