source: src/main/java/weka/classifiers/trees/lmt/LogisticBase.java @ 28

/*
 *    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.
 */

/*
 *    LogisticBase.java
 *    Copyright (C) 2003 University of Waikato, Hamilton, New Zealand
 *
 */

package weka.classifiers.trees.lmt;

import weka.classifiers.Classifier;
import weka.classifiers.AbstractClassifier;
import weka.classifiers.Evaluation;
import weka.classifiers.functions.SimpleLinearRegression;
import weka.core.Attribute;
import weka.core.Instance;
import weka.core.Instances;
import weka.core.RevisionUtils;
import weka.core.Utils;
import weka.core.WeightedInstancesHandler;

/**
 * Base/helper class for building logistic regression models with the LogitBoost algorithm.
 * Used for building logistic model trees (weka.classifiers.trees.lmt.LMT)
 * and standalone logistic regression (weka.classifiers.functions.SimpleLogistic).
 *
 <!-- 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>
 * 
 <!-- options-end -->
 *
 * @author Niels Landwehr
 * @author Marc Sumner
 * @version $Revision: 5928 $
 */
public class LogisticBase 
    extends AbstractClassifier 
    implements WeightedInstancesHandler {

    /** for serialization */
    static final long serialVersionUID = 168765678097825064L;
  
    /** Header-only version of the numeric version of the training data*/
    protected Instances m_numericDataHeader;
    /** 
     * Numeric version of the training data. Original class is replaced by a numeric pseudo-class.
     */
    protected Instances m_numericData;
    
    /** Training data */
    protected Instances m_train;
    
    /** Use cross-validation to determine best number of LogitBoost iterations ?*/
    protected boolean m_useCrossValidation;

    /**Use error on probabilities for stopping criterion of LogitBoost? */
    protected boolean m_errorOnProbabilities;

    /**Use fixed number of iterations for LogitBoost? (if negative, cross-validate number of iterations)*/
    protected int m_fixedNumIterations;
    
    /**Use heuristic to stop performing LogitBoost iterations earlier?
     * If enabled, LogitBoost is stopped if the current (local) minimum of the error on a test set as 
     * a function of the number of iterations has not changed for m_heuristicStop iterations.
     */
    protected int m_heuristicStop = 50;
 
    /**The number of LogitBoost iterations performed.*/
    protected int m_numRegressions = 0;
    
    /**The maximum number of LogitBoost iterations*/
    protected int m_maxIterations;
    
    /**The number of different classes*/
    protected int m_numClasses;

    /**Array holding the simple regression functions fit by LogitBoost*/
    protected SimpleLinearRegression[][] m_regressions;
        
    /**Number of folds for cross-validating number of LogitBoost iterations*/
    protected static int m_numFoldsBoosting = 5;

    /**Threshold on the Z-value for LogitBoost*/
    protected static final double Z_MAX = 3;
    
    /** If true, the AIC is used to choose the best iteration*/
    private boolean m_useAIC = false;
    
    /** Effective number of parameters used for AIC / BIC automatic stopping */
    protected double m_numParameters = 0;
    
    /**Threshold for trimming weights. Instances with a weight lower than this (as a percentage
     * of total weights) are not included in the regression fit.
     **/
    protected double m_weightTrimBeta = 0;

    /**
     * Constructor that creates LogisticBase object with standard options.
     */
    public LogisticBase(){
        m_fixedNumIterations = -1;
        m_useCrossValidation = true;
        m_errorOnProbabilities = false; 
        m_maxIterations = 500;
        m_useAIC = false;
        m_numParameters = 0;
    }
    
    /**
     * Constructor to create LogisticBase object.
     * @param numBoostingIterations fixed number of iterations for LogitBoost (if negative, use cross-validation or
     * stopping criterion on the training data).
     * @param useCrossValidation cross-validate number of LogitBoost iterations (if false, use stopping 
     * criterion on the training data).
     * @param errorOnProbabilities if true, use error on probabilities 
     * instead of misclassification for stopping criterion of LogitBoost
     */
    public LogisticBase(int numBoostingIterations, boolean useCrossValidation, boolean errorOnProbabilities){
        m_fixedNumIterations = numBoostingIterations;
        m_useCrossValidation = useCrossValidation;
        m_errorOnProbabilities = errorOnProbabilities;  
        m_maxIterations = 500;
        m_useAIC = false;
        m_numParameters = 0;
    }    

    /**
     * Builds the logistic regression model usiing LogitBoost.
     * 
     * @param data the training data
     * @throws Exception if something goes wrong
     */
    public void buildClassifier(Instances data) throws Exception {                      

        m_train = new Instances(data);
        
        m_numClasses = m_train.numClasses();
        
        //init the array of simple regression functions
        m_regressions = initRegressions();
        m_numRegressions = 0;

        //get numeric version of the training data (class variable replaced  by numeric pseudo-class)
        m_numericData = getNumericData(m_train);        
        
        //save header info
        m_numericDataHeader = new Instances(m_numericData, 0);
        
        
        if (m_fixedNumIterations > 0) {
            //run LogitBoost for fixed number of iterations
            performBoosting(m_fixedNumIterations);
        } else if (m_useAIC) { // Marc had this after the test for m_useCrossValidation. Changed by Eibe.
            //run LogitBoost using information criterion for stopping
            performBoostingInfCriterion();
        } else if (m_useCrossValidation) {
            //cross-validate number of LogitBoost iterations
            performBoostingCV();
        } else {
            //run LogitBoost with number of iterations that minimizes error on the training set
            performBoosting();
        }       
        
        //only keep the simple regression functions that correspond to the selected number of LogitBoost iterations
        m_regressions = selectRegressions(m_regressions);       
    }   

    /**
     * Runs LogitBoost, determining the best number of iterations by cross-validation.
     * 
     * @throws Exception if something goes wrong
     */
    protected void performBoostingCV() throws Exception{                        
        
        //completed iteration keeps track of the number of iterations that have been
        //performed in every fold (some might stop earlier than others). 
        //Best iteration is selected only from these.
        int completedIterations = m_maxIterations;
        
        Instances allData = new Instances(m_train);
        
        allData.stratify(m_numFoldsBoosting);         

        double[] error = new double[m_maxIterations + 1];       
        
        for (int i = 0; i < m_numFoldsBoosting; i++) {
            //split into training/test data in fold
            Instances train = allData.trainCV(m_numFoldsBoosting,i);
            Instances test = allData.testCV(m_numFoldsBoosting,i);

            //initialize LogitBoost
            m_numRegressions = 0;
            m_regressions = initRegressions();

            //run LogitBoost iterations
            int iterations = performBoosting(train,test,error,completedIterations);         
            if (iterations < completedIterations) completedIterations = iterations;         
        }
        
        //determine iteration with minimum error over the folds
        int bestIteration = getBestIteration(error,completedIterations);
        
        //rebuild model on all of the training data
        m_numRegressions = 0;
        performBoosting(bestIteration);
    }    
    
    /**
     * Runs LogitBoost, determining the best number of iterations by an information criterion (currently AIC).
     */
    protected void performBoostingInfCriterion() throws Exception{
        
        double criterion = 0.0;
        double bestCriterion = Double.MAX_VALUE;
        int bestIteration = 0;
        int noMin = 0;
        
        // Variable to keep track of criterion values (AIC)
        double criterionValue = Double.MAX_VALUE;
        
        // initialize Ys/Fs/ps
        double[][] trainYs = getYs(m_train);
        double[][] trainFs = getFs(m_numericData);
        double[][] probs = getProbs(trainFs);
        
        // Array with true/false if the attribute is included in the model or not
        boolean[][] attributes = new boolean[m_numClasses][m_numericDataHeader.numAttributes()];
        
        int iteration = 0;
        while (iteration < m_maxIterations) {
            
            //perform single LogitBoost iteration
            boolean foundAttribute = performIteration(iteration, trainYs, trainFs, probs, m_numericData);
            if (foundAttribute) {
                iteration++;
                m_numRegressions = iteration;
            } else {
                //could not fit simple linear regression: stop LogitBoost
                break;
            }
            
            double numberOfAttributes = m_numParameters + iteration;
            
            // Fill criterion array values
            criterionValue = 2.0 * negativeLogLikelihood(trainYs, probs) +
              2.0 * numberOfAttributes;

            //heuristic: stop LogitBoost if the current minimum has not changed for <m_heuristicStop> iterations
            if (noMin > m_heuristicStop) break;
            if (criterionValue < bestCriterion) {
                bestCriterion = criterionValue;
                bestIteration = iteration;
                noMin = 0;
            } else {
                noMin++;
            }
        }

        m_numRegressions = 0;
        performBoosting(bestIteration);
    }

    /**
     * Runs LogitBoost on a training set and monitors the error on a test set.
     * Used for running one fold when cross-validating the number of LogitBoost iterations.
     * @param train the training set
     * @param test the test set
     * @param error array to hold the logged error values
     * @param maxIterations the maximum number of LogitBoost iterations to run
     * @return the number of completed LogitBoost iterations (can be smaller than maxIterations 
     * if the heuristic for early stopping is active or there is a problem while fitting the regressions 
     * in LogitBoost).
     * @throws Exception if something goes wrong
     */
    protected int performBoosting(Instances train, Instances test, 
                                  double[] error, int maxIterations) throws Exception{
        
        //get numeric version of the (sub)set of training instances
        Instances numericTrain = getNumericData(train);         

        //initialize Ys/Fs/ps 
        double[][] trainYs = getYs(train);
        double[][] trainFs = getFs(numericTrain);               
        double[][] probs = getProbs(trainFs);   

        int iteration = 0;

        int noMin = 0;
        double lastMin = Double.MAX_VALUE;      
        
        if (m_errorOnProbabilities) error[0] += getMeanAbsoluteError(test);
        else error[0] += getErrorRate(test);
        
        while (iteration < maxIterations) {
          
            //perform single LogitBoost iteration
            boolean foundAttribute = performIteration(iteration, trainYs, trainFs, probs, numericTrain);
            if (foundAttribute) {
                iteration++;
                m_numRegressions = iteration;
            } else {
                //could not fit simple linear regression: stop LogitBoost
                break;
            }
            
            if (m_errorOnProbabilities) error[iteration] += getMeanAbsoluteError(test);
            else error[iteration] += getErrorRate(test);
          
            //heuristic: stop LogitBoost if the current minimum has not changed for <m_heuristicStop> iterations
            if (noMin > m_heuristicStop) break;
            if (error[iteration] < lastMin) {
                lastMin = error[iteration];
                noMin = 0;
            } else {
                noMin++;
            }                       
        }

        return iteration;
    }

    /**
     * Runs LogitBoost with a fixed number of iterations.
     * @param numIterations the number of iterations to run
     * @throws Exception if something goes wrong
     */
    protected void performBoosting(int numIterations) throws Exception{

        //initialize Ys/Fs/ps 
        double[][] trainYs = getYs(m_train);
        double[][] trainFs = getFs(m_numericData);              
        double[][] probs = getProbs(trainFs);
        
        int iteration = 0;

        //run iterations
        while (iteration < numIterations) {
            boolean foundAttribute = performIteration(iteration, trainYs, trainFs, probs, m_numericData);
            if (foundAttribute) iteration++;
            else break;
        }
        
        m_numRegressions = iteration;
    }
    
    /**
     * Runs LogitBoost using the stopping criterion on the training set.
     * The number of iterations is used that gives the lowest error on the training set, either misclassification
     * or error on probabilities (depending on the errorOnProbabilities option).
     * @throws Exception if something goes wrong
     */
    protected void performBoosting() throws Exception{
        
        //initialize Ys/Fs/ps
        double[][] trainYs = getYs(m_train);
        double[][] trainFs = getFs(m_numericData);              
        double[][] probs = getProbs(trainFs);   

        int iteration = 0;

        double[] trainErrors = new double[m_maxIterations+1];
        trainErrors[0] = getErrorRate(m_train);
        
        int noMin = 0;
        double lastMin = Double.MAX_VALUE;
        
        while (iteration < m_maxIterations) {
            boolean foundAttribute = performIteration(iteration, trainYs, trainFs, probs, m_numericData);
            if (foundAttribute) {
                iteration++;
                m_numRegressions = iteration;
            } else {            
                //could not fit simple regression
                break;
            }
            
            trainErrors[iteration] = getErrorRate(m_train);         
         
            //heuristic: stop LogitBoost if the current minimum has not changed for <m_heuristicStop> iterations
            if (noMin > m_heuristicStop) break;     
            if (trainErrors[iteration] < lastMin) {
                lastMin = trainErrors[iteration];
                noMin = 0;
            } else {
                noMin++;
            }
        }
        
        //find iteration with best error
        m_numRegressions = getBestIteration(trainErrors, iteration);    
    }

    /**
     * Returns the misclassification error of the current model on a set of instances.
     * @param data the set of instances
     * @return the error rate
     * @throws Exception if something goes wrong
     */
    protected double getErrorRate(Instances data) throws Exception {
        Evaluation eval = new Evaluation(data);
        eval.evaluateModel(this,data);
        return eval.errorRate();
    }

    /**
     * Returns the error of the probability estimates for the current model on a set of instances.
     * @param data the set of instances
     * @return the error
     * @throws Exception if something goes wrong
     */
    protected double getMeanAbsoluteError(Instances data) throws Exception {
        Evaluation eval = new Evaluation(data);
        eval.evaluateModel(this,data);
        return eval.meanAbsoluteError();
    }

    /**
     * Helper function to find the minimum in an array of error values.
     * 
     * @param errors an array containing errors
     * @param maxIteration the maximum of iterations
     * @return the minimum
     */
    protected int getBestIteration(double[] errors, int maxIteration) {
        double bestError = errors[0];
        int bestIteration = 0;
        for (int i = 1; i <= maxIteration; i++) {           
            if (errors[i] < bestError) {
                bestError = errors[i];
                bestIteration = i;              
            }
        } 
        return bestIteration;
    }

    /**
     * Performs a single iteration of LogitBoost, and updates the model accordingly.
     * A simple regression function is fit to the response and added to the m_regressions array.
     * @param iteration the current iteration 
     * @param trainYs the y-values (see description of LogitBoost) for the model trained so far
     * @param trainFs the F-values (see description of LogitBoost) for the model trained so far
     * @param probs the p-values (see description of LogitBoost) for the model trained so far
     * @param trainNumeric numeric version of the training data
     * @return returns true if iteration performed successfully, false if no simple regression function 
     * could be fitted.
     * @throws Exception if something goes wrong
     */
    protected boolean performIteration(int iteration, 
                                       double[][] trainYs,
                                       double[][] trainFs,
                                       double[][] probs,
                                       Instances trainNumeric) throws Exception {
        
        for (int j = 0; j < m_numClasses; j++) {
            // Keep track of sum of weights
            double[] weights = new double[trainNumeric.numInstances()];
            double weightSum = 0.0;
            
            //make copy of data (need to save the weights) 
            Instances boostData = new Instances(trainNumeric);
            
            for (int i = 0; i < trainNumeric.numInstances(); i++) {
                
                //compute response and weight
                double p = probs[i][j];
                double actual = trainYs[i][j];
                double z = getZ(actual, p);
                double w = (actual - p) / z;
                
                //set values for instance 
                Instance current = boostData.instance(i);
                current.setValue(boostData.classIndex(), z);
                current.setWeight(current.weight() * w);                                
                
                weights[i] = current.weight();
                weightSum += current.weight();
            }
            
            Instances instancesCopy = new Instances(boostData);
            
            if (weightSum > 0) {
                // Only the (1-beta)th quantile of instances are sent to the base classifier
                if (m_weightTrimBeta > 0) {
                    double weightPercentage = 0.0;
                    int[] weightsOrder = new int[trainNumeric.numInstances()];
                    weightsOrder = Utils.sort(weights);
                    instancesCopy.delete();
                    
                    
                    for (int i = weightsOrder.length-1; (i >= 0) && (weightPercentage < (1-m_weightTrimBeta)); i--) {
                        instancesCopy.add(boostData.instance(weightsOrder[i]));
                        weightPercentage += (weights[weightsOrder[i]] / weightSum);
                        
                    }
                }
                
                //Scale the weights
                weightSum = instancesCopy.sumOfWeights();
                for (int i = 0; i < instancesCopy.numInstances(); i++) {
                    Instance current = instancesCopy.instance(i);
                    current.setWeight(current.weight() * (double)instancesCopy.numInstances() / weightSum);
                }
            }
            
            //fit simple regression function
            m_regressions[j][iteration].buildClassifier(instancesCopy);
            
            boolean foundAttribute = m_regressions[j][iteration].foundUsefulAttribute();
            if (!foundAttribute) {
                //could not fit simple regression function
                return false;
            }
            
        }
        
        // Evaluate / increment trainFs from the classifier
        for (int i = 0; i < trainFs.length; i++) {
            double [] pred = new double [m_numClasses];
            double predSum = 0;
            for (int j = 0; j < m_numClasses; j++) {
                pred[j] = m_regressions[j][iteration]
                    .classifyInstance(trainNumeric.instance(i));
                predSum += pred[j];
            }
            predSum /= m_numClasses;
            for (int j = 0; j < m_numClasses; j++) {
                trainFs[i][j] += (pred[j] - predSum) * (m_numClasses - 1) 
                    / m_numClasses;
            }
        }
        
        // Compute the current probability estimates
        for (int i = 0; i < trainYs.length; i++) {
            probs[i] = probs(trainFs[i]);
        }
        return true;
    }    

    /**
     * Helper function to initialize m_regressions.
     * 
     * @return the generated classifiers
     */
    protected SimpleLinearRegression[][] initRegressions(){
        SimpleLinearRegression[][] classifiers =   
            new SimpleLinearRegression[m_numClasses][m_maxIterations];
        for (int j = 0; j < m_numClasses; j++) {
            for (int i = 0; i < m_maxIterations; i++) {
                classifiers[j][i] = new SimpleLinearRegression();
                classifiers[j][i].setSuppressErrorMessage(true);
            }
        }
        return classifiers;
    }

    /**
     * Converts training data to numeric version. The class variable is replaced by a pseudo-class 
     * used by LogitBoost.
     * 
     * @param data the data to convert
     * @return the converted data
     * @throws Exception if something goes wrong
     */
    protected Instances getNumericData(Instances data) throws Exception{
        Instances numericData = new Instances(data);
        
        int classIndex = numericData.classIndex();
        numericData.setClassIndex(-1);
        numericData.deleteAttributeAt(classIndex);
        numericData.insertAttributeAt(new Attribute("'pseudo class'"), classIndex);
        numericData.setClassIndex(classIndex);
        return numericData;
    }
    
    /**
     * Helper function for cutting back m_regressions to the set of classifiers 
     * (corresponsing to the number of LogitBoost iterations) that gave the 
     * smallest error.
     * 
     * @param classifiers the original set of classifiers
     * @return the cut back set of classifiers
     */
    protected SimpleLinearRegression[][] selectRegressions(SimpleLinearRegression[][] classifiers){
        SimpleLinearRegression[][] goodClassifiers = 
            new SimpleLinearRegression[m_numClasses][m_numRegressions];
        
        for (int j = 0; j < m_numClasses; j++) {
            for (int i = 0; i < m_numRegressions; i++) {
                goodClassifiers[j][i] = classifiers[j][i];
            }
        }
        return goodClassifiers;
    }           
    
    /**
     * Computes the LogitBoost response variable from y/p values 
     * (actual/estimated class probabilities).
     * 
     * @param actual the actual class probability
     * @param p the estimated class probability
     * @return the LogitBoost response
     */
    protected double getZ(double actual, double p) {
        double z;
        if (actual == 1) {
            z = 1.0 / p;
            if (z > Z_MAX) { // threshold
                z = Z_MAX;
            }
        } else {
            z = -1.0 / (1.0 - p);
            if (z < -Z_MAX) { // threshold
                z = -Z_MAX;
            }
        }
        return z;
    }
    
    /**
     * Computes the LogitBoost response for an array of y/p values 
     * (actual/estimated class probabilities).
     * 
     * @param dataYs the actual class probabilities
     * @param probs the estimated class probabilities
     * @return the LogitBoost response
     */
    protected double[][] getZs(double[][] probs, double[][] dataYs) {
        
        double[][] dataZs = new double[probs.length][m_numClasses];
        for (int j = 0; j < m_numClasses; j++) 
            for (int i = 0; i < probs.length; i++) dataZs[i][j] = getZ(dataYs[i][j], probs[i][j]);
        return dataZs;
    }
    
    /**
     * Computes the LogitBoost weights from an array of y/p values 
     * (actual/estimated class probabilities).
     * 
     * @param dataYs the actual class probabilities
     * @param probs the estimated class probabilities
     * @return the LogitBoost weights
     */
    protected double[][] getWs(double[][] probs, double[][] dataYs) {
        
        double[][] dataWs = new double[probs.length][m_numClasses];
        for (int j = 0; j < m_numClasses; j++) 
            for (int i = 0; i < probs.length; i++){
            double z = getZ(dataYs[i][j], probs[i][j]);
            dataWs[i][j] = (dataYs[i][j] - probs[i][j]) / z;
            }
        return dataWs;
    }

    /**
     * Computes the p-values (probabilities for the classes) from the F-values 
     * of the logistic model.
     * 
     * @param Fs the F-values
     * @return the p-values
     */
    protected double[] probs(double[] Fs) {
        
        double maxF = -Double.MAX_VALUE;
        for (int i = 0; i < Fs.length; i++) {
            if (Fs[i] > maxF) {
                maxF = Fs[i];
            }
        }   
        double sum = 0;
        double[] probs = new double[Fs.length];
        for (int i = 0; i < Fs.length; i++) {
            probs[i] = Math.exp(Fs[i] - maxF);   
            sum += probs[i];
        }
        
        Utils.normalize(probs, sum);
        return probs;
    }

    /**
     * Computes the Y-values (actual class probabilities) for a set of instances.
     * 
     * @param data the data to compute the Y-values from
     * @return the Y-values
     */
    protected double[][] getYs(Instances data){
        
        double [][] dataYs = new double [data.numInstances()][m_numClasses];
        for (int j = 0; j < m_numClasses; j++) {
            for (int k = 0; k < data.numInstances(); k++) {
                dataYs[k][j] = (data.instance(k).classValue() == j) ? 
                    1.0: 0.0;
            }
        }
        return dataYs;
    }

    /**
     * Computes the F-values for a single instance.
     * 
     * @param instance the instance to compute the F-values for
     * @return the F-values
     * @throws Exception if something goes wrong
     */
    protected double[] getFs(Instance instance) throws Exception{
        
        double [] pred = new double [m_numClasses];
        double [] instanceFs = new double [m_numClasses]; 
        
        //add up the predictions from the simple regression functions
        for (int i = 0; i < m_numRegressions; i++) {
            double predSum = 0;
            for (int j = 0; j < m_numClasses; j++) {
                pred[j] = m_regressions[j][i].classifyInstance(instance);
                predSum += pred[j];
            }
            predSum /= m_numClasses;
            for (int j = 0; j < m_numClasses; j++) {
                instanceFs[j] += (pred[j] - predSum) * (m_numClasses - 1) 
                    / m_numClasses;
            }
        }       
        
        return instanceFs; 
    } 
    
    /**
     * Computes the F-values for a set of instances.
     * 
     * @param data the data to work on
     * @return the F-values
     * @throws Exception if something goes wrong
     */
    protected double[][] getFs(Instances data) throws Exception{
        
        double[][] dataFs = new double[data.numInstances()][];
       
        for (int k = 0; k < data.numInstances(); k++) {
            dataFs[k] = getFs(data.instance(k));
        }
        
        return dataFs;  
    }   

    /**
     * Computes the p-values (probabilities for the different classes) from 
     * the F-values for a set of instances.
     * 
     * @param dataFs the F-values
     * @return the p-values
     */
    protected double[][] getProbs(double[][] dataFs){
        
        int numInstances = dataFs.length;
        double[][] probs = new double[numInstances][];
        
        for (int k = 0; k < numInstances; k++) {       
            probs[k] = probs(dataFs[k]);
        }
        return probs;
    }
    
    /**
     * Returns the negative loglikelihood of the Y-values (actual class probabilities) given the 
     * p-values (current probability estimates).
     * 
     * @param dataYs the Y-values
     * @param probs the p-values
     * @return the likelihood
     */
    protected double negativeLogLikelihood(double[][] dataYs, double[][] probs) {
        
        double logLikelihood = 0;
        for (int i = 0; i < dataYs.length; i++) {
            for (int j = 0; j < m_numClasses; j++) {
                if (dataYs[i][j] == 1.0) {
                    logLikelihood -= Math.log(probs[i][j]);
                }
            }
        }
        return logLikelihood;// / (double)dataYs.length;
    }

    /**
     * Returns an array of the indices of the attributes used in the logistic model.
     * The first dimension is the class, the second dimension holds a list of attribute indices.
     * Attribute indices start at zero.
     * @return the array of attribute indices
     */
    public int[][] getUsedAttributes(){
        
        int[][] usedAttributes = new int[m_numClasses][];
        
        //first extract coefficients
        double[][] coefficients = getCoefficients();
        
        for (int j = 0; j < m_numClasses; j++){
            
            //boolean array indicating if attribute used
            boolean[] attributes = new boolean[m_numericDataHeader.numAttributes()];
            for (int i = 0; i < attributes.length; i++) {
                //attribute used if coefficient > 0
                if (!Utils.eq(coefficients[j][i + 1],0)) attributes[i] = true;
            }
                    
            int numAttributes = 0;
            for (int i = 0; i < m_numericDataHeader.numAttributes(); i++) if (attributes[i]) numAttributes++;
            
            //"collect" all attributes into array of indices
            int[] usedAttributesClass = new int[numAttributes];
            int count = 0;
            for (int i = 0; i < m_numericDataHeader.numAttributes(); i++) {
                if (attributes[i]) {
                usedAttributesClass[count] = i;
                count++;
                } 
            }
            
            usedAttributes[j] = usedAttributesClass;
        }
        
        return usedAttributes;
    }

    /**
     * The number of LogitBoost iterations performed (= the number of simple 
     * regression functions fit).
     * 
     * @return the number of LogitBoost iterations performed 
     */
    public int getNumRegressions() {
        return m_numRegressions;
    }
    
    /**
     * Get the value of weightTrimBeta.
     *
     * @return Value of weightTrimBeta.
     */
    public double getWeightTrimBeta(){
        return m_weightTrimBeta;
    }
    
    /**
     * Get the value of useAIC.
     *
     * @return Value of useAIC.
     */
    public boolean getUseAIC(){
        return m_useAIC;
    }

    /**
     * Sets the parameter "maxIterations".
     * 
     * @param maxIterations the maximum iterations
     */
    public void setMaxIterations(int maxIterations) {
        m_maxIterations = maxIterations;
    }
    
    /**
     * Sets the option "heuristicStop".
     * 
     * @param heuristicStop the heuristic stop to use
     */
    public void setHeuristicStop(int heuristicStop){
        m_heuristicStop = heuristicStop;
    }
    
    /**
     * Sets the option "weightTrimBeta".
     */
    public void setWeightTrimBeta(double w){
        m_weightTrimBeta = w;
    }
    
    /**
     * Set the value of useAIC.
     *
     * @param c Value to assign to useAIC.
     */
    public void setUseAIC(boolean c){
        m_useAIC = c;
    }

    /**
     * Returns the maxIterations parameter.
     * 
     * @return the maximum iteration
     */
    public int getMaxIterations(){
        return m_maxIterations;
    }
        
    /**
     * Returns an array holding the coefficients of the logistic model.
     * First dimension is the class, the second one holds a list of coefficients.
     * At position zero, the constant term of the model is stored, then, the coefficients for
     * the attributes in ascending order.
     * @return the array of coefficients
     */
    protected double[][] getCoefficients(){
        double[][] coefficients = new double[m_numClasses][m_numericDataHeader.numAttributes() + 1];
        for (int j = 0; j < m_numClasses; j++) {
            //go through simple regression functions and add their coefficient to the coefficient of
            //the attribute they are built on.
            for (int i = 0; i < m_numRegressions; i++) {
                
                double slope = m_regressions[j][i].getSlope();
                double intercept = m_regressions[j][i].getIntercept();
                int attribute = m_regressions[j][i].getAttributeIndex();
                
                coefficients[j][0] += intercept;
                coefficients[j][attribute + 1] += slope;
            }
        }
        
        // Need to multiply all coefficients by (J-1) / J
        for (int j = 0; j < coefficients.length; j++) {
          for (int i = 0; i < coefficients[0].length; i++) {
            coefficients[j][i] *= (double)(m_numClasses - 1) / (double)m_numClasses;
          }
        }

        return coefficients;
    }

    /**
     * Returns the fraction of all attributes in the data that are used in the 
     * logistic model (in percent). 
     * An attribute is used in the model if it is used in any of the models for 
     * the different classes.
     * 
     * @return the fraction of all attributes that are used
     */
    public double percentAttributesUsed(){      
        boolean[] attributes = new boolean[m_numericDataHeader.numAttributes()];
        
        double[][] coefficients = getCoefficients();
        for (int j = 0; j < m_numClasses; j++){
            for (int i = 1; i < m_numericDataHeader.numAttributes() + 1; i++) {
                //attribute used if it is used in any class, note coefficients are shifted by one (because
                //of constant term).
                if (!Utils.eq(coefficients[j][i],0)) attributes[i - 1] = true;
            }
        }
        
        //count number of used attributes (without the class attribute)
        double count = 0;
        for (int i = 0; i < attributes.length; i++) if (attributes[i]) count++;
        return count / (double)(m_numericDataHeader.numAttributes() - 1) * 100.0;
    }
    
    /**
     * Returns a description of the logistic model (i.e., attributes and 
     * coefficients).
     * 
     * @return the description of the model
     */
    public String toString(){
        
        StringBuffer s = new StringBuffer();    

        //get used attributes
        int[][] attributes = getUsedAttributes();
        
        //get coefficients
        double[][] coefficients = getCoefficients();
        
        for (int j = 0; j < m_numClasses; j++) {
            s.append("\nClass "+j+" :\n");
            //constant term
            s.append(Utils.doubleToString(coefficients[j][0],4,2)+" + \n");
            for (int i = 0; i < attributes[j].length; i++) {            
                //attribute/coefficient pairs
                s.append("["+m_numericDataHeader.attribute(attributes[j][i]).name()+"]");
                s.append(" * " + Utils.doubleToString(coefficients[j][attributes[j][i]+1],4,2));
                if (i != attributes[j].length - 1) s.append(" +");
                s.append("\n");     
            }
        }       
        return new String(s);
    }

    /** 
     * Returns class probabilities for an instance.
     *
     * @param instance the instance to compute the distribution for
     * @return the class probabilities
     * @throws Exception if distribution can't be computed successfully
     */
    public double[] distributionForInstance(Instance instance) throws Exception {
        
        instance = (Instance)instance.copy();   

        //set to numeric pseudo-class
        instance.setDataset(m_numericDataHeader);               
        
        //calculate probs via Fs
        return probs(getFs(instance));
    }

    /**
     * Cleanup in order to save memory.
     */
    public void cleanup() {
        //save just header info
        m_train = new Instances(m_train,0);
        m_numericData = null;   
    }
    
    /**
     * Returns the revision string.
     * 
     * @return          the revision
     */
    public String getRevision() {
      return RevisionUtils.extract("$Revision: 5928 $");
    }
}