Distribution to Distribution Regression
Abstract
We analyze ’Distribution to Distribution regression’ where one is regressing a mapping where both the covariate (inputs) and response (outputs) are distributions. No parameters on the input or output distributions are assumed, nor are any strong assumptions made on the measure from which input distributions are drawn from. We develop an estimator and derive an upper bound for the L2 risk; also, we show that when the effective dimension is small enough (as measured by the doubling dimension), then the risk converges to zero with a polynomial rate.
Cite
Text
Oliva et al. "Distribution to Distribution Regression." International Conference on Machine Learning, 2013.Markdown
[Oliva et al. "Distribution to Distribution Regression." International Conference on Machine Learning, 2013.](https://mlanthology.org/icml/2013/oliva2013icml-distribution/)BibTeX
@inproceedings{oliva2013icml-distribution,
title = {{Distribution to Distribution Regression}},
author = {Oliva, Junier and Poczos, Barnabas and Schneider, Jeff},
booktitle = {International Conference on Machine Learning},
year = {2013},
pages = {1049-1057},
volume = {28},
url = {https://mlanthology.org/icml/2013/oliva2013icml-distribution/}
}