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2018 Slice inverse regression with score functions
Dmitry Babichev, Francis Bach
Electron. J. Statist. 12(1): 1507-1543 (2018). DOI: 10.1214/18-EJS1428


We consider non-linear regression problems where we assume that the response depends non-linearly on a linear projection of the covariates. We propose score function extensions to sliced inverse regression problems, both for the first- order and second-order score functions. We show that they provably improve estimation in the population case over the non-sliced versions and we study finite sample estimators and their consistency given the exact score functions. We also propose to learn the score function as well, in two steps, i.e., first learning the score function and then learning the effective dimension reduction space, or directly, by solving a convex optimization problem regularized by the nuclear norm. We illustrate our results on a series of experiments.


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Dmitry Babichev. Francis Bach. "Slice inverse regression with score functions." Electron. J. Statist. 12 (1) 1507 - 1543, 2018.


Received: 1 October 2016; Published: 2018
First available in Project Euclid: 21 May 2018

zbMATH: 06875407
MathSciNet: MR3804844
Digital Object Identifier: 10.1214/18-EJS1428

Primary: 62G20 , 62J02
Secondary: 62G05

Keywords: Dimension reduction , multi-index model , non-linear regression , slice inverse regression


Vol.12 • No. 1 • 2018
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