Uncoupled isotonic regression via minimum Wasserstein deconvolution
Name
1806.10648.pdf
Description
Accepted version
Size
475.36 KB
Format
Adobe PDF
Checksum (MD5)
29592f7b7994b671205471b4a4ef7f0f
Author(s)
Rigollet, Philippe
Weed, Jonathan
Date Issued
April 2019
Journal
Information and Inference
Publisher
Oxford University Press (OUP)
Citation
Rigollet, Philippe and Jonathan Weed. “Uncoupled isotonic regression via minimum Wasserstein deconvolution.” Information and Inference, 8, 4 (April 2019): 691–717 © 2019 The Author(s)
Version
Author's final manuscript
Abstract
Isotonic regression is a standard problem in shape-constrainedestimation where the goal is to estimate an unknown nondecreasingregression functionffrom independent pairs (xi,yi) whereE[yi] =f(xi),i= 1,...n. While this problem is well understood both statis-tically and computationally, much less is known about its uncoupledcounterpart where one is given only the unordered sets{x1,...,xn}and{y1,...,yn}. In this work, we leverage tools from optimal trans-port theory to derive minimax rates under weak moments conditionsonyiand to give an efficient algorithm achieving optimal rates. Bothupper and lower bounds employ moment-matching arguments that arealso pertinent to learning mixtures of distributions and deconvolution.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1093/IMAIAI/IAZ006
