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arXiv · 1302.0082

Distribution-Free Distribution Regression

Barnabas Poczos·Alessandro Rinaldo·Aarti Singh·Larry Wasserman
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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.

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BibTeXRIS

Barnabas Poczos, Alessandro Rinaldo, Aarti Singh, Larry Wasserman. 2013-02-01. Distribution-Free Distribution Regression. https://arxiv.org/abs/1302.0082

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