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Title: Uncoupled isotonic regression via minimum Wasserstein deconvolution

Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown non-decreasing regression function $f$ from independent pairs $(x_i, y_i)$ where ${\mathbb{E}}[y_i]=f(x_i), i=1, \ldots n$. While this problem is well understood both statistically and computationally, much less is known about its uncoupled counterpart, where one is given only the unordered sets $\{x_1, \ldots , x_n\}$ and $\{y_1, \ldots , y_n\}$. In this work, we leverage tools from optimal transport theory to derive minimax rates under weak moments conditions on $y_i$ and to give an efficient algorithm achieving optimal rates. Both upper and lower bounds employ moment-matching arguments that are also pertinent to learning mixtures of distributions and deconvolution.

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Award ID(s):
1712596 1838071
Author(s) / Creator(s):
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Information and Inference: A Journal of the IMA
Page Range / eLocation ID:
p. 691-717
Medium: X
Sponsoring Org:
National Science Foundation
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