Distribution-on-distribution regression via optimal transport maps

Upper and lower risk bounds for estimating the Wasserstein barycenter of random measures on the real line

Laya Ghodrati and Victor M Panaretos

Biometrika, 2022, vol. 109, issue 4, 957-974

Abstract: SummaryWe present a framework for performing regression when both covariate and response are probability distributions on a compact interval. Our regression model is based on the theory of optimal transportation, and links the conditional Fréchet mean of the response to the covariate via an optimal transport map. We define a Fréchet-least-squares estimator of this regression map, and establish its consistency and rate of convergence to the true map, under both full and partial observations of the regression pairs. Computation of the estimator is shown to reduce to a standard convex optimization problem, and thus our regression model can be implemented with ease. We illustrate our methodology using real and simulated data.

Keywords: Functional regression; Optimal transportation; Random measure; Wasserstein metric (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (8)

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