// // The sum of the specific conditional entropies * the probability of
    // each
    // // value for each value in ix_attr.
    public static double conditionalEntropy(List<Instance> instances,
            Integer ix_attr) {
        double sum = 0.0;
        Map<Integer, List<Instance>> instancesByAttrVal = binInstancesByVal(
                instances, ix_attr);
        for (List<Instance> filteredInstances : instancesByAttrVal.values()) {
            // probability of being in this set is equal to the number of items
            // in the set divided by the total number of items
            double probability = filteredInstances.size()
                    / (double) instances.size();
            // specific conditional entropy
            sum += entropy(filteredInstances) * probability;
        }

        return sum;
    }

    public static Map<Integer, List<Instance>> binInstancesByVal(
            List<Instance> instances, Integer ix_attr) {
        if (instances == null || ix_attr < 0)
            throw new IllegalArgumentException();

        Map<Integer, List<Instance>> instancesByVal = new HashMap<Integer, List<Instance>>();

        for (Instance i : instances) {
            int val = i.attributes.get(ix_attr);
            instancesByVal.putIfAbsent(val, new ArrayList<Instance>());
            List<Instance> l = instancesByVal.get(val);
            l.add(i);
        }

        return instancesByVal;
    }

    // Based on diversity of label
    public static double entropy(List<Instance> instances) {
        if (instances == null)
            throw new IllegalArgumentException();

        double sum = 0.0;
        Map<Integer, Integer> numInstancesByLabel = countInstancesByLabel(instances);
        for (int num : numInstancesByLabel.values()) {
            double probability = (double) num / instances.size();
            // add Pr(i) * lg_2(Pr(i))
            sum -= probability * Math.log(probability) / Math.log(2);
        }

        return sum;
    }

    public static Map<Integer, Integer> countInstancesByLabel(
            List<Instance> instances) {
        if (instances == null)
            throw new IllegalArgumentException();

        Map<Integer, Integer> numInstancesByLabel = new HashMap<Integer, Integer>();
        for (Instance i : instances) {
            int num = 0;
            if (numInstancesByLabel.containsKey(i.label))
                num = numInstancesByLabel.get(i.label);
            numInstancesByLabel.put(i.label, num + 1);
        }
        return numInstancesByLabel;
    }
    public void rootInfoGain(DataSet train) {
        this.labels = train.labels;
        this.attributes = train.attributes;
        this.attributeValues = train.attributeValues;

        for (int i = 0; i < attributes.size(); i++) {
            System.out
                    .printf("%s %.5f\n", attributes.get(i),
                            1.0 - DecisionTreeImpl.conditionalEntropy(
                                    train.instances, i));
        }
    }