* @misc{Webb2002,
* address = {School of Computer Science and Software Engineering, Victoria, Australia},
* author = {Geoffrey I. Webb and Paul Conilione},
* institution = {Monash University},
* title = {Estimating bias and variance from data},
* year = {2002},
* PDF = {http://www.csse.monash.edu.au/\~webb/Files/WebbConilione04.pdf}
* }
*
* @inproceedings{Kohavi1996,
* author = {Ron Kohavi and David H. Wolpert},
* booktitle = {Machine Learning: Proceedings of the Thirteenth International Conference},
* editor = {Lorenza Saitta},
* pages = {275-283},
* publisher = {Morgan Kaufmann},
* title = {Bias Plus Variance Decomposition for Zero-One Loss Functions},
* year = {1996},
* PS = {http://robotics.stanford.edu/\~ronnyk/biasVar.ps}
* }
*
* @article{Webb2000,
* author = {Geoffrey I. Webb},
* journal = {Machine Learning},
* number = {2},
* pages = {159-196},
* title = {MultiBoosting: A Technique for Combining Boosting and Wagging},
* volume = {40},
* year = {2000}
* }
*
*
*
* Valid options are:
*
* -c <class index> * The index of the class attribute. * (default last)* *
-D * Turn on debugging output.* *
-l <num> * The number of times each instance is classified. * (default 10)* *
-p <proportion of objects in common> * The average proportion of instances common between any two training sets* *
-s <seed> * The random number seed used.* *
-t <name of arff file> * The name of the arff file used for the decomposition.* *
-T <number of instances in training set> * The number of instances in the training set.* *
-W <classifier class name> * Full class name of the learner used in the decomposition. * eg: weka.classifiers.bayes.NaiveBayes* *
* Options specific to learner weka.classifiers.rules.ZeroR: ** *
-D * If set, classifier is run in debug mode and * may output additional info to the console* * * Options after -- are passed to the designated sub-learner.
*
* @author Paul Conilione (paulc4321@yahoo.com.au)
* @version $Revision: 6041 $
*/
public class BVDecomposeSegCVSub
implements OptionHandler, TechnicalInformationHandler, RevisionHandler {
/** Debugging mode, gives extra output if true. */
protected boolean m_Debug;
/** An instantiated base classifier used for getting and testing options. */
protected Classifier m_Classifier = new weka.classifiers.rules.ZeroR();
/** The options to be passed to the base classifier. */
protected String [] m_ClassifierOptions;
/** The number of times an instance is classified*/
protected int m_ClassifyIterations;
/** The name of the data file used for the decomposition */
protected String m_DataFileName;
/** The index of the class attribute */
protected int m_ClassIndex = -1;
/** The random number seed */
protected int m_Seed = 1;
/** The calculated Kohavi & Wolpert bias (squared) */
protected double m_KWBias;
/** The calculated Kohavi & Wolpert variance */
protected double m_KWVariance;
/** The calculated Kohavi & Wolpert sigma */
protected double m_KWSigma;
/** The calculated Webb bias */
protected double m_WBias;
/** The calculated Webb variance */
protected double m_WVariance;
/** The error rate */
protected double m_Error;
/** The training set size */
protected int m_TrainSize;
/** Proportion of instances common between any two training sets. */
protected double m_P;
/**
* Returns a string describing this object
* @return a description of the classifier suitable for
* displaying in the explorer/experimenter gui
*/
public String globalInfo() {
return
"This class performs Bias-Variance decomposion on any classifier using the "
+ "sub-sampled cross-validation procedure as specified in (1).\n"
+ "The Kohavi and Wolpert definition of bias and variance is specified in (2).\n"
+ "The Webb definition of bias and variance is specified in (3).\n\n"
+ getTechnicalInformation().toString();
}
/**
* 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;
TechnicalInformation additional;
result = new TechnicalInformation(Type.MISC);
result.setValue(Field.AUTHOR, "Geoffrey I. Webb and Paul Conilione");
result.setValue(Field.YEAR, "2002");
result.setValue(Field.TITLE, "Estimating bias and variance from data");
result.setValue(Field.INSTITUTION, "Monash University");
result.setValue(Field.ADDRESS, "School of Computer Science and Software Engineering, Victoria, Australia");
result.setValue(Field.PDF, "http://www.csse.monash.edu.au/~webb/Files/WebbConilione04.pdf");
additional = result.add(Type.INPROCEEDINGS);
additional.setValue(Field.AUTHOR, "Ron Kohavi and David H. Wolpert");
additional.setValue(Field.YEAR, "1996");
additional.setValue(Field.TITLE, "Bias Plus Variance Decomposition for Zero-One Loss Functions");
additional.setValue(Field.BOOKTITLE, "Machine Learning: Proceedings of the Thirteenth International Conference");
additional.setValue(Field.PUBLISHER, "Morgan Kaufmann");
additional.setValue(Field.EDITOR, "Lorenza Saitta");
additional.setValue(Field.PAGES, "275-283");
additional.setValue(Field.PS, "http://robotics.stanford.edu/~ronnyk/biasVar.ps");
additional = result.add(Type.ARTICLE);
additional.setValue(Field.AUTHOR, "Geoffrey I. Webb");
additional.setValue(Field.YEAR, "2000");
additional.setValue(Field.TITLE, "MultiBoosting: A Technique for Combining Boosting and Wagging");
additional.setValue(Field.JOURNAL, "Machine Learning");
additional.setValue(Field.VOLUME, "40");
additional.setValue(Field.NUMBER, "2");
additional.setValue(Field.PAGES, "159-196");
return result;
}
/**
* Returns an enumeration describing the available options.
*
* @return an enumeration of all the available options.
*/
public Enumeration listOptions() {
Vector newVector = new Vector(8);
newVector.addElement(new Option(
"\tThe index of the class attribute.\n"+
"\t(default last)",
"c", 1, "-c
*
* For example, instance 'x' may be classified out of 3 classes y = {1, 2, 3},
* so if x is classified 10 times, and is classified as follows, '1' = 2 times, '2' = 5 times
* and '3' = 3 times. Then the central tendency is '2'.
*
* However, it is important to note that this method returns a list of all classes
* that have the highest number of classifications.
*
* In cases where there are several classes with the largest number of classifications, then
* all of these classes are returned. For example if 'x' is classified '1' = 4 times,
* '2' = 4 times and '3' = 2 times. Then '1' and '2' are returned.
*
* @param predProbs the array of classifications for a single instance.
*
* @return a Vector containing Integer objects which store the class(s) which
* are the central tendency.
*/
public Vector findCentralTendencies(double[] predProbs) {
int centralTValue = 0;
int currentValue = 0;
//array to store the list of classes the have the greatest number of classifictions.
Vector centralTClasses;
centralTClasses = new Vector(); //create an array with size of the number of classes.
// Go through array, finding the central tendency.
for( int i = 0; i < predProbs.length; i++) {
currentValue = (int) predProbs[i];
// if current value is greater than the central tendency value then
// clear vector and add new class to vector array.
if( currentValue > centralTValue) {
centralTClasses.clear();
centralTClasses.addElement( new Integer(i) );
centralTValue = currentValue;
} else if( currentValue != 0 && currentValue == centralTValue) {
centralTClasses.addElement( new Integer(i) );
}
}
//return all classes that have the greatest number of classifications.
if( centralTValue != 0){
return centralTClasses;
} else {
return null;
}
}
/**
* Returns description of the bias-variance decomposition results.
*
* @return the bias-variance decomposition results as a string
*/
public String toString() {
String result = "\nBias-Variance Decomposition Segmentation, Cross Validation\n" +
"with subsampling.\n";
if (getClassifier() == null) {
return "Invalid setup";
}
result += "\nClassifier : " + getClassifier().getClass().getName();
if (getClassifier() instanceof OptionHandler) {
result += Utils.joinOptions(((OptionHandler)m_Classifier).getOptions());
}
result += "\nData File : " + getDataFileName();
result += "\nClass Index : ";
if (getClassIndex() == 0) {
result += "last";
} else {
result += getClassIndex();
}
result += "\nIterations : " + getClassifyIterations();
result += "\np : " + getP();
result += "\nTraining Size : " + getTrainSize();
result += "\nSeed : " + getSeed();
result += "\n\nDefinition : " +"Kohavi and Wolpert";
result += "\nError :" + Utils.doubleToString(getError(), 4);
result += "\nBias^2 :" + Utils.doubleToString(getKWBias(), 4);
result += "\nVariance :" + Utils.doubleToString(getKWVariance(), 4);
result += "\nSigma^2 :" + Utils.doubleToString(getKWSigma(), 4);
result += "\n\nDefinition : " +"Webb";
result += "\nError :" + Utils.doubleToString(getError(), 4);
result += "\nBias :" + Utils.doubleToString(getWBias(), 4);
result += "\nVariance :" + Utils.doubleToString(getWVariance(), 4);
return result;
}
/**
* Returns the revision string.
*
* @return the revision
*/
public String getRevision() {
return RevisionUtils.extract("$Revision: 6041 $");
}
/**
* Test method for this class
*
* @param args the command line arguments
*/
public static void main(String [] args) {
try {
BVDecomposeSegCVSub bvd = new BVDecomposeSegCVSub();
try {
bvd.setOptions(args);
Utils.checkForRemainingOptions(args);
} catch (Exception ex) {
String result = ex.getMessage() + "\nBVDecompose Options:\n\n";
Enumeration enu = bvd.listOptions();
while (enu.hasMoreElements()) {
Option option = (Option) enu.nextElement();
result += option.synopsis() + "\n" + option.description() + "\n";
}
throw new Exception(result);
}
bvd.decompose();
System.out.println(bvd.toString());
} catch (Exception ex) {
System.err.println(ex.getMessage());
}
}
/**
* Accepts an array of ints and randomises the values in the array, using the
* random seed.
*
*@param index is the array of integers
*@param random is the Random seed.
*/
public final void randomize(int[] index, Random random) {
for( int j = index.length - 1; j > 0; j-- ){
int k = random.nextInt( j + 1 );
int temp = index[j];
index[j] = index[k];
index[k] = temp;
}
}
}
-c <class index>
* The index of the class attribute.
* (default last)
*
* -D
* Turn on debugging output.
*
* -l <num>
* The number of times each instance is classified.
* (default 10)
*
* -p <proportion of objects in common>
* The average proportion of instances common between any two training sets
*
* -s <seed>
* The random number seed used.
*
* -t <name of arff file>
* The name of the arff file used for the decomposition.
*
* -T <number of instances in training set>
* The number of instances in the training set.
*
* -W <classifier class name>
* Full class name of the learner used in the decomposition.
* eg: weka.classifiers.bayes.NaiveBayes
*
*
* Options specific to learner weka.classifiers.rules.ZeroR:
*
*
* -D
* If set, classifier is run in debug mode and
* may output additional info to the console
*
*
* @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 {
setDebug(Utils.getFlag('D', options));
String classIndex = Utils.getOption('c', options);
if (classIndex.length() != 0) {
if (classIndex.toLowerCase().equals("last")) {
setClassIndex(0);
} else if (classIndex.toLowerCase().equals("first")) {
setClassIndex(1);
} else {
setClassIndex(Integer.parseInt(classIndex));
}
} else {
setClassIndex(0);
}
String classifyIterations = Utils.getOption('l', options);
if (classifyIterations.length() != 0) {
setClassifyIterations(Integer.parseInt(classifyIterations));
} else {
setClassifyIterations(10);
}
String prob = Utils.getOption('p', options);
if (prob.length() != 0) {
setP( Double.parseDouble(prob));
} else {
setP(-1);
}
//throw new Exception("A proportion must be specified" + " with a -p option.");
String seedString = Utils.getOption('s', options);
if (seedString.length() != 0) {
setSeed(Integer.parseInt(seedString));
} else {
setSeed(1);
}
String dataFile = Utils.getOption('t', options);
if (dataFile.length() != 0) {
setDataFileName(dataFile);
} else {
throw new Exception("An arff file must be specified"
+ " with the -t option.");
}
String trainSize = Utils.getOption('T', options);
if (trainSize.length() != 0) {
setTrainSize(Integer.parseInt(trainSize));
} else {
setTrainSize(-1);
}
//throw new Exception("A training set size must be specified" + " with a -T option.");
String classifierName = Utils.getOption('W', options);
if (classifierName.length() != 0) {
setClassifier(AbstractClassifier.forName(classifierName, Utils.partitionOptions(options)));
} else {
throw new Exception("A learner must be specified with the -W option.");
}
}
/**
* Gets the current settings of the CheckClassifier.
*
* @return an array of strings suitable for passing to setOptions
*/
public String [] getOptions() {
String [] classifierOptions = new String [0];
if ((m_Classifier != null) &&
(m_Classifier instanceof OptionHandler)) {
classifierOptions = ((OptionHandler)m_Classifier).getOptions();
}
String [] options = new String [classifierOptions.length + 14];
int current = 0;
if (getDebug()) {
options[current++] = "-D";
}
options[current++] = "-c"; options[current++] = "" + getClassIndex();
options[current++] = "-l"; options[current++] = "" + getClassifyIterations();
options[current++] = "-p"; options[current++] = "" + getP();
options[current++] = "-s"; options[current++] = "" + getSeed();
if (getDataFileName() != null) {
options[current++] = "-t"; options[current++] = "" + getDataFileName();
}
options[current++] = "-T"; options[current++] = "" + getTrainSize();
if (getClassifier() != null) {
options[current++] = "-W";
options[current++] = getClassifier().getClass().getName();
}
options[current++] = "--";
System.arraycopy(classifierOptions, 0, options, current,
classifierOptions.length);
current += classifierOptions.length;
while (current < options.length) {
options[current++] = "";
}
return options;
}
/**
* Set the classifiers being analysed
*
* @param newClassifier the Classifier to use.
*/
public void setClassifier(Classifier newClassifier) {
m_Classifier = newClassifier;
}
/**
* Gets the name of the classifier being analysed
*
* @return the classifier being analysed.
*/
public Classifier getClassifier() {
return m_Classifier;
}
/**
* Sets debugging mode
*
* @param debug true if debug output should be printed
*/
public void setDebug(boolean debug) {
m_Debug = debug;
}
/**
* Gets whether debugging is turned on
*
* @return true if debugging output is on
*/
public boolean getDebug() {
return m_Debug;
}
/**
* Sets the random number seed
*
* @param seed the random number seed
*/
public void setSeed(int seed) {
m_Seed = seed;
}
/**
* Gets the random number seed
*
* @return the random number seed
*/
public int getSeed() {
return m_Seed;
}
/**
* Sets the number of times an instance is classified
*
* @param classifyIterations number of times an instance is classified
*/
public void setClassifyIterations(int classifyIterations) {
m_ClassifyIterations = classifyIterations;
}
/**
* Gets the number of times an instance is classified
*
* @return the maximum number of times an instance is classified
*/
public int getClassifyIterations() {
return m_ClassifyIterations;
}
/**
* Sets the name of the dataset file.
*
* @param dataFileName name of dataset file.
*/
public void setDataFileName(String dataFileName) {
m_DataFileName = dataFileName;
}
/**
* Get the name of the data file used for the decomposition
*
* @return the name of the data file
*/
public String getDataFileName() {
return m_DataFileName;
}
/**
* Get the index (starting from 1) of the attribute used as the class.
*
* @return the index of the class attribute
*/
public int getClassIndex() {
return m_ClassIndex + 1;
}
/**
* Sets index of attribute to discretize on
*
* @param classIndex the index (starting from 1) of the class attribute
*/
public void setClassIndex(int classIndex) {
m_ClassIndex = classIndex - 1;
}
/**
* Get the calculated bias squared according to the Kohavi and Wolpert definition
*
* @return the bias squared
*/
public double getKWBias() {
return m_KWBias;
}
/**
* Get the calculated bias according to the Webb definition
*
* @return the bias
*
*/
public double getWBias() {
return m_WBias;
}
/**
* Get the calculated variance according to the Kohavi and Wolpert definition
*
* @return the variance
*/
public double getKWVariance() {
return m_KWVariance;
}
/**
* Get the calculated variance according to the Webb definition
*
* @return the variance according to Webb
*
*/
public double getWVariance() {
return m_WVariance;
}
/**
* Get the calculated sigma according to the Kohavi and Wolpert definition
*
* @return the sigma
*
*/
public double getKWSigma() {
return m_KWSigma;
}
/**
* Set the training size.
*
* @param size the size of the training set
*
*/
public void setTrainSize(int size) {
m_TrainSize = size;
}
/**
* Get the training size
*
* @return the size of the training set
*
*/
public int getTrainSize() {
return m_TrainSize;
}
/**
* Set the proportion of instances that are common between two training sets
* used to train a classifier.
*
* @param proportion the proportion of instances that are common between training
* sets.
*
*/
public void setP(double proportion) {
m_P = proportion;
}
/**
* Get the proportion of instances that are common between two training sets.
*
* @return the proportion
*
*/
public double getP() {
return m_P;
}
/**
* Get the calculated error rate
*
* @return the error rate
*/
public double getError() {
return m_Error;
}
/**
* Carry out the bias-variance decomposition using the sub-sampled cross-validation method.
*
* @throws Exception if the decomposition couldn't be carried out
*/
public void decompose() throws Exception {
Reader dataReader;
Instances data;
int tps; // training pool size, size of segment E.
int k; // number of folds in segment E.
int q; // number of segments of size tps.
dataReader = new BufferedReader(new FileReader(m_DataFileName)); //open file
data = new Instances(dataReader); // encapsulate in wrapper class called weka.Instances()
if (m_ClassIndex < 0) {
data.setClassIndex(data.numAttributes() - 1);
} else {
data.setClassIndex(m_ClassIndex);
}
if (data.classAttribute().type() != Attribute.NOMINAL) {
throw new Exception("Class attribute must be nominal");
}
int numClasses = data.numClasses();
data.deleteWithMissingClass();
if ( data.checkForStringAttributes() ) {
throw new Exception("Can't handle string attributes!");
}
// Dataset size must be greater than 2
if ( data.numInstances() <= 2 ){
throw new Exception("Dataset size must be greater than 2.");
}
if ( m_TrainSize == -1 ){ // default value
m_TrainSize = (int) Math.floor( (double) data.numInstances() / 2.0 );
}else if ( m_TrainSize < 0 || m_TrainSize >= data.numInstances() - 1 ) { // Check if 0 < training Size < D - 1
throw new Exception("Training set size of "+m_TrainSize+" is invalid.");
}
if ( m_P == -1 ){ // default value
m_P = (double) m_TrainSize / ( (double)data.numInstances() - 1 );
}else if ( m_P < ( m_TrainSize / ( (double)data.numInstances() - 1 ) ) || m_P >= 1.0 ) { //Check if p is in range: m/(|D|-1) <= p < 1.0
throw new Exception("Proportion is not in range: "+ (m_TrainSize / ((double) data.numInstances() - 1 )) +" <= p < 1.0 ");
}
//roundup tps from double to integer
tps = (int) Math.ceil( ((double)m_TrainSize / (double)m_P) + 1 );
k = (int) Math.ceil( tps / (tps - (double) m_TrainSize));
// number of folds cannot be more than the number of instances in the training pool
if ( k > tps ) {
throw new Exception("The required number of folds is too many."
+ "Change p or the size of the training set.");
}
// calculate the number of segments, round down.
q = (int) Math.floor( (double) data.numInstances() / (double)tps );
//create confusion matrix, columns = number of instances in data set, as all will be used, by rows = number of classes.
double [][] instanceProbs = new double [data.numInstances()][numClasses];
int [][] foldIndex = new int [ k ][ 2 ];
Vector segmentList = new Vector(q + 1);
//Set random seed
Random random = new Random(m_Seed);
data.randomize(random);
//create index arrays for different segments
int currentDataIndex = 0;
for( int count = 1; count <= (q + 1); count++ ){
if( count > q){
int [] segmentIndex = new int [ (data.numInstances() - (q * tps)) ];
for(int index = 0; index < segmentIndex.length; index++, currentDataIndex++){
segmentIndex[index] = currentDataIndex;
}
segmentList.add(segmentIndex);
} else {
int [] segmentIndex = new int [ tps ];
for(int index = 0; index < segmentIndex.length; index++, currentDataIndex++){
segmentIndex[index] = currentDataIndex;
}
segmentList.add(segmentIndex);
}
}
int remainder = tps % k; // remainder is used to determine when to shrink the fold size by 1.
//foldSize = ROUNDUP( tps / k ) (round up, eg 3 -> 3, 3.3->4)
int foldSize = (int) Math.ceil( (double)tps /(double) k); //roundup fold size double to integer
int index = 0;
int currentIndex;
for( int count = 0; count < k; count ++){
if( remainder != 0 && count == remainder ){
foldSize -= 1;
}
foldIndex[count][0] = index;
foldIndex[count][1] = foldSize;
index += foldSize;
}
for( int l = 0; l < m_ClassifyIterations; l++) {
for(int i = 1; i <= q; i++){
int [] currentSegment = (int[]) segmentList.get(i - 1);
randomize(currentSegment, random);
//CROSS FOLD VALIDATION for current Segment
for( int j = 1; j <= k; j++){
Instances TP = null;
for(int foldNum = 1; foldNum <= k; foldNum++){
if( foldNum != j){
int startFoldIndex = foldIndex[ foldNum - 1 ][ 0 ]; //start index
foldSize = foldIndex[ foldNum - 1 ][ 1 ];
int endFoldIndex = startFoldIndex + foldSize - 1;
for(int currentFoldIndex = startFoldIndex; currentFoldIndex <= endFoldIndex; currentFoldIndex++){
if( TP == null ){
TP = new Instances(data, currentSegment[ currentFoldIndex ], 1);
}else{
TP.add( data.instance( currentSegment[ currentFoldIndex ] ) );
}
}
}
}
TP.randomize(random);
if( getTrainSize() > TP.numInstances() ){
throw new Exception("The training set size of " + getTrainSize() + ", is greater than the training pool "
+ TP.numInstances() );
}
Instances train = new Instances(TP, 0, m_TrainSize);
Classifier current = AbstractClassifier.makeCopy(m_Classifier);
current.buildClassifier(train); // create a clssifier using the instances in train.
int currentTestIndex = foldIndex[ j - 1 ][ 0 ]; //start index
int testFoldSize = foldIndex[ j - 1 ][ 1 ]; //size
int endTestIndex = currentTestIndex + testFoldSize - 1;
while( currentTestIndex <= endTestIndex ){
Instance testInst = data.instance( currentSegment[currentTestIndex] );
int pred = (int)current.classifyInstance( testInst );
if(pred != testInst.classValue()) {
m_Error++; // add 1 to mis-classifications.
}
instanceProbs[ currentSegment[ currentTestIndex ] ][ pred ]++;
currentTestIndex++;
}
if( i == 1 && j == 1){
int[] segmentElast = (int[])segmentList.lastElement();
for( currentIndex = 0; currentIndex < segmentElast.length; currentIndex++){
Instance testInst = data.instance( segmentElast[currentIndex] );
int pred = (int)current.classifyInstance( testInst );
if(pred != testInst.classValue()) {
m_Error++; // add 1 to mis-classifications.
}
instanceProbs[ segmentElast[ currentIndex ] ][ pred ]++;
}
}
}
}
}
m_Error /= (double)( m_ClassifyIterations * data.numInstances() );
m_KWBias = 0.0;
m_KWVariance = 0.0;
m_KWSigma = 0.0;
m_WBias = 0.0;
m_WVariance = 0.0;
for (int i = 0; i < data.numInstances(); i++) {
Instance current = data.instance( i );
double [] predProbs = instanceProbs[ i ];
double pActual, pPred;
double bsum = 0, vsum = 0, ssum = 0;
double wBSum = 0, wVSum = 0;
Vector centralTendencies = findCentralTendencies( predProbs );
if( centralTendencies == null ){
throw new Exception("Central tendency was null.");
}
for (int j = 0; j < numClasses; j++) {
pActual = (current.classValue() == j) ? 1 : 0;
pPred = predProbs[j] / m_ClassifyIterations;
bsum += (pActual - pPred) * (pActual - pPred) - pPred * (1 - pPred) / (m_ClassifyIterations - 1);
vsum += pPred * pPred;
ssum += pActual * pActual;
}
m_KWBias += bsum;
m_KWVariance += (1 - vsum);
m_KWSigma += (1 - ssum);
for( int count = 0; count < centralTendencies.size(); count++ ) {
int wB = 0, wV = 0;
int centralTendency = ((Integer)centralTendencies.get(count)).intValue();
// For a single instance xi, find the bias and variance.
for (int j = 0; j < numClasses; j++) {
//Webb definition
if( j != (int)current.classValue() && j == centralTendency ) {
wB += predProbs[j];
}
if( j != (int)current.classValue() && j != centralTendency ) {
wV += predProbs[j];
}
}
wBSum += (double) wB;
wVSum += (double) wV;
}
// calculate bais by dividing bSum by the number of central tendencies and
// total number of instances. (effectively finding the average and dividing
// by the number of instances to get the nominalised probability).
m_WBias += ( wBSum / ((double) ( centralTendencies.size() * m_ClassifyIterations )));
// calculate variance by dividing vSum by the total number of interations
m_WVariance += ( wVSum / ((double) ( centralTendencies.size() * m_ClassifyIterations )));
}
m_KWBias /= (2.0 * (double) data.numInstances());
m_KWVariance /= (2.0 * (double) data.numInstances());
m_KWSigma /= (2.0 * (double) data.numInstances());
// bias = bias / number of data instances
m_WBias /= (double) data.numInstances();
// variance = variance / number of data instances.
m_WVariance /= (double) data.numInstances();
if (m_Debug) {
System.err.println("Decomposition finished");
}
}
/** Finds the central tendency, given the classifications for an instance.
*
* Where the central tendency is defined as the class that was most commonly
* selected for a given instance.