Distribution-Free Distribution Regression

Barnabas Poczos, Aarti Singh, Alessandro Rinaldo, Larry Wasserman
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:507-515, 2013.

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) + e where f is an unknown regression function and e 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 e 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 this Paper

BibTeX
@InProceedings{pmlr-v31-poczos13a, title = {Distribution-Free Distribution Regression}, author = {Poczos, Barnabas and Singh, Aarti and Rinaldo, Alessandro and Wasserman, Larry}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {507--515}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/poczos13a.pdf}, url = {https://proceedings.mlr.press/v31/poczos13a.html}, 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) + e where f is an unknown regression function and e 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 e 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.} }
Endnote
%0 Conference Paper %T Distribution-Free Distribution Regression %A Barnabas Poczos %A Aarti Singh %A Alessandro Rinaldo %A Larry Wasserman %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-poczos13a %I PMLR %P 507--515 %U https://proceedings.mlr.press/v31/poczos13a.html %V 31 %X 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) + e where f is an unknown regression function and e 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 e 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.
RIS
TY - CPAPER TI - Distribution-Free Distribution Regression AU - Barnabas Poczos AU - Aarti Singh AU - Alessandro Rinaldo AU - Larry Wasserman BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-poczos13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 507 EP - 515 L1 - http://proceedings.mlr.press/v31/poczos13a.pdf UR - https://proceedings.mlr.press/v31/poczos13a.html AB - 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) + e where f is an unknown regression function and e 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 e 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. ER -
APA
Poczos, B., Singh, A., Rinaldo, A. & Wasserman, L.. (2013). Distribution-Free Distribution Regression. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:507-515 Available from https://proceedings.mlr.press/v31/poczos13a.html.

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