Distribution-on-Distribution Regression via Optimal Transport Maps
By Laya Ghodrati, Victor M. Panaretos. Biometrika, 2021
56 citations recorded by the source corpus.
We 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 observation 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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a0cf6d0161a46aea19170eaded516c005644fd18
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In Statistics and Probability
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Citations in the corpus
- Plugin estimation of smooth optimal transport maps (2021, background): “They have also found recent uses in distributional regression (Ghodrati and Panaretos, 2021), generative modeling (Finlay et al.”