content: /** 
   *     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: 6984 $
   */
  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);
    }
  }
  