LWPR Library Documentation


Locally Weighted Projection Regression (LWPR) is an incremental algorithm for learning possibly high-dimensional input-output relations online. It is composed of linear sub-models, the output/responsibility of which is weighted by a locality kernel. The regression parameters of the sub-models are updated using an online formulation of partial least squares (PLS). Each submodel is endowed with a distance metric, which governs its region of validity, and which also gets updated during training. For an in-depth description of the LWPR algorithm, please see [1].

This library started life as a Matlab-only implementation, whose subroutines were then succesively transformed into C. Therefore, the C library is very closely modelled after the LWPR implementation in Matlab. Indeed, most Matlab functions (lwpr_*.m) have a C/MEX-equivalent.

For easy inter-operation, the data format of vectors and matrices used in this library is that of Matlab (or Fortran). That is, vectors are just arrays of doubles. Matrices are also 1-D arrays of doubles, with the elements stored in column-major order. A 2x2 matrix

\[M = \left(\begin{array}{cc} m_{11} & m_{12} \\ m_{21} & m_{22} \end{array}\right)\]

is thus stored as

         double M[4] = {m11,m21,m12,m22};

Apart from the using the C-library stand-alone or from Matlab, there is also a slim C++ wrapper, and a Python module. The C++ wrapper uses STL vectors, and the Python module uses NumPy arrays. LWPR models can be interchanged between all implementations via binary files (platform-dependent, see lwpr_binio.h) or XML files (see lwpr_xml.h).

In order to possibly exploit speedups using SSE2 on newer x86-machines, all internally stored vectors whose length is equal to the input dimensionality are aligned on 16 byte boundaries. This is also the case for the columns of matrices.

[1] Sethu Vijayakumar, Aaron D'Souza and Stefan Schaal, Incremental Online Learning in High Dimensions, Neural Computation, vol. 17, no. 12, pp. 2602-2634 (2005).

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