Distribution to Distribution Regression

Junier Oliva, Barnabas Poczos, Jeff Schneider
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1049-1057, 2013.

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 this Paper

BibTeX
@InProceedings{pmlr-v28-oliva13, title = {Distribution to Distribution Regression}, author = {Oliva, Junier and Poczos, Barnabas and Schneider, Jeff}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {1049--1057}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/oliva13.pdf}, url = {https://proceedings.mlr.press/v28/oliva13.html}, 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.} }
Endnote
%0 Conference Paper %T Distribution to Distribution Regression %A Junier Oliva %A Barnabas Poczos %A Jeff Schneider %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-oliva13 %I PMLR %P 1049--1057 %U https://proceedings.mlr.press/v28/oliva13.html %V 28 %N 3 %X 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.
RIS
TY - CPAPER TI - Distribution to Distribution Regression AU - Junier Oliva AU - Barnabas Poczos AU - Jeff Schneider BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-oliva13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 1049 EP - 1057 L1 - http://proceedings.mlr.press/v28/oliva13.pdf UR - https://proceedings.mlr.press/v28/oliva13.html AB - 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. ER -
APA
Oliva, J., Poczos, B. & Schneider, J.. (2013). Distribution to Distribution Regression. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):1049-1057 Available from https://proceedings.mlr.press/v28/oliva13.html.

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