A New Algorithm for Estimating the Effective Dimension-Reduction Subspace
Abstract
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR subspace is proposed. Many methods for estimating the EDR subspace perform principal component analysis on a family of vectors, say β1,...,βL, nearly lying in the EDR subspace. This is in particular the case for the structure-adaptive approach proposed by Hristache et al. (2001a). In the present work, we propose to estimate the projector onto the EDR subspace by the solution to the optimization problem
Cite
Text
Dalalyan et al. "A New Algorithm for Estimating the Effective Dimension-Reduction Subspace." Journal of Machine Learning Research, 2008.Markdown
[Dalalyan et al. "A New Algorithm for Estimating the Effective Dimension-Reduction Subspace." Journal of Machine Learning Research, 2008.](https://mlanthology.org/jmlr/2008/dalalyan2008jmlr-new/)BibTeX
@article{dalalyan2008jmlr-new,
title = {{A New Algorithm for Estimating the Effective Dimension-Reduction Subspace}},
author = {Dalalyan, Arnak S. and Juditsky, Anatoly and Spokoiny, Vladimir},
journal = {Journal of Machine Learning Research},
year = {2008},
pages = {1647-1678},
volume = {9},
url = {https://mlanthology.org/jmlr/2008/dalalyan2008jmlr-new/}
}