Locally Weighted Projection Regression (LWPR)

Locally Weighted Projection Regression (LWPR) is a new algorithm that achieves nonlinear function approximation in high dimensional spaces with redundant  and irrelevant input dimensions. At its core, it uses locally linear models , spanned by a small number of univariate regressions in selected directions in input space. A locally weighted variant of Partial Least Squares (PLS) is employed for doing the dimensionality reduction.  This nonparametric local learning system i) learns rapidly with second order learning methods based on incremental training, ii) uses statistically sound stochastic cross validation to learn iii) adjusts its weighting kernels based on local information only, iv) has a computational complexity that is linear in the number of inputs, and v) can deal with a large number of - possibly redundant - inputs, as shown in evaluations with up to 50  dimensional data sets. To our knowledge, this is the first truly incremental spatially localized learning method to combine all these properties.
[Thanks to: Stefan Schaal, Marc Toussaint, Giorgos Petkos, Narayanan Edakunni for the implementations]

LWPR Users Manual (28 pages)
LWPR Other References References (pdf)
LWPR Matlab Code LWPR test
LWPR C++ Code (Beta) -gzip