edu.udo.cs.myGP
Class Regression

java.lang.Object
  edu.udo.cs.myGP.GPBase
      edu.udo.cs.myGP.Regression

public class Regression
extends GPBase

Gaussian Process Regression. REFERENCES: Lehel Csato. Gaussian Processes --- Iterative Sparse Approximations. PhD thesis, Aston University, Birmingham, UK, March 2002. TODO: - own Matrix implementation with SE-cholesky-decomposition and the ability to constrain matrix operation on sub matrices - CompositeKernel implementation for kernels based on finite basis functions

Version:

$Id: Regression.java,v 1.5 2006/08/03 14:39:35 ingomierswa Exp $

Author:

Piotr Kasprzak

Nested Class Summary

protected class

Regression.Score Used to hold a score value with an associated index

Field Summary

Fields inherited from class edu.udo.cs.myGP.GPBase

model, parameter, problem

Constructor Summary

Regression(RegressionProblem problem, Parameter parameter)
Constructor

Method Summary

private void	deleteBV(Jama.Matrix alpha, Jama.Matrix C, Jama.Matrix Q, double[][] basisVectors, int d, int index) Delete the given BV from the BV set by adjusting the parametrisation of the GP using eqs. (3.19), (3.21) and (3.22): alpha_t+1 = alpha^{(r)} - alpha^star / (c^star + q^star) * (Q^star + C^star) C_t+1 = C^{(r)} + Q^star * Q^star^T / q^star - (Q^star + C^star) * (Q^star + C^star)^T / (q^star + c^star) Q_t+1 = Q^{(r)} - Q^star * Q^star^T / q^star
private java.util.TreeSet	getMinScoresGeometrical(Jama.Matrix alpha, Jama.Matrix C, Jama.Matrix Q, int d) Return the scores of all BVs.
private java.util.TreeSet	getMinScoresKLApprox(Jama.Matrix alpha, Jama.Matrix C, Jama.Matrix Q, int d) Return the scores of all BVs.
Model	learn() The hard work is done here
private double	scalarProduct(double[][] x, double[][] y, int d) Compute the (canonical) scalar product between x and y, using only the first d components of the vectors
private void	swapRowsAndColumns(double[][] A, int i, int j) Swap the rows / columns of a symmetric n x n matrix, which is represented as a double[][].
java.lang.String	toString() Identify the GP

Methods inherited from class edu.udo.cs.myGP.GPBase

getModel

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Regression

public Regression(RegressionProblem problem,
                  Parameter parameter)

Constructor

Method Detail

scalarProduct

private double scalarProduct(double[][] x,
                             double[][] y,
                             int d)
                      throws java.lang.Exception

Compute the (canonical) scalar product between x and y, using only the first d components of the vectors

Throws:

java.lang.Exception

swapRowsAndColumns

private void swapRowsAndColumns(double[][] A,
                                int i,
                                int j)

Swap the rows / columns of a symmetric n x n matrix, which is represented as a double[][].

learn

public Model learn()
            throws java.lang.Exception

The hard work is done here

Specified by:

learn in class GPBase

Throws:

java.lang.Exception

getMinScoresKLApprox

private java.util.TreeSet getMinScoresKLApprox(Jama.Matrix alpha,
                                               Jama.Matrix C,
                                               Jama.Matrix Q,
                                               int d)

Return the scores of all BVs. The score used is a mean based approximation to the true KL-distance between the full GP and the GP without the current BV for which the score is calculated.

getMinScoresGeometrical

private java.util.TreeSet getMinScoresGeometrical(Jama.Matrix alpha,
                                                  Jama.Matrix C,
                                                  Jama.Matrix Q,
                                                  int d)

Return the scores of all BVs. The score used is based on the euclidean distance between the current BV and it's orthogonal projection into the span of all the other BVs. This score is especially important since it can (must!) be used to prevent the kernel gram matrix from becoming too badly conditioned.

deleteBV

private void deleteBV(Jama.Matrix alpha,
                      Jama.Matrix C,
                      Jama.Matrix Q,
                      double[][] basisVectors,
                      int d,
                      int index)

Delete the given BV from the BV set by adjusting the parametrisation of the GP using eqs. (3.19), (3.21) and (3.22): alpha_t+1 = alpha^{(r)} - alpha^star / (c^star + q^star) * (Q^star + C^star) C_t+1 = C^{(r)} + Q^star * Q^star^T / q^star - (Q^star + C^star) * (Q^star + C^star)^T / (q^star + c^star) Q_t+1 = Q^{(r)} - Q^star * Q^star^T / q^star

toString

public java.lang.String toString()

Identify the GP

Overrides:

toString in class java.lang.Object