Regression analysis of distributional data through Multi-Marginal Optimal transport
Systems and Control
2021-06-30 v1 Systems and Control
Abstract
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images, power spectra, point clouds of particles, and so on. The regression seeks a curve in the Wasserstein space that passes closest to the dataset. Our regression problem allows utilizing general curves in a Euclidean setting (linear, quadratic, sinusoidal, and so on), lifted to corresponding measure-valued curves in the Wasserstein space. It can be cast as a multi-marginal optimal transport problem that allows efficient computation. Illustrative academic examples are presented.
Cite
@article{arxiv.2106.15031,
title = {Regression analysis of distributional data through Multi-Marginal Optimal transport},
author = {Amirhossein Karimi and Tryphon T. Georgiou},
journal= {arXiv preprint arXiv:2106.15031},
year = {2021}
}