Examples with IImpurity org.knime.base.node.mine.treeensemble2.learner.IImpurity used on opensource projects

Example 1 with IImpurity

use of org.knime.base.node.mine.treeensemble2.learner.IImpurity in project knime-core by knime.

the class TreeNominalColumnData method calcBestSplitClassificationBinaryPCA.

/**
 * Implements the approach proposed by Coppersmith et al. (1999) in their paper
 * "Partitioning Nominal Attributes in Decision Trees"
 *
 * @param membershipController
 * @param rowWeights
 * @param targetPriors
 * @param targetColumn
 * @param impCriterion
 * @param nomVals
 * @param targetVals
 * @param originalIndexInColumnList
 * @return the best binary split candidate or null if there is no valid split with positive gain
 */
private NominalBinarySplitCandidate calcBestSplitClassificationBinaryPCA(final ColumnMemberships columnMemberships, final ClassificationPriors targetPriors, final TreeTargetNominalColumnData targetColumn, final IImpurity impCriterion, final NominalValueRepresentation[] nomVals, final NominalValueRepresentation[] targetVals, final RandomData rd) {
    final TreeEnsembleLearnerConfiguration config = getConfiguration();
    final int minChildSize = config.getMinChildSize();
    final boolean useXGBoostMissingValueHandling = config.getMissingValueHandling() == MissingValueHandling.XGBoost;
    // The algorithm combines attribute values with the same class probabilities into a single attribute
    // therefore it is necessary to track the known classProbabilities
    final LinkedHashMap<ClassProbabilityVector, CombinedAttributeValues> combinedAttValsMap = new LinkedHashMap<ClassProbabilityVector, CombinedAttributeValues>();
    columnMemberships.next();
    double totalWeight = 0.0;
    boolean branchContainsMissingValues = containsMissingValues();
    int start = 0;
    final int lengthNonMissing = containsMissingValues() ? nomVals.length - 1 : nomVals.length;
    final int attToConsider = useXGBoostMissingValueHandling ? nomVals.length : lengthNonMissing;
    for (int att = 0; att < lengthNonMissing; /*attToConsider*/
    att++) {
        int end = start + m_nominalValueCounts[att];
        double attWeight = 0.0;
        final double[] classFrequencies = new double[targetVals.length];
        boolean reachedEnd = false;
        for (int index = columnMemberships.getIndexInColumn(); index < end; index = columnMemberships.getIndexInColumn()) {
            double weight = columnMemberships.getRowWeight();
            assert weight > EPSILON : "Instances in columnMemberships must have weights larger than EPSILON.";
            int instanceClass = targetColumn.getValueFor(columnMemberships.getOriginalIndex());
            classFrequencies[instanceClass] += weight;
            attWeight += weight;
            totalWeight += weight;
            if (!columnMemberships.next()) {
                // reached end of columnMemberships
                reachedEnd = true;
                if (att == nomVals.length - 1) {
                    // if the column contains no missing values, the last possible nominal value is
                    // not the missing value and therefore branchContainsMissingValues needs to be false
                    branchContainsMissingValues = branchContainsMissingValues && true;
                }
                break;
            }
        }
        start = end;
        if (attWeight < EPSILON) {
            // attribute value did not occur in this branch or sample
            continue;
        }
        final double[] classProbabilities = new double[targetVals.length];
        for (int i = 0; i < classProbabilities.length; i++) {
            classProbabilities[i] = truncateDouble(8, classFrequencies[i] / attWeight);
        }
        CombinedAttributeValues attVal = new CombinedAttributeValues(classFrequencies, classProbabilities, attWeight, nomVals[att]);
        ClassProbabilityVector classProbabilityVector = new ClassProbabilityVector(classProbabilities);
        CombinedAttributeValues knownAttVal = combinedAttValsMap.get(classProbabilityVector);
        if (knownAttVal == null) {
            combinedAttValsMap.put(classProbabilityVector, attVal);
        } else {
            knownAttVal.combineAttributeValues(attVal);
        }
        if (reachedEnd) {
            break;
        }
    }
    // account for missing values and their weight
    double missingWeight = 0.0;
    double[] missingClassCounts = null;
    // otherwise the current indexInColumn won't be larger than start
    if (columnMemberships.getIndexInColumn() >= start) {
        missingClassCounts = new double[targetVals.length];
        do {
            final double recordWeight = columnMemberships.getRowWeight();
            final int recordClass = targetColumn.getValueFor(columnMemberships.getOriginalIndex());
            missingWeight += recordWeight;
            missingClassCounts[recordClass] += recordWeight;
        } while (columnMemberships.next());
    }
    if (missingWeight > EPSILON) {
        branchContainsMissingValues = true;
    } else {
        branchContainsMissingValues = false;
    }
    ArrayList<CombinedAttributeValues> attValList = Lists.newArrayList(combinedAttValsMap.values());
    CombinedAttributeValues[] attVals = combinedAttValsMap.values().toArray(new CombinedAttributeValues[combinedAttValsMap.size()]);
    attVals = BinaryNominalSplitsPCA.calculatePCAOrdering(attVals, totalWeight, targetVals.length);
    // EigenDecomposition failed
    if (attVals == null) {
        return null;
    }
    // Start searching for split candidates
    final int highestBitPosition = containsMissingValues() ? nomVals.length - 2 : nomVals.length - 1;
    final double[] binaryImpurityValues = new double[2];
    final double[] binaryPartitionWeights = new double[2];
    double sumRemainingWeights = totalWeight;
    double sumCurrPartitionWeight = 0.0;
    RealVector targetFrequenciesCurrentPartition = MatrixUtils.createRealVector(new double[targetVals.length]);
    RealVector targetFrequenciesRemaining = MatrixUtils.createRealVector(new double[targetVals.length]);
    for (CombinedAttributeValues attVal : attValList) {
        targetFrequenciesRemaining = targetFrequenciesRemaining.add(attVal.m_classFrequencyVector);
    }
    BigInteger currPartitionBitMask = BigInteger.ZERO;
    double bestPartitionGain = Double.NEGATIVE_INFINITY;
    BigInteger bestPartitionMask = null;
    boolean isBestSplitValid = false;
    boolean missingsGoLeft = false;
    final double priorImpurity = useXGBoostMissingValueHandling ? targetPriors.getPriorImpurity() : impCriterion.getPartitionImpurity(subtractMissingClassCounts(targetPriors.getDistribution(), missingClassCounts), totalWeight);
    // no need to iterate over full list because at least one value must remain on the other side of the split
    for (int i = 0; i < attVals.length - 1; i++) {
        CombinedAttributeValues currAttVal = attVals[i];
        sumCurrPartitionWeight += currAttVal.m_totalWeight;
        sumRemainingWeights -= currAttVal.m_totalWeight;
        assert sumCurrPartitionWeight + sumRemainingWeights == totalWeight : "The weights of the partitions do not sum up to the total weight.";
        targetFrequenciesCurrentPartition = targetFrequenciesCurrentPartition.add(currAttVal.m_classFrequencyVector);
        targetFrequenciesRemaining = targetFrequenciesRemaining.subtract(currAttVal.m_classFrequencyVector);
        currPartitionBitMask = currPartitionBitMask.or(currAttVal.m_bitMask);
        boolean partitionIsRightBranch = currPartitionBitMask.testBit(highestBitPosition);
        boolean isValidSplit;
        double gain;
        boolean tempMissingsGoLeft = true;
        if (branchContainsMissingValues && useXGBoostMissingValueHandling) {
            // send missing values with partition
            boolean isValidSplitFirst = sumCurrPartitionWeight + missingWeight >= minChildSize && sumRemainingWeights >= minChildSize;
            binaryImpurityValues[0] = impCriterion.getPartitionImpurity(addMissingClassCounts(targetFrequenciesCurrentPartition.toArray(), missingClassCounts), sumCurrPartitionWeight + missingWeight);
            binaryImpurityValues[1] = impCriterion.getPartitionImpurity(targetFrequenciesRemaining.toArray(), sumRemainingWeights);
            binaryPartitionWeights[0] = sumCurrPartitionWeight + missingWeight;
            binaryPartitionWeights[1] = sumRemainingWeights;
            double postSplitImpurity = impCriterion.getPostSplitImpurity(binaryImpurityValues, binaryPartitionWeights, totalWeight + missingWeight);
            double gainFirst = impCriterion.getGain(priorImpurity, postSplitImpurity, binaryPartitionWeights, totalWeight + missingWeight);
            // send missing values with remaining
            boolean isValidSplitSecond = sumCurrPartitionWeight >= minChildSize && sumRemainingWeights + missingWeight >= minChildSize;
            binaryImpurityValues[0] = impCriterion.getPartitionImpurity(targetFrequenciesCurrentPartition.toArray(), sumCurrPartitionWeight);
            binaryImpurityValues[1] = impCriterion.getPartitionImpurity(addMissingClassCounts(targetFrequenciesRemaining.toArray(), missingClassCounts), sumRemainingWeights + missingWeight);
            binaryPartitionWeights[0] = sumCurrPartitionWeight;
            binaryPartitionWeights[1] = sumRemainingWeights + missingWeight;
            postSplitImpurity = impCriterion.getPostSplitImpurity(binaryImpurityValues, binaryPartitionWeights, totalWeight + missingWeight);
            double gainSecond = impCriterion.getGain(priorImpurity, postSplitImpurity, binaryPartitionWeights, totalWeight + missingWeight);
            // choose alternative with better gain
            if (gainFirst >= gainSecond) {
                gain = gainFirst;
                isValidSplit = isValidSplitFirst;
                tempMissingsGoLeft = !partitionIsRightBranch;
            } else {
                gain = gainSecond;
                isValidSplit = isValidSplitSecond;
                tempMissingsGoLeft = partitionIsRightBranch;
            }
        } else {
            // TODO if invalid splits should not be considered skip partition
            isValidSplit = sumCurrPartitionWeight >= minChildSize && sumRemainingWeights >= minChildSize;
            binaryImpurityValues[0] = impCriterion.getPartitionImpurity(targetFrequenciesCurrentPartition.toArray(), sumCurrPartitionWeight);
            binaryImpurityValues[1] = impCriterion.getPartitionImpurity(targetFrequenciesRemaining.toArray(), sumRemainingWeights);
            binaryPartitionWeights[0] = sumCurrPartitionWeight;
            binaryPartitionWeights[1] = sumRemainingWeights;
            double postSplitImpurity = impCriterion.getPostSplitImpurity(binaryImpurityValues, binaryPartitionWeights, totalWeight);
            gain = impCriterion.getGain(priorImpurity, postSplitImpurity, binaryPartitionWeights, totalWeight);
        }
        // use random tie breaker if gains are equal
        boolean randomTieBreaker = gain == bestPartitionGain ? rd.nextInt(0, 1) == 1 : false;
        // store if better than before or first valid split
        if (gain > bestPartitionGain || (!isBestSplitValid && isValidSplit) || randomTieBreaker) {
            if (isValidSplit || !isBestSplitValid) {
                bestPartitionGain = gain;
                bestPartitionMask = partitionIsRightBranch ? currPartitionBitMask : BigInteger.ZERO.setBit(highestBitPosition + 1).subtract(BigInteger.ONE).xor(currPartitionBitMask);
                isBestSplitValid = isValidSplit;
                if (branchContainsMissingValues) {
                    missingsGoLeft = tempMissingsGoLeft;
                // missing values are encountered during the search for the best split
                // missingsGoLeft = partitionIsRightBranch;
                } else {
                    // no missing values were encountered during the search for the best split
                    // missing values should be sent with the majority
                    missingsGoLeft = partitionIsRightBranch ? sumCurrPartitionWeight < sumRemainingWeights : sumCurrPartitionWeight >= sumRemainingWeights;
                }
            }
        }
    }
    if (isBestSplitValid && bestPartitionGain > 0.0) {
        if (useXGBoostMissingValueHandling) {
            return new NominalBinarySplitCandidate(this, bestPartitionGain, bestPartitionMask, NO_MISSED_ROWS, missingsGoLeft ? NominalBinarySplitCandidate.MISSINGS_GO_LEFT : NominalBinarySplitCandidate.MISSINGS_GO_RIGHT);
        }
        return new NominalBinarySplitCandidate(this, bestPartitionGain, bestPartitionMask, getMissedRows(columnMemberships), NominalBinarySplitCandidate.NO_MISSINGS);
    }
    return null;
}

Example 2 with IImpurity

use of org.knime.base.node.mine.treeensemble2.learner.IImpurity in project knime-core by knime.

the class TreeNominalColumnData method calcBestSplitClassificationBinary.

NominalBinarySplitCandidate calcBestSplitClassificationBinary(final ColumnMemberships columnMemberships, final ClassificationPriors targetPriors, final TreeTargetNominalColumnData targetColumn, final IImpurity impCriterion, final NominalValueRepresentation[] nomVals, final NominalValueRepresentation[] targetVals, final RandomData rd) {
    if (nomVals.length <= 1) {
        return null;
    }
    final int minChildSize = getConfiguration().getMinChildSize();
    final int lengthNonMissing = containsMissingValues() ? nomVals.length - 1 : nomVals.length;
    // distribution of target for each attribute value
    final double[][] targetCountsSplitPerAttribute = new double[lengthNonMissing][targetVals.length];
    // number of valid records for each attribute value
    final double[] attWeights = new double[lengthNonMissing];
    // number (sum) of total valid values
    double totalWeight = 0.0;
    int start = 0;
    columnMemberships.next();
    for (int att = 0; att < lengthNonMissing; att++) {
        final int end = start + m_nominalValueCounts[att];
        double currentAttValWeight = 0.0;
        for (int index = columnMemberships.getIndexInColumn(); index < end; columnMemberships.next(), index = columnMemberships.getIndexInColumn()) {
            final double weight = columnMemberships.getRowWeight();
            assert weight > EPSILON : "The usage of datamemberships should ensure that no rows with zero weight are encountered";
            int target = targetColumn.getValueFor(columnMemberships.getOriginalIndex());
            targetCountsSplitPerAttribute[att][target] += weight;
            currentAttValWeight += weight;
        }
        totalWeight += currentAttValWeight;
        attWeights[att] = currentAttValWeight;
        start = end;
    }
    BinarySplitEnumeration splitEnumeration;
    if (nomVals.length <= 10) {
        splitEnumeration = new FullBinarySplitEnumeration(nomVals.length);
    } else {
        int maxSearch = (1 << 10 - 2);
        splitEnumeration = new RandomBinarySplitEnumeration(nomVals.length, maxSearch, rd);
    }
    BigInteger bestPartitionMask = null;
    boolean isBestSplitValid = false;
    double bestPartitionGain = Double.NEGATIVE_INFINITY;
    final double[] targetCountsSplitLeft = new double[targetVals.length];
    final double[] targetCountsSplitRight = new double[targetVals.length];
    final double[] binaryImpurityValues = new double[2];
    final double[] binaryPartitionWeights = new double[2];
    do {
        Arrays.fill(targetCountsSplitLeft, 0.0);
        Arrays.fill(targetCountsSplitRight, 0.0);
        double weightLeft = 0.0;
        double weightRight = 0.0;
        for (int i = 0; i < nomVals.length; i++) {
            final boolean isAttributeInRightBranch = splitEnumeration.isInRightBranch(i);
            double[] targetCountsCurrentAttribute = targetCountsSplitPerAttribute[i];
            for (int targetVal = 0; targetVal < targetVals.length; targetVal++) {
                if (isAttributeInRightBranch) {
                    targetCountsSplitRight[targetVal] += targetCountsCurrentAttribute[targetVal];
                } else {
                    targetCountsSplitLeft[targetVal] += targetCountsCurrentAttribute[targetVal];
                }
            }
            if (isAttributeInRightBranch) {
                weightRight += attWeights[i];
            } else {
                weightLeft += attWeights[i];
            }
        }
        binaryPartitionWeights[0] = weightRight;
        binaryPartitionWeights[1] = weightLeft;
        boolean isValidSplit = weightRight >= minChildSize && weightLeft >= minChildSize;
        binaryImpurityValues[0] = impCriterion.getPartitionImpurity(targetCountsSplitRight, weightRight);
        binaryImpurityValues[1] = impCriterion.getPartitionImpurity(targetCountsSplitLeft, weightLeft);
        double postSplitImpurity = impCriterion.getPostSplitImpurity(binaryImpurityValues, binaryPartitionWeights, totalWeight);
        double gain = impCriterion.getGain(targetPriors.getPriorImpurity(), postSplitImpurity, binaryPartitionWeights, totalWeight);
        // use random tie breaker if gains are equal
        boolean randomTieBreaker = gain == bestPartitionGain ? rd.nextInt(0, 1) == 1 : false;
        // store if better than before or first valid split
        if (gain > bestPartitionGain || (!isBestSplitValid && isValidSplit) || randomTieBreaker) {
            if (isValidSplit || !isBestSplitValid) {
                bestPartitionGain = gain;
                bestPartitionMask = splitEnumeration.getValueMask();
                isBestSplitValid = isValidSplit;
            }
        }
    } while (splitEnumeration.next());
    if (bestPartitionGain > 0.0) {
        return new NominalBinarySplitCandidate(this, bestPartitionGain, bestPartitionMask, getMissedRows(columnMemberships), NominalBinarySplitCandidate.NO_MISSINGS);
    }
    return null;
}

Example 3 with IImpurity

use of org.knime.base.node.mine.treeensemble2.learner.IImpurity in project knime-core by knime.

the class TreeNominalColumnData method calcBestSplitClassification.

/**
 * {@inheritDoc}
 */
@Override
public SplitCandidate calcBestSplitClassification(final DataMemberships dataMemberships, final ClassificationPriors targetPriors, final TreeTargetNominalColumnData targetColumn, final RandomData rd) {
    final NominalValueRepresentation[] targetVals = targetColumn.getMetaData().getValues();
    IImpurity impCriterion = targetPriors.getImpurityCriterion();
    // distribution of target for each attribute value
    final NominalValueRepresentation[] nomVals = getMetaData().getValues();
    final boolean useBinaryNominalSplits = getConfiguration().isUseBinaryNominalSplits();
    final ColumnMemberships columnMemberships = dataMemberships.getColumnMemberships(getMetaData().getAttributeIndex());
    if (useBinaryNominalSplits) {
        if (targetVals.length == 2) {
            return calcBestSplitClassificationBinaryTwoClass(columnMemberships, targetPriors, targetColumn, impCriterion, nomVals, targetVals, rd);
        } else {
            return calcBestSplitClassificationBinaryPCA(columnMemberships, targetPriors, targetColumn, impCriterion, nomVals, targetVals, rd);
        // return calcBestSplitClassificationBinary(membershipController, rowWeights, targetPriors, targetColumn,
        // impCriterion, nomVals, targetVals, originalIndexInColumnList, rd);
        }
    } else {
        return calcBestSplitClassificationMultiway(columnMemberships, targetPriors, targetColumn, impCriterion, nomVals, targetVals, rd);
    }
}

Example 4 with IImpurity

use of org.knime.base.node.mine.treeensemble2.learner.IImpurity in project knime-core by knime.

the class TreeBitVectorColumnData method calcBestSplitClassification.

/**
 * {@inheritDoc}
 */
@Override
public SplitCandidate calcBestSplitClassification(final DataMemberships dataMemberships, final ClassificationPriors targetPriors, final TreeTargetNominalColumnData targetColumn, final RandomData rd) {
    final NominalValueRepresentation[] targetVals = targetColumn.getMetaData().getValues();
    final IImpurity impurityCriterion = targetPriors.getImpurityCriterion();
    final int minChildSize = getConfiguration().getMinChildSize();
    // distribution of target for On ('1') and Off ('0') bits
    final double[] onTargetWeights = new double[targetVals.length];
    final double[] offTargetWeights = new double[targetVals.length];
    double onWeights = 0.0;
    double offWeights = 0.0;
    final ColumnMemberships columnMemberships = dataMemberships.getColumnMemberships(getMetaData().getAttributeIndex());
    while (columnMemberships.next()) {
        final double weight = columnMemberships.getRowWeight();
        if (weight < EPSILON) {
            // ignore record: not in current branch or not in sample
            assert false : "This code should never be reached!";
        } else {
            final int target = targetColumn.getValueFor(columnMemberships.getOriginalIndex());
            if (m_columnBitSet.get(columnMemberships.getIndexInColumn())) {
                onWeights += weight;
                onTargetWeights[target] += weight;
            } else {
                offWeights += weight;
                offTargetWeights[target] += weight;
            }
        }
    }
    if (onWeights < minChildSize || offWeights < minChildSize) {
        return null;
    }
    final double weightSum = onWeights + offWeights;
    final double onImpurity = impurityCriterion.getPartitionImpurity(onTargetWeights, onWeights);
    final double offImpurity = impurityCriterion.getPartitionImpurity(offTargetWeights, offWeights);
    final double[] partitionWeights = new double[] { onWeights, offWeights };
    final double postSplitImpurity = impurityCriterion.getPostSplitImpurity(new double[] { onImpurity, offImpurity }, partitionWeights, weightSum);
    final double gainValue = impurityCriterion.getGain(targetPriors.getPriorImpurity(), postSplitImpurity, partitionWeights, weightSum);
    return new BitSplitCandidate(this, gainValue);
}

Example 5 with IImpurity

use of org.knime.base.node.mine.treeensemble2.learner.IImpurity in project knime-core by knime.

the class TreeNumericColumnData method calcBestSplitClassification.

@Override
public NumericSplitCandidate calcBestSplitClassification(final DataMemberships dataMemberships, final ClassificationPriors targetPriors, final TreeTargetNominalColumnData targetColumn, final RandomData rd) {
    final TreeEnsembleLearnerConfiguration config = getConfiguration();
    final NominalValueRepresentation[] targetVals = targetColumn.getMetaData().getValues();
    final boolean useAverageSplitPoints = config.isUseAverageSplitPoints();
    final int minChildNodeSize = config.getMinChildSize();
    // distribution of target for each attribute value
    final int targetCounts = targetVals.length;
    final double[] targetCountsLeftOfSplit = new double[targetCounts];
    final double[] targetCountsRightOfSplit = targetPriors.getDistribution().clone();
    assert targetCountsRightOfSplit.length == targetCounts;
    final double totalSumWeight = targetPriors.getNrRecords();
    final IImpurity impurityCriterion = targetPriors.getImpurityCriterion();
    final boolean useXGBoostMissingValueHandling = config.getMissingValueHandling() == MissingValueHandling.XGBoost;
    // get columnMemberships
    final ColumnMemberships columnMemberships = dataMemberships.getColumnMemberships(getMetaData().getAttributeIndex());
    // missing value handling
    boolean branchContainsMissingValues = containsMissingValues();
    boolean missingsGoLeft = true;
    final int lengthNonMissing = getLengthNonMissing();
    final double[] missingTargetCounts = new double[targetCounts];
    int lastValidSplitPosition = -1;
    double missingWeight = 0;
    columnMemberships.goToLast();
    do {
        final int indexInColumn = columnMemberships.getIndexInColumn();
        if (indexInColumn >= lengthNonMissing) {
            final double weight = columnMemberships.getRowWeight();
            final int classIdx = targetColumn.getValueFor(columnMemberships.getOriginalIndex());
            targetCountsRightOfSplit[classIdx] -= weight;
            missingTargetCounts[classIdx] += weight;
            missingWeight += weight;
        } else {
            if (lastValidSplitPosition < 0) {
                lastValidSplitPosition = indexInColumn;
            } else if ((getSorted(lastValidSplitPosition) - getSorted(indexInColumn)) >= EPSILON) {
                break;
            } else {
                lastValidSplitPosition = indexInColumn;
            }
        }
    } while (columnMemberships.previous());
    // it is possible that the column contains missing values but in the current branch there are no missing values
    branchContainsMissingValues = missingWeight > 0.0;
    columnMemberships.reset();
    double sumWeightsLeftOfSplit = 0.0;
    double sumWeightsRightOfSplit = totalSumWeight - missingWeight;
    final double priorImpurity = useXGBoostMissingValueHandling || !branchContainsMissingValues ? targetPriors.getPriorImpurity() : impurityCriterion.getPartitionImpurity(TreeNominalColumnData.subtractMissingClassCounts(targetPriors.getDistribution(), missingTargetCounts), sumWeightsRightOfSplit);
    // all values in branch are missing
    if (sumWeightsRightOfSplit == 0) {
        // it is impossible to determine a split
        return null;
    }
    double bestSplit = Double.NEGATIVE_INFINITY;
    // gain for best split point, unnormalized (not using info gain ratio)
    double bestGain = Double.NEGATIVE_INFINITY;
    // gain for best split, normalized by attribute entropy when
    // info gain ratio is used.
    double bestGainValueForSplit = Double.NEGATIVE_INFINITY;
    final double[] tempArray1 = new double[2];
    double[] tempArray2 = new double[2];
    double lastSeenValue = Double.NEGATIVE_INFINITY;
    boolean mustTestOnNextValueChange = false;
    boolean testSplitOnStart = true;
    boolean firstIteration = true;
    int lastSeenTarget = -1;
    int indexInCol = -1;
    // We iterate over the instances in the sample/branch instead of the whole data set
    while (columnMemberships.next() && (indexInCol = columnMemberships.getIndexInColumn()) < lengthNonMissing) {
        final double weight = columnMemberships.getRowWeight();
        assert weight >= EPSILON : "Rows with zero row weight should never be seen!";
        final double value = getSorted(indexInCol);
        final int target = targetColumn.getValueFor(columnMemberships.getOriginalIndex());
        final boolean hasValueChanged = (value - lastSeenValue) >= EPSILON;
        final boolean hasTargetChanged = lastSeenTarget != target || indexInCol == lastValidSplitPosition;
        if (hasTargetChanged && !firstIteration) {
            mustTestOnNextValueChange = true;
            testSplitOnStart = false;
        }
        if (!firstIteration && hasValueChanged && (mustTestOnNextValueChange || testSplitOnStart) && sumWeightsLeftOfSplit >= minChildNodeSize && sumWeightsRightOfSplit >= minChildNodeSize) {
            double postSplitImpurity;
            boolean tempMissingsGoLeft = false;
            // missing value handling
            if (branchContainsMissingValues && useXGBoostMissingValueHandling) {
                final double[] targetCountsLeftPlusMissing = new double[targetCounts];
                final double[] targetCountsRightPlusMissing = new double[targetCounts];
                for (int i = 0; i < targetCounts; i++) {
                    targetCountsLeftPlusMissing[i] = targetCountsLeftOfSplit[i] + missingTargetCounts[i];
                    targetCountsRightPlusMissing[i] = targetCountsRightOfSplit[i] + missingTargetCounts[i];
                }
                final double[][] temp = new double[2][2];
                final double[] postSplitImpurities = new double[2];
                // send all missing values left
                tempArray1[0] = impurityCriterion.getPartitionImpurity(targetCountsLeftPlusMissing, sumWeightsLeftOfSplit + missingWeight);
                tempArray1[1] = impurityCriterion.getPartitionImpurity(targetCountsRightOfSplit, sumWeightsRightOfSplit);
                temp[0][0] = sumWeightsLeftOfSplit + missingWeight;
                temp[0][1] = sumWeightsRightOfSplit;
                postSplitImpurities[0] = impurityCriterion.getPostSplitImpurity(tempArray1, temp[0], totalSumWeight);
                // send all missing values right
                tempArray1[0] = impurityCriterion.getPartitionImpurity(targetCountsLeftOfSplit, sumWeightsLeftOfSplit);
                tempArray1[1] = impurityCriterion.getPartitionImpurity(targetCountsRightPlusMissing, sumWeightsRightOfSplit + missingWeight);
                temp[1][0] = sumWeightsLeftOfSplit;
                temp[1][1] = sumWeightsRightOfSplit + missingWeight;
                postSplitImpurities[1] = impurityCriterion.getPostSplitImpurity(tempArray1, temp[1], totalSumWeight);
                // take better split
                if (postSplitImpurities[0] < postSplitImpurities[1]) {
                    postSplitImpurity = postSplitImpurities[0];
                    tempArray2 = temp[0];
                    tempMissingsGoLeft = true;
                // TODO random tie breaker
                } else {
                    postSplitImpurity = postSplitImpurities[1];
                    tempArray2 = temp[1];
                    tempMissingsGoLeft = false;
                }
            } else {
                tempArray1[0] = impurityCriterion.getPartitionImpurity(targetCountsLeftOfSplit, sumWeightsLeftOfSplit);
                tempArray1[1] = impurityCriterion.getPartitionImpurity(targetCountsRightOfSplit, sumWeightsRightOfSplit);
                tempArray2[0] = sumWeightsLeftOfSplit;
                tempArray2[1] = sumWeightsRightOfSplit;
                postSplitImpurity = impurityCriterion.getPostSplitImpurity(tempArray1, tempArray2, totalSumWeight);
            }
            if (postSplitImpurity < priorImpurity) {
                // Use absolute gain (IG) for split calculation even
                // if the split criterion is information gain ratio (IGR).
                // IGR wouldn't work as it favors extreme unfair splits,
                // i.e. 1:9999 would have an attribute entropy
                // (IGR denominator) of
                // 9999/10000*log(9999/10000) + 1/10000*log(1/10000)
                // which is ~0.00148
                double gain = (priorImpurity - postSplitImpurity);
                boolean randomTieBreaker = gain == bestGain ? rd.nextInt(0, 1) == 1 : false;
                if (gain > bestGain || randomTieBreaker) {
                    bestGainValueForSplit = impurityCriterion.getGain(priorImpurity, postSplitImpurity, tempArray2, totalSumWeight);
                    bestGain = gain;
                    bestSplit = useAverageSplitPoints ? getCenter(lastSeenValue, value) : lastSeenValue;
                    // Go with the majority if there are no missing values during training this is because we should
                    // still provide a missing direction for the case that there are missing values during prediction
                    missingsGoLeft = branchContainsMissingValues ? tempMissingsGoLeft : sumWeightsLeftOfSplit > sumWeightsRightOfSplit;
                }
            }
            mustTestOnNextValueChange = false;
        }
        targetCountsLeftOfSplit[target] += weight;
        sumWeightsLeftOfSplit += weight;
        targetCountsRightOfSplit[target] -= weight;
        sumWeightsRightOfSplit -= weight;
        lastSeenTarget = target;
        lastSeenValue = value;
        firstIteration = false;
    }
    columnMemberships.reset();
    if (bestGainValueForSplit < 0.0) {
        // (see info gain ratio implementation)
        return null;
    }
    if (useXGBoostMissingValueHandling) {
        // return new NumericMissingSplitCandidate(this, bestSplit, bestGainValueForSplit, missingsGoLeft);
        return new NumericSplitCandidate(this, bestSplit, bestGainValueForSplit, new BitSet(), missingsGoLeft ? NumericSplitCandidate.MISSINGS_GO_LEFT : NumericSplitCandidate.MISSINGS_GO_RIGHT);
    }
    return new NumericSplitCandidate(this, bestSplit, bestGainValueForSplit, getMissedRows(columnMemberships), NumericSplitCandidate.NO_MISSINGS);
}