Distribution-Free Distribution Regression
Machine Learning
2013-02-04 v1 Machine Learning
Statistics Theory
Statistics Theory
Abstract
`Distribution regression' refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + mu where f is an unknown regression function and mu is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P. In this paper we develop theory and methods for distribution-free versions of distribution regression. This means that we do not make distributional assumptions about the error term mu and covariate P. We prove that when the effective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.
Cite
@article{arxiv.1302.0082,
title = {Distribution-Free Distribution Regression},
author = {Barnabas Poczos and Alessandro Rinaldo and Aarti Singh and Larry Wasserman},
journal= {arXiv preprint arXiv:1302.0082},
year = {2013}
}