Distribution-Free Distribution Regression
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 ) + where f is an unknown regression function and 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 strong distributional assumptions about the error term and covariate P . We prove that when the eective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.
Cite
Text
Póczos et al. "Distribution-Free Distribution Regression." International Conference on Artificial Intelligence and Statistics, 2013.Markdown
[Póczos et al. "Distribution-Free Distribution Regression." International Conference on Artificial Intelligence and Statistics, 2013.](https://mlanthology.org/aistats/2013/poczos2013aistats-distribution/)BibTeX
@inproceedings{poczos2013aistats-distribution,
title = {{Distribution-Free Distribution Regression}},
author = {Póczos, Barnabás and Singh, Aarti and Rinaldo, Alessandro and Wasserman, Larry A.},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2013},
pages = {507-515},
url = {https://mlanthology.org/aistats/2013/poczos2013aistats-distribution/}
}