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Local dimensionality reduction for non-parametric regression




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

Department(s): Autonome Motorik
Bibtex Type: Article (article)

Cross Ref: p10336
Note: clmc
URL: http://www-clmc.usc.edu/publications/H/hoffmann-NPL2009.pdf


  title = {Local dimensionality reduction for non-parametric regression},
  author = {Hoffman, H. and Schaal, S. and Vijayakumar, S.},
  booktitle = {Neural Processing Letters},
  year = {2009},
  note = {clmc},
  crossref = {p10336},
  url = {http://www-clmc.usc.edu/publications/H/hoffmann-NPL2009.pdf}