Locally-weighted regression is a computationally-efficient technique for non-linear regression. However, for high-dimensional data, this technique becomes numerically brittle and computationally too expensive if many local models need to be maintained simultaneously. Thus, local linear dimensionality reduction combined with locally-weighted regression seems to be a promising solution. In this context, we review linear dimensionality-reduction methods, compare their performance on nonparametric locally-linear regression, and discuss their ability to extend to incremental learning. The considered methods belong to the following three groups: (1) reducing dimensionality only on the input data, (2) modeling the joint input-output data distribution, and (3) optimizing the correlation between projection directions and output data. Group 1 contains principal component regression (PCR); group 2 contains principal component analysis (PCA) in joint input and output space, factor analysis, and probabilistic PCA; and group 3 contains reduced rank regression (RRR) and partial least squares (PLS) regression. Among the tested methods, only group 3 managed to achieve robust performance even for a non-optimal number of components (factors or projection directions). In contrast, group 1 and 2 failed for fewer components since these methods rely on the correct estimate of the true intrinsic dimensionality. In group 3, PLS is the only method for which a computationally-efficient incremental implementation exists. Thus, PLS appears to be ideally suited as a building block for a locally-weighted regressor in which projection directions are incrementally added on the fly.
| Author(s): | Hoffman, H. and Schaal, S. and Vijayakumar, S. |
| Book Title: | Neural Processing Letters |
| Year: | 2009 |
| Bibtex Type: | Article (article) |
| URL: | http://www-clmc.usc.edu/publications/H/hoffmann-NPL2009.pdf |
| Cross Ref: | p10336 |
| Electronic Archiving: | grant_archive |
| Note: | clmc |
BibTex
@article{Hoffman_NPL_2009,
title = {Local dimensionality reduction for non-parametric regression},
booktitle = {Neural Processing Letters},
abstract = {Locally-weighted regression is a computationally-efficient technique for non-linear regression.
However, for high-dimensional data, this technique becomes numerically brittle and computationally
too expensive if many local models need to be maintained simultaneously. Thus, local linear
dimensionality reduction combined with locally-weighted regression seems to be a promising solution.
In this context, we review linear dimensionality-reduction methods, compare their performance on nonparametric
locally-linear regression, and discuss their ability to extend to incremental learning. The
considered methods belong to the following three groups: (1) reducing dimensionality only on the input
data, (2) modeling the joint input-output data distribution, and (3) optimizing the correlation between
projection directions and output data. Group 1 contains principal component regression (PCR); group
2 contains principal component analysis (PCA) in joint input and output space, factor analysis, and
probabilistic PCA; and group 3 contains reduced rank regression (RRR) and partial least squares
(PLS) regression. Among the tested methods, only group 3 managed to achieve robust performance
even for a non-optimal number of components (factors or projection directions). In contrast, group 1
and 2 failed for fewer components since these methods rely on the correct estimate of the true intrinsic
dimensionality. In group 3, PLS is the only method for which a computationally-efficient incremental
implementation exists. Thus, PLS appears to be ideally suited as a building block for a locally-weighted
regressor in which projection directions are incrementally added on the fly.},
year = {2009},
note = {clmc},
slug = {hoffman_npl_2009},
author = {Hoffman, H. and Schaal, S. and Vijayakumar, S.},
crossref = {p10336},
url = {http://www-clmc.usc.edu/publications/H/hoffmann-NPL2009.pdf}
}