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18 August 2022
 
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Fast Distribution To Real Regression
Junier B. Oliva ; Willie Neiswanger ; Barnabas Poczos ; Jeff Schneider ; Eric Xing ;
Date 10 Nov 2013
AbstractWe study the problem of distribution to real-value regression, where one aims to regress a mapping $f$ that takes in a distribution input covariate $Pin mathcal{I}$ (for a non-parametric family of distributions $mathcal{I}$) and outputs a real-valued response $Y=f(P) + epsilon$. This setting was recently studied, and a "Kernel-Kernel" estimator was introduced and shown to have a polynomial rate of convergence. However, evaluating a new prediction with the Kernel-Kernel estimator scales as $O(N)$. This causes the difficult situation where a large amount of data may be necessary for a low estimation risk, but the computation cost of estimation becomes unfeasible when the data-set is too large. To this end, we propose the Double-Basis estimator, which looks to alleviate this big data problem in two ways: first, the Double-Basis estimator is shown to have a computation complexity that is independent of the number of of instances $N$ when evaluating new predictions after training; secondly, the Double-Basis estimator is shown to have a fast rate of convergence for a general class of mappings $finmathcal{F}$.
Source arXiv, 1311.2236
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