Single index model is a powerful yet simple model, widely used in statistics,
machine learning, and other scientific fields. It models the regression
function as $g()$, where a is an unknown index vector and x are the
features. This paper deals with a nonlinear generalization of this framework to
allow for a regressor that uses multiple index vectors, adapting to local
changes in the responses. To do so we exploit the conditional distribution over
function-driven partitions, and use linear regression to locally estimate index
vectors. We then regress by applying a kNN type estimator that uses a localized
proxy of the geodesic metric. We present theoretical guarantees for estimation
of local index vectors and out-of-sample prediction, and demonstrate the
performance of our method with experiments on synthetic and real-world data
sets, comparing it with state-of-the-art methods.
@article{1902.09024,
author = {Kereta, Zeljko and Klock, Timo and Naumova, Valeriya},
title = {Nonlinear generalization of the single index model},
journal = {arXiv},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/1902.09024}
}
Kereta, Zeljko; Klock, Timo; Naumova, Valeriya. Nonlinear generalization of the single index model. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1902.09024/