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Fast Distribution To Real Regression | | Junier B. Oliva
; Willie Neiswanger
; Barnabas Poczos
; Jeff Schneider
; Eric Xing
; | | Date: |
10 Nov 2013 | | Abstract: | We 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 | | Services: | Forum | Review | PDF | Favorites | |
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