source: src/main/java/weka/classifiers/functions/GaussianProcesses.java @ 15

/** 
 *     This program is free software; you can redistribute it and/or modify
 *    it under the terms of the GNU General Public License as published by
 *    the Free Software Foundation; either version 2 of the License, or
 *    (at your option) any later version.
 *
 *    This program is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU General Public License for more details.
 *
 *    You should have received a copy of the GNU General Public License
 *    along with this program; if not, write to the Free Software
 *    Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/*
 *    GaussianProcesses.java
 *    Copyright (C) 2005-2009 University of Waikato
 */

package weka.classifiers.functions;


import weka.classifiers.Classifier;
import weka.classifiers.AbstractClassifier;
import weka.classifiers.ConditionalDensityEstimator;
import weka.classifiers.Evaluation;
import weka.classifiers.IntervalEstimator;
import weka.classifiers.functions.supportVector.CachedKernel;
import weka.classifiers.functions.supportVector.Kernel;
import weka.classifiers.functions.supportVector.PolyKernel;
import weka.classifiers.functions.supportVector.RBFKernel;
import weka.core.Capabilities;
import weka.core.Instance;
import weka.core.Instances;
import weka.core.matrix.Matrix;
import weka.core.Option;
import weka.core.OptionHandler;
import weka.core.SelectedTag;
import weka.core.Statistics;
import weka.core.Tag;
import weka.core.TechnicalInformation;
import weka.core.TechnicalInformationHandler;
import weka.core.WeightedInstancesHandler;
import weka.core.Utils;
import weka.core.Capabilities.Capability;
import weka.core.TechnicalInformation.Field;
import weka.core.TechnicalInformation.Type;
import weka.filters.Filter;
import weka.filters.unsupervised.attribute.NominalToBinary;
import weka.filters.unsupervised.attribute.Normalize;
import weka.filters.unsupervised.attribute.ReplaceMissingValues;
import weka.filters.unsupervised.attribute.Standardize;

import java.io.FileReader;
import java.io.Serializable;
import java.util.Enumeration;
import java.util.Vector;

/**
 * <!-- globalinfo-start --> 
 * Implements Gaussian processes for
 * regression without hyperparameter-tuning. To make choosing an
 * appropriate noise level easier, this implementation applies
 * normalization/standardization to the target attribute as well (if
 * normalization/standardizaton is turned on). Missing values
 * are replaced by the global mean/mode. Nominal attributes are
 * converted to binary ones. 
 * <!-- globalinfo-end -->
 * 
 * <!-- technical-bibtex-start --> BibTeX:
 * 
 * <pre>
 *        @misc{Mackay1998,
 *          address = {Dept. of Physics, Cambridge University, UK},
 *          author = {David J.C. Mackay},
 *          title = {Introduction to Gaussian Processes},
 *          year = {1998},
 *          PS = {http://wol.ra.phy.cam.ac.uk/mackay/gpB.ps.gz}
 *       }
 * </pre>
 * 
 * <p/> <!-- technical-bibtex-end -->
 * 
 * <!-- options-start --> Valid options are: <p/>
 * 
 * <pre>
 *       -D
 *        If set, classifier is run in debug mode and
 *        may output additional info to the console
 * </pre>
 * 
 * <pre>
 *       -L &lt;double&gt;
 *        Level of Gaussian Noise. (default 0.1)
 * </pre>
 * 
 * <pre>
 *       -N
 *        Whether to 0=normalize/1=standardize/2=neither. (default 0=normalize)
 * </pre>
 * 
 * <pre>
 *       -K &lt;classname and parameters&gt;
 *        The Kernel to use.
 *        (default: weka.classifiers.functions.supportVector.PolyKernel)
 * </pre>
 * 
 * <pre>
 *       
 *       Options specific to kernel weka.classifiers.functions.supportVector.RBFKernel:
 * </pre>
 * 
 * <pre>
 *       -D
 *        Enables debugging output (if available) to be printed.
 *        (default: off)
 * </pre>
 * 
 * <pre>
 *       -no-checks
 *        Turns off all checks - use with caution!
 *        (default: checks on)
 * </pre>
 * 
 * <pre>
 *       -C &lt;num&gt;
 *        The size of the cache (a prime number).
 *        (default: 250007)
 * </pre>
 * 
 * <pre>
 *       -G &lt;num&gt;
 *        The Gamma parameter.
 *        (default: 0.01)
 * </pre>
 * 
 * <!-- options-end -->
 * 
 * @author Kurt Driessens (kurtd@cs.waikato.ac.nz)
 * @author Remco Bouckaert (remco@cs.waikato.ac.nz)
 * @version $Revision: 5952 $
 */
public class GaussianProcesses extends AbstractClassifier implements OptionHandler, IntervalEstimator,
                                                                     ConditionalDensityEstimator,
                                                                     TechnicalInformationHandler, WeightedInstancesHandler {

  /** for serialization */
  static final long serialVersionUID = -8620066949967678545L;

  /** The filter used to make attributes numeric. */
  protected NominalToBinary m_NominalToBinary;

  /** normalizes the data */
  public static final int FILTER_NORMALIZE = 0;

  /** standardizes the data */
  public static final int FILTER_STANDARDIZE = 1;

  /** no filter */
  public static final int FILTER_NONE = 2;

  /** The filter to apply to the training data */
  public static final Tag[] TAGS_FILTER = { new Tag(FILTER_NORMALIZE, "Normalize training data"),
                                            new Tag(FILTER_STANDARDIZE, "Standardize training data"),
                                            new Tag(FILTER_NONE, "No normalization/standardization"), };

  /** The filter used to standardize/normalize all values. */
  protected Filter m_Filter = null;

  /** Whether to normalize/standardize/neither */
  protected int m_filterType = FILTER_NORMALIZE;

  /** The filter used to get rid of missing values. */
  protected ReplaceMissingValues m_Missing;

  /**
   * Turn off all checks and conversions? Turning them off assumes that data
   * is purely numeric, doesn't contain any missing values, and has a numeric
   * class.
   */
  protected boolean m_checksTurnedOff = false;

  /** Gaussian Noise Value. */
  protected double m_delta = 1;

  /**
   * The parameters of the linear transforamtion realized by the filter on the
   * class attribute
   */
  protected double m_Alin;
  protected double m_Blin;

  /** Kernel to use * */
  protected Kernel m_kernel = new PolyKernel();

  /** The number of training instances */
  protected int m_NumTrain = 0;

  /** The training data. */
  protected double m_avg_target;

  /** (negative) covariance matrix in symmetric matrix representation **/
  public double[][] m_L;

  /** The vector of target values. */
  protected Matrix m_t;

  /**
   * Returns a string describing classifier
   * 
   * @return a description suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String globalInfo() {

    return " Implements Gaussian processes for "
      + "regression without hyperparameter-tuning. To make choosing an "
      + "appropriate noise level easier, this implementation applies "
      + "normalization/standardization to the target attribute as well "
      + "as the other attributes (if "
      + " normalization/standardizaton is turned on). Missing values "
      + "are replaced by the global mean/mode. Nominal attributes are "
      + "converted to binary ones. Note that kernel caching is turned off "
      + "if the kernel used implements CachedKernel.";
  }

  /**
   * Returns an instance of a TechnicalInformation object, containing detailed
   * information about the technical background of this class, e.g., paper
   * reference or book this class is based on.
   * 
   * @return the technical information about this class
   */
  public TechnicalInformation getTechnicalInformation() {
    TechnicalInformation result;

    result = new TechnicalInformation(Type.MISC);
    result.setValue(Field.AUTHOR, "David J.C. Mackay");
    result.setValue(Field.YEAR, "1998");
    result.setValue(Field.TITLE, "Introduction to Gaussian Processes");
    result.setValue(Field.ADDRESS, "Dept. of Physics, Cambridge University, UK");
    result.setValue(Field.PS, "http://wol.ra.phy.cam.ac.uk/mackay/gpB.ps.gz");

    return result;
  }

  /**
   * Returns default capabilities of the classifier.
   * 
   * @return the capabilities of this classifier
   */
  public Capabilities getCapabilities() {
    Capabilities result = getKernel().getCapabilities();
    result.setOwner(this);

    // attribute
    result.enableAllAttributeDependencies();
    // with NominalToBinary we can also handle nominal attributes, but only
    // if the kernel can handle numeric attributes
    if (result.handles(Capability.NUMERIC_ATTRIBUTES))
      result.enable(Capability.NOMINAL_ATTRIBUTES);
    result.enable(Capability.MISSING_VALUES);

    // class
    result.disableAllClasses();
    result.disableAllClassDependencies();
    result.enable(Capability.NUMERIC_CLASS);
    result.enable(Capability.DATE_CLASS);
    result.enable(Capability.MISSING_CLASS_VALUES);

    return result;
  }

  /**
   * Method for building the classifier.
   * 
   * @param insts
   *            the set of training instances
   * @throws Exception
   *             if the classifier can't be built successfully
   */
  public void buildClassifier(Instances insts) throws Exception {

    /* check the set of training instances */
    if (!m_checksTurnedOff) {
      // can classifier handle the data?
      getCapabilities().testWithFail(insts);

      // remove instances with missing class
      insts = new Instances(insts);
      insts.deleteWithMissingClass();
    }

    if (!m_checksTurnedOff) {
      m_Missing = new ReplaceMissingValues();
      m_Missing.setInputFormat(insts);
      insts = Filter.useFilter(insts, m_Missing);
    } else {
      m_Missing = null;
    }

    if (getCapabilities().handles(Capability.NUMERIC_ATTRIBUTES)) {
      boolean onlyNumeric = true;
      if (!m_checksTurnedOff) {
        for (int i = 0; i < insts.numAttributes(); i++) {
          if (i != insts.classIndex()) {
            if (!insts.attribute(i).isNumeric()) {
              onlyNumeric = false;
              break;
            }
          }
        }
      }

      if (!onlyNumeric) {
        m_NominalToBinary = new NominalToBinary();
        m_NominalToBinary.setInputFormat(insts);
        insts = Filter.useFilter(insts, m_NominalToBinary);
      } else {
        m_NominalToBinary = null;
      }
    } else {
      m_NominalToBinary = null;
    }

    if (m_filterType == FILTER_STANDARDIZE) {
      m_Filter = new Standardize();
      ((Standardize)m_Filter).setIgnoreClass(true);
      m_Filter.setInputFormat(insts);
      insts = Filter.useFilter(insts, m_Filter);
    } else if (m_filterType == FILTER_NORMALIZE) {
      m_Filter = new Normalize();
      ((Normalize)m_Filter).setIgnoreClass(true);
      m_Filter.setInputFormat(insts);
      insts = Filter.useFilter(insts, m_Filter);
    } else {
      m_Filter = null;
    }

    m_NumTrain = insts.numInstances();

    // determine which linear transformation has been
    // applied to the class by the filter
    if (m_Filter != null) {
      Instance witness = (Instance) insts.instance(0).copy();
      witness.setValue(insts.classIndex(), 0);
      m_Filter.input(witness);
      m_Filter.batchFinished();
      Instance res = m_Filter.output();
      m_Blin = res.value(insts.classIndex());
      witness.setValue(insts.classIndex(), 1);
      m_Filter.input(witness);
      m_Filter.batchFinished();
      res = m_Filter.output();
      m_Alin = res.value(insts.classIndex()) - m_Blin;
    } else {
      m_Alin = 1.0;
      m_Blin = 0.0;
    }

    // Initialize kernel
    try {
      CachedKernel cachedKernel = (CachedKernel) m_kernel;
      cachedKernel.setCacheSize(0);
    } catch (Exception e) {
      // ignore
    }
    m_kernel.buildKernel(insts);

    // Compute average target value
    double sum = 0.0;
    for (int i = 0; i < insts.numInstances(); i++) {
      sum += insts.instance(i).classValue();
    }
    m_avg_target = sum / insts.numInstances();

    // initialize kernel matrix/covariance matrix
    int n = insts.numInstances();
    m_L = new double[n][];
    for (int i = 0; i < n; i++) {
      m_L[i] = new double[i+1];
    }
    double kv = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < i; j++) {
        kv = m_kernel.eval(i, j, insts.instance(i));
        m_L[i][j] = kv;
      }
      kv = m_kernel.eval(i, i, insts.instance(i));
      m_L[i][i] = kv + m_delta * m_delta;
    }

    // Calculate inverse matrix exploiting symmetry of covariance matrix
    // NB this replaces the kernel matrix with (the negative of) its inverse and does
    // not require any extra memory for a solution matrix
    double [] tmprow = new double [n];
    double tmp2 = 0, tmp = 0;
    for (int i = 0; i < n; i++) {
      tmp = -m_L[i][i];
      m_L[i][i] = 1.0 / tmp;
      for (int j = 0; j < n; j++) {
        if (j != i) {
          if (j < i) {
            tmprow[j] = m_L[i][j]; 
            m_L[i][j] /= tmp;
            tmp2 = m_L[i][j];
            m_L[j][j] += tmp2 * tmp2 * tmp;
          } else if (j > i) {
            tmprow[j] = m_L[j][i]; 
            m_L[j][i] /= tmp;
            tmp2 = m_L[j][i];
            m_L[j][j] += tmp2 * tmp2 * tmp;
          }
        }
      }

      for (int j = 0; j < n; j++) {
        if (j != i) {
          if (i < j) {
            for (int k = 0; k < i; k++) {
              m_L[j][k] += tmprow[j] * m_L[i][k];
            }
          } else {
            for (int k = 0; k < j; k++) {
              m_L[j][k] += tmprow[j] * m_L[i][k];
            }
                                                
          }
          for (int k = i + 1; k < j; k++) {
            m_L[j][k] += tmprow[j] * m_L[k][i];
          }
        }
      }
    }
                
    m_t = new Matrix(insts.numInstances(), 1);          
    double [] tt = new double[n]; 
    for (int i = 0; i < n; i++) {
      tt[i] = insts.instance(i).classValue() - m_avg_target;
    }

    // calculate m_t = tt . m_L
    for (int i = 0; i < n; i++) {
      double s = 0;
      for (int k = 0; k < i; k++) {
        s -= m_L[i][k] * tt[k];
      }
      for (int k = i; k < n; k++) {
        s -= m_L[k][i] * tt[k];
      }
      m_t.set(i, 0, s);
    }
                
  } // buildClassifier

  /**
   * Classifies a given instance.
   * 
   * @param inst
   *            the instance to be classified
   * @return the classification
   * @throws Exception
   *             if instance could not be classified successfully
   */
  public double classifyInstance(Instance inst) throws Exception {
                
    // Filter instance
    inst = filterInstance(inst);

    // Build K vector
    Matrix k = new Matrix(m_NumTrain, 1);
    for (int i = 0; i < m_NumTrain; i++) {
      k.set(i, 0, m_kernel.eval(-1, i, inst));
    }

    double result = k.transpose().times(m_t).get(0, 0) + m_avg_target;
    result = (result - m_Blin) / m_Alin;

    return result;

  }

  /**
   * Filters an instance.
   */
  protected Instance filterInstance(Instance inst) throws Exception {

    if (!m_checksTurnedOff) {
      m_Missing.input(inst);
      m_Missing.batchFinished();
      inst = m_Missing.output();
    }

    if (m_NominalToBinary != null) {
      m_NominalToBinary.input(inst);
      m_NominalToBinary.batchFinished();
      inst = m_NominalToBinary.output();
    }

    if (m_Filter != null) {
      m_Filter.input(inst);
      m_Filter.batchFinished();
      inst = m_Filter.output();
    }
    return inst;
  }

  /**
   * Computes standard deviation for given instance, without
   * transforming target back into original space.
   */
  protected double computeStdDev(Instance inst, Matrix k) throws Exception {

    double kappa = m_kernel.eval(-1, -1, inst) + m_delta * m_delta;

    double s = 0;
    int n = m_L.length;
    for (int i = 0; i < n; i++) {
      double t = 0;
      for (int j = 0; j < n; j++) {
        t -= k.get(j,0) * (i>j? m_L[i][j] : m_L[j][i]);
      }                 
      s += t * k.get(i,0);
    }
                
    double sigma = m_delta;
    if (kappa > s) {
      sigma = Math.sqrt(kappa - s);
    }

    return sigma;
  }

  /**
   * Computes a prediction interval for the given instance and confidence
   * level.
   * 
   * @param inst
   *            the instance to make the prediction for
   * @param confidenceLevel
   *            the percentage of cases the interval should cover
   * @return a 1*2 array that contains the boundaries of the interval
   * @throws Exception
   *             if interval could not be estimated successfully
   */
  public double[][] predictIntervals(Instance inst, double confidenceLevel) throws Exception {

    inst = filterInstance(inst);

    // Build K vector (and Kappa)
    Matrix k = new Matrix(m_NumTrain, 1);
    for (int i = 0; i < m_NumTrain; i++) {
      k.set(i, 0, m_kernel.eval(-1, i, inst));
    }

    double estimate = k.transpose().times(m_t).get(0, 0) + m_avg_target;

    double sigma = computeStdDev(inst, k);

    confidenceLevel = 1.0 - ((1.0 - confidenceLevel) / 2.0);

    double z = Statistics.normalInverse(confidenceLevel);

    double[][] interval = new double[1][2];

    interval[0][0] = estimate - z * sigma;
    interval[0][1] = estimate + z * sigma;

    interval[0][0] = (interval[0][0] - m_Blin) / m_Alin;
    interval[0][1] = (interval[0][1] - m_Blin) / m_Alin;
                
    return interval;

  }

  /**
   * Gives standard deviation of the prediction at the given instance.
   * 
   * @param inst
   *            the instance to get the standard deviation for
   * @return the standard deviation
   * @throws Exception
   *             if computation fails
   */
  public double getStandardDeviation(Instance inst) throws Exception {

    inst = filterInstance(inst);

    // Build K vector (and Kappa)
    Matrix k = new Matrix(m_NumTrain, 1);
    for (int i = 0; i < m_NumTrain; i++) {
      k.set(i, 0, m_kernel.eval(-1, i, inst));
    }

    return computeStdDev(inst, k) / m_Alin;
  }

  /**
   * Returns natural logarithm of density estimate for given value based on given instance.
   *   
   * @param instance the instance to make the prediction for.
   * @param value the value to make the prediction for.
   * @return the natural logarithm of the density estimate
   * @exception Exception if the density cannot be computed
   */
  public double logDensity(Instance inst, double value) throws Exception {
    
    inst = filterInstance(inst);

    // Build K vector (and Kappa)
    Matrix k = new Matrix(m_NumTrain, 1);
    for (int i = 0; i < m_NumTrain; i++) {
      k.set(i, 0, m_kernel.eval(-1, i, inst));
    }
    
    double estimate = k.transpose().times(m_t).get(0, 0) + m_avg_target;

    double sigma = computeStdDev(inst, k);
    
    // transform to GP space
    value = value * m_Alin + m_Blin;
    // center around estimate
    value = value - estimate;
    double z = -Math.log(sigma * Math.sqrt(2 * Math.PI)) 
      - value * value /(2.0*sigma*sigma); 
    
    return z + Math.log(m_Alin);
  }
  
  /**
   * Returns an enumeration describing the available options.
   * 
   * @return an enumeration of all the available options.
   */
  public Enumeration listOptions() {

    Vector<Option> result = new Vector<Option>();

    Enumeration enm = super.listOptions();
    while (enm.hasMoreElements())
      result.addElement((Option)enm.nextElement());

    result.addElement(new Option("\tLevel of Gaussian Noise wrt transformed target." + " (default 1)", "L", 1, "-L <double>"));

    result.addElement(new Option("\tWhether to 0=normalize/1=standardize/2=neither. " + "(default 0=normalize)",
                                 "N", 1, "-N"));

    result.addElement(new Option("\tThe Kernel to use.\n"
                                 + "\t(default: weka.classifiers.functions.supportVector.PolyKernel)", "K", 1,
                                 "-K <classname and parameters>"));

    result.addElement(new Option("", "", 0, "\nOptions specific to kernel " + getKernel().getClass().getName()
                                 + ":"));

    enm = ((OptionHandler) getKernel()).listOptions();
    while (enm.hasMoreElements())
      result.addElement((Option)enm.nextElement());

    return result.elements();
  }

  /**
   * Parses a given list of options. <p/>
   * 
   * <!-- options-start --> Valid options are: <p/>
   * 
   * <pre>
   *       -D
   *        If set, classifier is run in debug mode and
   *        may output additional info to the console
   * </pre>
   * 
   * <pre>
   *       -L &lt;double&gt;
   *        Level of Gaussian Noise. (default 0.1)
   * </pre>
   * 
   * <pre>
   *       -M &lt;double&gt;
   *        Level of Gaussian Noise for the class. (default 0.1)
   * </pre>
   * 
   * <pre>
   *       -N
   *        Whether to 0=normalize/1=standardize/2=neither. (default 0=normalize)
   * </pre>
   * 
   * <pre>
   *       -K &lt;classname and parameters&gt;
   *        The Kernel to use.
   *        (default: weka.classifiers.functions.supportVector.PolyKernel)
   * </pre>
   * 
   * <pre>
   *       
   *       Options specific to kernel weka.classifiers.functions.supportVector.RBFKernel:
   * </pre>
   * 
   * <pre>
   *       -D
   *        Enables debugging output (if available) to be printed.
   *        (default: off)
   * </pre>
   * 
   * <pre>
   *       -no-checks
   *        Turns off all checks - use with caution!
   *        (default: checks on)
   * </pre>
   * 
   * <pre>
   *       -C &lt;num&gt;
   *        The size of the cache (a prime number).
   *        (default: 250007)
   * </pre>
   * 
   * <pre>
   *       -G &lt;num&gt;
   *        The Gamma parameter.
   *        (default: 0.01)
   * </pre>
   * 
   * <!-- options-end -->
   * 
   * @param options
   *            the list of options as an array of strings
   * @throws Exception
   *             if an option is not supported
   */
  public void setOptions(String[] options) throws Exception {
    String tmpStr;
    String[] tmpOptions;

    tmpStr = Utils.getOption('L', options);
    if (tmpStr.length() != 0)
      setNoise(Double.parseDouble(tmpStr));
    else
      setNoise(1);
                
    tmpStr = Utils.getOption('N', options);
    if (tmpStr.length() != 0)
      setFilterType(new SelectedTag(Integer.parseInt(tmpStr), TAGS_FILTER));
    else
      setFilterType(new SelectedTag(FILTER_NORMALIZE, TAGS_FILTER));

    tmpStr = Utils.getOption('K', options);
    tmpOptions = Utils.splitOptions(tmpStr);
    if (tmpOptions.length != 0) {
      tmpStr = tmpOptions[0];
      tmpOptions[0] = "";
      setKernel(Kernel.forName(tmpStr, tmpOptions));
    }

    super.setOptions(options);
  }

  /**
   * Gets the current settings of the classifier.
   * 
   * @return an array of strings suitable for passing to setOptions
   */
  public String[] getOptions() {
    int i;
    Vector<String> result;
    String[] options;

    result = new Vector<String>();
    options = super.getOptions();
    for (i = 0; i < options.length; i++)
      result.addElement(options[i]);

    result.addElement("-L");
    result.addElement("" + getNoise());

    result.addElement("-N");
    result.addElement("" + m_filterType);

    result.addElement("-K");
    result.addElement("" + m_kernel.getClass().getName() + " " + Utils.joinOptions(m_kernel.getOptions()));

    return (String[]) result.toArray(new String[result.size()]);
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String kernelTipText() {
    return "The kernel to use.";
  }

  /**
   * Gets the kernel to use.
   * 
   * @return the kernel
   */
  public Kernel getKernel() {
    return m_kernel;
  }

  /**
   * Sets the kernel to use.
   * 
   * @param value
   *            the new kernel
   */
  public void setKernel(Kernel value) {
    m_kernel = value;
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String filterTypeTipText() {
    return "Determines how/if the data will be transformed.";
  }

  /**
   * Gets how the training data will be transformed. Will be one of
   * FILTER_NORMALIZE, FILTER_STANDARDIZE, FILTER_NONE.
   * 
   * @return the filtering mode
   */
  public SelectedTag getFilterType() {

    return new SelectedTag(m_filterType, TAGS_FILTER);
  }

  /**
   * Sets how the training data will be transformed. Should be one of
   * FILTER_NORMALIZE, FILTER_STANDARDIZE, FILTER_NONE.
   * 
   * @param newType
   *            the new filtering mode
   */
  public void setFilterType(SelectedTag newType) {

    if (newType.getTags() == TAGS_FILTER) {
      m_filterType = newType.getSelectedTag().getID();
    }
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String noiseTipText() {
    return "The level of Gaussian Noise (added to the diagonal of the Covariance Matrix), after the " +
      "target has been normalized/standardized/left unchanged).";
  }

  /**
   * Get the value of noise.
   * 
   * @return Value of noise.
   */
  public double getNoise() {
    return m_delta;
  }

  /**
   * Set the level of Gaussian Noise.
   * 
   * @param v
   *            Value to assign to noise.
   */
  public void setNoise(double v) {
    m_delta = v;
  }

  /**
   * Prints out the classifier.
   * 
   * @return a description of the classifier as a string
   */
  public String toString() {

    StringBuffer text = new StringBuffer();

    if (m_t == null)
      return "Gaussian Processes: No model built yet.";

    try {

      text.append("Gaussian Processes\n\n");
      text.append("Kernel used:\n  " + m_kernel.toString() + "\n\n");

      text.append("All values shown based on: " + 
                  TAGS_FILTER[m_filterType].getReadable() + "\n\n");


      text.append("Average Target Value : " + m_avg_target + "\n");

      text.append("Inverted Covariance Matrix:\n");
      double min = -m_L[0][0];
      double max = -m_L[0][0];
      for (int i = 0; i < m_NumTrain; i++)
        for (int j = 0; j <= i; j++) {
          if (-m_L[i][j] < min)
            min = -m_L[i][j];
          else if (-m_L[i][j] > max)
            max = -m_L[i][j];
        }
      text.append("    Lowest Value = " + min + "\n");
      text.append("    Highest Value = " + max + "\n");
      text.append("Inverted Covariance Matrix * Target-value Vector:\n");
      min = m_t.get(0, 0);
      max = m_t.get(0, 0);
      for (int i = 0; i < m_NumTrain; i++) {
        if (m_t.get(i, 0) < min)
          min = m_t.get(i, 0);
        else if (m_t.get(i, 0) > max)
          max = m_t.get(i, 0);
      }
      text.append("    Lowest Value = " + min + "\n");
      text.append("    Highest Value = " + max + "\n \n");

    } catch (Exception e) {
      return "Can't print the classifier.";
    }

    return text.toString();
  }

  /**
   * Main method for testing this class.
   * 
   * @param argv
   *            the commandline parameters
   */
  public static void main(String[] argv) {

    runClassifier(new GaussianProcesses(), argv);
  }
}