Source

orange-reliability / orangecontrib / reliability / __init__.py

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import Orange

import random
from Orange import statc
import math
import warnings
import numpy

from collections import defaultdict
from itertools import izip

# All the estimator method constants
SAVAR_ABSOLUTE = 0
SABIAS_SIGNED = 1
SABIAS_ABSOLUTE = 2
BAGV_ABSOLUTE = 3
CNK_SIGNED = 4
CNK_ABSOLUTE = 5
LCV_ABSOLUTE = 6
BVCK_ABSOLUTE = 7
MAHAL_ABSOLUTE = 8
BLENDING_ABSOLUTE = 9
ICV_METHOD = 10
MAHAL_TO_CENTER_ABSOLUTE = 13
DENS_ABSOLUTE = 14
ERR_ABSOLUTE = 15
STACKING = 101

# Type of estimator constant
SIGNED = 0
ABSOLUTE = 1

# Names of all the estimator methods
METHOD_NAME = {0: "SAvar absolute", 1: "SAbias signed", 2: "SAbias absolute",
               3: "BAGV absolute", 4: "CNK signed", 5: "CNK absolute",
               6: "LCV absolute", 7: "BVCK absolute", 8: "Mahalanobis absolute",
               9: "BLENDING absolute", 10: "ICV", 11: "RF Variance", 12: "RF Std",
               13: "Mahalanobis to center", 14: "Density based", 15: "Reference expected error",
               101: "Stacking" }

def get_reliability_estimation_list(res, i):
    return [ result.probabilities[0].reliability_estimate[i].estimate for result in res.results], \
        res.results[0].probabilities[0].reliability_estimate[i].signed_or_absolute, \
        res.results[0].probabilities[0].reliability_estimate[i].method

def get_prediction_error_list(res):
    return [result.actual_class - result.classes[0] for result in res.results]

def get_description_list(res, i):
    return [result.probabilities[0].reliability_estimate[i].text_description for result in res.results]

def get_pearson_r(res):
    """
    :param res: Evaluation results with :obj:`reliability_estimate`.
    :type res: :class:`Orange.evaluation.testing.ExperimentResults`

    Pearson's coefficients between the prediction error and 
    reliability estimates with p-values.
    """
    prediction_error = get_prediction_error_list(res)
    results = []
    for i in xrange(len(res.results[0].probabilities[0].reliability_estimate)):
        reliability_estimate, signed_or_absolute, method = get_reliability_estimation_list(res, i)
        try:
            if signed_or_absolute == SIGNED:
                r, p = statc.pearsonr(prediction_error, reliability_estimate)
            else:
                r, p = statc.pearsonr([abs(pe) for pe in prediction_error], reliability_estimate)
        except Exception:
            r = p = float("NaN")
        results.append((r, p, signed_or_absolute, method))
    return results

def get_spearman_r(res):
    """
    :param res: Evaluation results with :obj:`reliability_estimate`.
    :type res: :class:`Orange.evaluation.testing.ExperimentResults`

    Spearman's coefficients between the prediction error and 
    reliability estimates with p-values.
    """
    prediction_error = get_prediction_error_list(res)
    results = []
    for i in xrange(len(res.results[0].probabilities[0].reliability_estimate)):
        reliability_estimate, signed_or_absolute, method = get_reliability_estimation_list(res, i)
        try:
            if signed_or_absolute == SIGNED:
                r, p = statc.spearmanr(prediction_error, reliability_estimate)
            else:
                r, p = statc.spearmanr([abs(pe) for pe in prediction_error], reliability_estimate)
        except Exception:
            r = p = float("NaN")
        results.append((r, p, signed_or_absolute, method))
    return results

def get_pearson_r_by_iterations(res):
    """
    :param res: Evaluation results with :obj:`reliability_estimate`.
    :type res: :class:`Orange.evaluation.testing.ExperimentResults`

    Pearson's coefficients between prediction error
    and reliability estimates averaged over all folds.
    """
    results_by_fold = Orange.evaluation.scoring.split_by_iterations(res)
    number_of_estimates = len(res.results[0].probabilities[0].reliability_estimate)
    number_of_instances = len(res.results)
    number_of_folds = len(results_by_fold)
    results = [0 for _ in xrange(number_of_estimates)]
    M
    sig = [0 for _ in xrange(number_of_estimates)]
    method_list = [0 for _ in xrange(number_of_estimates)]

    for res in results_by_fold:
        prediction_error = get_prediction_error_list(res)
        for i in xrange(number_of_estimates):
            reliability_estimate, signed_or_absolute, method = get_reliability_estimation_list(res, i)
            try:
                if signed_or_absolute == SIGNED:
                    r, _ = statc.pearsonr(prediction_error, reliability_estimate)
                else:
                    r, _ = statc.pearsonr([abs(pe) for pe in prediction_error], reliability_estimate)
            except Exception:
                r = float("NaN")
            results[i] += r
            sig[i] = signed_or_absolute
            method_list[i] = method

    # Calculate p-values
    results = [float(res) / number_of_folds for res in results]
    ps = [p_value_from_r(r, number_of_instances) for r in results]

    return zip(results, ps, sig, method_list)

def p_value_from_r(r, n):
    """
    Calculate p-value from the paerson coefficient and the sample size.
    """
    df = n - 2
    t = r * (df / ((-r + 1.0 + 1e-30) * (r + 1.0 + 1e-30))) ** 0.5
    return statc.betai (df * 0.5, 0.5, df / (df + t * t))


# Distances between two discrete probability distributions
#TODO Document those.
def normalize_both(p, q):
    if not p.normalized:
        p.normalize()
    if not q.normalized:
        q.normalize()
    return p, q

def minkowsky_dist(p, q, m=2):
    p, q = normalize_both(p, q)
    dist = 0
    for i in range(len(p)):
        dist += abs(p[i]-q[i])**m
    return dist**(1./m)

def manhattan_distance(p, q):
    return minkowsky_dist(p, q, m=1)

def euclidean_dist(p, q):
    return minkowsky_dist(p, q, m=2)

def variance_dist(p, q):
    return euclidean_dist(p, q) ** 2

def max_dist(p, q):
    p, q = normalize_both(p, q)
    return max([abs(p[i]-q[i]) for i in range(len(p))])

def hellinger_dist(p, q):
    p, q = normalize_both(p, q)
    dist = 0
    for i in range(len(p)):
        dist += (math.sqrt(p[i])-math.sqrt(q[i])) ** 2
    return dist

def my_log(x):
    return 0 if x == 0 else x * math.log(x)

def kullback_leibler(p, q):
    p, q = normalize_both(p, q)
    dist = 0
    for i in range(len(p)):
        dist += my_log(p[i]-q[i])
    return dist

def cosine(p, q):
    p, q = normalize_both(p, q)
    p, q = [pp for pp in p], [qq for qq in q]
    return 1 - numpy.dot(x,y) / (numpy.linalg.norm(p)*numpy.linalg.norm(q))


class Estimate:
    """
    Describes a reliability estimate.

    .. attribute:: estimate

        Value of reliability.

    .. attribute:: signed_or_absolute

        Determines whether the method returned a signed or absolute result.
        Has a value of either :obj:`SIGNED` or :obj:`ABSOLUTE`.

    .. attribute:: method

        An integer ID of the reliability estimation method used.

    .. attribute:: method_name

        Name (string) of the reliability estimation method used.

    """
    def __init__(self, estimate, signed_or_absolute, method):
        self.estimate = estimate
        self.signed_or_absolute = signed_or_absolute
        self.method = method
        self.method_name = METHOD_NAME[method]
        self.text_description = None

class DescriptiveAnalysis:
    def __init__(self, estimator, desc=["high", "medium", "low"], procentage=[0.00, 0.33, 0.66], name="da"):
        self.desc = desc
        self.procentage = procentage
        self.estimator = estimator
        self.name = name

    def __call__(self, instances, weight=None, **kwds):

        # Calculate borders using cross validation
        res = Orange.evaluation.testing.cross_validation([self.estimator], instances)
        all_borders = []
        for i in xrange(len(res.results[0].probabilities[0].reliability_estimate)):
            estimates, signed_or_absolute, method = get_reliability_estimation_list(res, i)
            sorted_estimates = sorted(abs(x) for x in estimates)
            borders = [sorted_estimates[int(len(estimates) * p) - 1]  for p in self.procentage]
            all_borders.append(borders)

        # Learn on whole train data
        estimator_classifier = self.estimator(instances)

        return DescriptiveAnalysisClassifier(estimator_classifier, all_borders, self.desc)

class DescriptiveAnalysisClassifier:
    def __init__(self, estimator_classifier, all_borders, desc):
        self.estimator_classifier = estimator_classifier
        self.all_borders = all_borders
        self.desc = desc

    def __call__(self, instance, result_type=Orange.core.GetValue):
        predicted, probabilities = self.estimator_classifier(instance, Orange.core.GetBoth)

        for borders, estimate in zip(self.all_borders, probabilities.reliability_estimate):
            estimate.text_description = self.desc[0]
            for lower_border, text_desc in zip(borders, self.desc):
                if estimate.estimate >= lower_border:
                    estimate.text_description = text_desc

        # Return the appropriate type of result
        if result_type == Orange.core.GetValue:
            return predicted
        elif result_type == Orange.core.GetProbabilities:
            return probabilities
        else:
            return predicted, probabilities

class SensitivityAnalysis:
    """
    
    :param e: Values of :math:`\epsilon`.
    :type e: list of floats
    
    :rtype: :class:`Orange.evaluation.reliability.SensitivityAnalysisClassifier`
    
    The learning set is extended with that instancem, where the label is changed to 
    :math:`K + \epsilon (l_{max} - l_{min})` (:math:`K` is  the initial prediction,
    :math:`\epsilon` a sensitivity parameter, and :math:`l_{min}` and
    :math:`l_{max}` the lower and upper bounds of labels on training data).
    Results for multiple values of :math:`\epsilon` are combined
    into SAvar and SAbias. SAbias has a signed or absolute form.

    :math:`SAvar = \\frac{\sum_{\epsilon \in E}(K_{\epsilon} - K_{-\epsilon})}{|E|}`
    :math:`SAbias = \\frac{\sum_{\epsilon \in E} (K_{\epsilon} - K ) + (K_{-\epsilon} - K)}{2 |E|}`
    
    
    """
    def __init__(self, e=[0.01, 0.1, 0.5, 1.0, 2.0], name="sa"):
        self.e = e
        self.name = name

    def __call__(self, instances, learner):
        min_value = max_value = instances[0].getclass().value
        for ex in instances:
            if ex.getclass().value > max_value:
                max_value = ex.getclass().value
            if ex.getclass().value < min_value:
                min_value = ex.getclass().value
        return SensitivityAnalysisClassifier(self.e, instances, min_value, max_value, learner)

class SensitivityAnalysisClassifier:
    def __init__(self, e, instances, min_value, max_value, learner):
        self.e = e
        self.instances = instances
        self.max_value = max_value
        self.min_value = min_value
        self.learner = learner

    def __call__(self, instance, predicted, probabilities):
        # Create new dataset
        r_data = Orange.data.Table(self.instances)

        # Create new instance
        modified_instance = Orange.data.Instance(instance)

        # Append it to the data
        r_data.append(modified_instance)

        # Calculate SAvar & SAbias
        SAvar = SAbias = 0

        for eps in self.e:
            # +epsilon
            r_data[-1].setclass(predicted.value + eps * (self.max_value - self.min_value))
            c = self.learner(r_data)
            k_plus = c(instance, Orange.core.GetValue)

            # -epsilon
            r_data[-1].setclass(predicted.value - eps * (self.max_value - self.min_value))
            c = self.learner(r_data)
            k_minus = c(instance, Orange.core.GetValue)
            #print len(r_data)
            #print eps*(self.max_value - self.min_value)
            #print k_plus
            #print k_minus
            # calculate part SAvar and SAbias
            SAvar += k_plus.value - k_minus.value
            SAbias += k_plus.value + k_minus.value - 2 * predicted.value

        SAvar /= len(self.e)
        SAbias /= 2 * len(self.e)

        return [Estimate(SAvar, ABSOLUTE, SAVAR_ABSOLUTE),
                Estimate(SAbias, SIGNED, SABIAS_SIGNED),
                Estimate(abs(SAbias), ABSOLUTE, SABIAS_ABSOLUTE)]



class ReferenceExpectedError:
    """

    :rtype: :class:`Orange.evaluation.reliability.ReferenceExpectedErrorClassifier`

    Reference estimate for classification: :math:`O_{ref} = 2 (\hat y - \hat y ^2) = 2 \hat y (1-\hat y)`, where :math:`\hat y` is the estimated probability of the predicted class [Pevec2011]_.

    A greater estimate means a greater expected error.

    """
    def __init__(self, name="reference"):
        self.name = name

    def __call__(self, instances, learner):
        classifier = learner(instances)
        return ReferenceExpectedErrorClassifier(classifier)

    
class ReferenceExpectedErrorClassifier:

    def __init__(self, classifier):
        self.classifier = classifier

    def __call__(self, instance, *args):
        y_hat = max(self.classifier(instance, Orange.classification.Classifier.GetProbabilities))
        return [Estimate(2 * y_hat * (1 - y_hat), ABSOLUTE, ERR_ABSOLUTE)]


class BaggingVariance:
    """
    
    :param m: Number of bagged models. Default: 50.
    :type m: int
    
    :param for_instances:  Optional. If test instances
      are given as a parameter, this class can compute their reliabilities
      on the fly, which saves memory. 

    :type for_intances: Orange.data.Table
    
    :rtype: :class:`Orange.evaluation.reliability.BaggingVarianceClassifier`
    
    For regression, BAGV is the variance of predictions:

    :math:`BAGV = \\frac{1}{m} \sum_{i=1}^{m} (K_i - K)^2`, where 
    :math:`K = \\frac{\sum_{i=1}^{m} K_i}{m}` and :math:`K_i` are
    predictions of individual models.

    For classification, BAGV is 1 minus the average Euclidean
    distance between class probability distributions predicted by the
    model, and distributions predicted by the individual bagged model;
    a greater value implies a better prediction.

    This reliability measure can run out of memory if individual classifiers themselves
    use a lot of memory; it needs :math:`m` times memory
    for a single classifier. 
    """
    def __init__(self, m=50, name="bv", randseed=0, for_instances=None):

        self.m = m
        self.name = name
        self.select_with_repeat = Orange.core.MakeRandomIndicesMultiple()
        self.select_with_repeat.random_generator = Orange.misc.Random(randseed)
        self.for_instances = for_instances

    def __call__(self, instances, learner):
        classifiers = []

        if instances.domain.class_var.var_type == Orange.feature.Descriptor.Discrete:
            classifier = learner(instances)
        else:
            classifier = None

        for_inst_class = defaultdict(list)
        this_iteration = None
        
        if self.for_instances:
            his = map(_hashable_instance, self.for_instances)

        # Create bagged classifiers using sampling with replacement
        for i in xrange(self.m):
            this_iteration = set()
            selection = self.select_with_repeat(len(instances))
            data = instances.select(selection)
            cl = learner(data)
            if cl:
                if self.for_instances: # predict reliability for testing instances and throw cl away
                    for instance, hi in zip(self.for_instances, his):
                        if hi not in this_iteration:
                            for_inst_class[hi].append(_bagged_value(instance, cl, classifier))
                            this_iteration.add(hi)
                else:
                    classifiers.append(cl)

        return BaggingVarianceClassifier(classifiers, classifier, for_inst_class=dict(for_inst_class))

class BaggingVarianceClassifier:
    def __init__(self, classifiers, classifier=None, for_inst_class=None):
        self.classifiers = classifiers
        self.classifier = classifier
        self.for_inst_class = for_inst_class

    def __call__(self, instance, *args):
        BAGV = 0

        # Calculate the bagging variance
        if self.for_inst_class:
            bagged_values = self.for_inst_class[_hashable_instance(instance)]
        else:
            bagged_values = [ _bagged_value(instance, c, self.classifier) for c in self.classifiers ]

        k = sum(bagged_values) / len(bagged_values)

        BAGV = sum((bagged_value - k) ** 2 for bagged_value in bagged_values) / len(bagged_values)
        if instance.domain.class_var.var_type == Orange.feature.Descriptor.Discrete:
            BAGV = 1 - BAGV

        return [Estimate(BAGV, ABSOLUTE, BAGV_ABSOLUTE)]

def _hashable_instance(instance):
    return tuple(instance[i].value for i in range(len(instance.domain.attributes)))

def _bagged_value(instance, c, classifier):
    if instance.domain.class_var.var_type == Orange.feature.Descriptor.Continuous:
        return c(instance, Orange.core.GetValue).value
    elif instance.domain.class_var.var_type == Orange.feature.Descriptor.Discrete:
        estimate = classifier(instance, Orange.core.GetProbabilities)
        return euclidean_dist(c(instance, Orange.core.GetProbabilities), estimate)


class LocalCrossValidation:
    """

    :param k: Number of nearest neighbours used. Default: 0, which denotes
        1/20 of data set size (or 5, whichever is greater).
    :type k: int

    :param distance: Function that computes a distance between two discrete
        distributions (used only in classification problems). The default
        is Hellinger distance.
    :type distance: function

    :param distance_weighted: Relevant only for classification;
        use an average distance between distributions, weighted by :math:`e^{-d}`,
        where :math:`d` is the distance between predicted instance and the
        neighbour.

    :rtype: :class:`Orange.evaluation.reliability.LocalCrossValidationClassifier`

    Leave-one-out validation is
    performed on :math:`k` nearest neighbours to the given instance.
    Reliability estimate for regression is then the distance
    weighted absolute prediction error. For classification, it is 1 minus the average
    distance between the predicted class probability distribution and the
    (trivial) probability distributions of the nearest neighbour.
    """
    def __init__(self, k=0, distance=hellinger_dist, distance_weighted=True, name="lcv"):
        self.k = k
        self.distance = distance
        self.distance_weighted = distance_weighted
        self.name = name

    def __call__(self, instances, learner):
        nearest_neighbours_constructor = Orange.classification.knn.FindNearestConstructor()
        nearest_neighbours_constructor.distanceConstructor = Orange.distance.Euclidean()

        distance_id = Orange.feature.Descriptor.new_meta_id()
        nearest_neighbours = nearest_neighbours_constructor(instances, 0, distance_id)

        if self.k == 0:
            self.k = max(5, len(instances) / 20)

        return LocalCrossValidationClassifier(distance_id, nearest_neighbours, self.k, learner,
            distance=self.distance, distance_weighted=self.distance_weighted)

class LocalCrossValidationClassifier:
    def __init__(self, distance_id, nearest_neighbours, k, learner, **kwds):
        self.distance_id = distance_id
        self.nearest_neighbours = nearest_neighbours
        self.k = k
        self.learner = learner
        for a,b in kwds.items():
            setattr(self, a, b)

    def __call__(self, instance, *args):
        LCVer = 0
        LCVdi = 0

        # Find k nearest neighbors

        knn = [ex for ex in self.nearest_neighbours(instance, self.k)]

        # leave one out of prediction error
        for i in xrange(len(knn)):
            train = knn[:]
            del train[i]

            classifier = self.learner(Orange.data.Table(train))

            if instance.domain.class_var.var_type == Orange.feature.Descriptor.Continuous:
                returned_value = classifier(knn[i], Orange.core.GetValue)
                e = abs(knn[i].getclass().value - returned_value.value)

            elif instance.domain.class_var.var_type == Orange.feature.Descriptor.Discrete:
                returned_value = classifier(knn[i], Orange.core.GetProbabilities)
                probabilities = [knn[i].get_class() == val for val in instance.domain.class_var.values]
                e = self.distance(returned_value, Orange.statistics.distribution.Discrete(probabilities))

            dist = math.exp(-knn[i][self.distance_id]) if self.distance_weighted else 1.0
            LCVer += e * dist
            LCVdi += dist

        LCV = LCVer / LCVdi if LCVdi != 0 else 0
        if math.isnan(LCV):
            LCV = 0.0

        if instance.domain.class_var.var_type == Orange.feature.Descriptor.Discrete:
            LCV = 1 - LCV

        return [ Estimate(LCV, ABSOLUTE, LCV_ABSOLUTE) ]

class CNeighbours:
    """
    
    :param k: Number of nearest neighbours.
    :type k: int

    :param distance: function that computes a distance between two discrete
        distributions (used only in classification problems). The default
        is Hellinger distance.
    :type distance: function
    
    :rtype: :class:`Orange.evaluation.reliability.CNeighboursClassifier`
    
    For regression, CNK is a difference
    between average label of its nearest neighbours and the prediction. CNK
    can be either signed or absolute. A greater value implies greater prediction error.

    For classification, CNK is equal to 1 minus the average distance between
    predicted class distribution and (trivial) class distributions of the
    $k$ nearest neighbours from the learning set. A greater value implies better prediction.
    
    """
    def __init__(self, k=5, distance=hellinger_dist, name = "cnk"):
        self.k = k
        self.distance = distance
        self.name = name

    def __call__(self, instances, learner):
        nearest_neighbours_constructor = Orange.classification.knn.FindNearestConstructor()
        nearest_neighbours_constructor.distanceConstructor = Orange.distance.Euclidean()

        distance_id = Orange.feature.Descriptor.new_meta_id()
        nearest_neighbours = nearest_neighbours_constructor(instances, 0, distance_id)
        return CNeighboursClassifier(nearest_neighbours, self.k, distance=self.distance)

class CNeighboursClassifier:
    def __init__(self, nearest_neighbours, k, distance):
        self.nearest_neighbours = nearest_neighbours
        self.k = k
        self.distance = distance

    def __call__(self, instance, predicted, probabilities):
        CNK = 0

        # Find k nearest neighbors

        knn = [ex for ex in self.nearest_neighbours(instance, self.k)]

        # average label of neighbors
        if ex.domain.class_var.var_type == Orange.feature.Descriptor.Continuous:
            for ex in knn:
                CNK += ex.getclass().value
            CNK /= self.k
            CNK -= predicted.value

            return [Estimate(CNK, SIGNED, CNK_SIGNED),
                    Estimate(abs(CNK), ABSOLUTE, CNK_ABSOLUTE)]
        elif ex.domain.class_var.var_type == Orange.feature.Descriptor.Discrete:
            knn_l = Orange.classification.knn.kNNLearner(k=self.k)
            knn_c = knn_l(knn)
            for ex in knn:
                CNK -= self.distance(probabilities, knn_c(ex, Orange.classification.Classifier.GetProbabilities))
            CNK /= self.k
            CNK += 1

            return [Estimate(CNK, ABSOLUTE, CNK_ABSOLUTE)]

class Mahalanobis:
    """
    
    :param k: Number of nearest neighbours used in Mahalanobis estimate.
    :type k: int
    
    :rtype: :class:`Orange.evaluation.reliability.MahalanobisClassifier`
    
    Mahalanobis distance reliability estimate is defined as
    `Mahalanobis distance <http://en.wikipedia.org/wiki/Mahalanobis_distance>`_
    to the evaluated instance's :math:`k` nearest neighbours.

    
    """
    def __init__(self, k=3, name="mahalanobis"):
        self.k = k
        self.name = name

    def __call__(self, instances, *args):
        nnm = Orange.classification.knn.FindNearestConstructor()
        nnm.distanceConstructor = Orange.distance.Mahalanobis()

        mid = Orange.feature.Descriptor.new_meta_id()
        nnm = nnm(instances, 0, mid)
        return MahalanobisClassifier(self.k, nnm, mid)

class MahalanobisClassifier:
    def __init__(self, k, nnm, mid):
        self.k = k
        self.nnm = nnm
        self.mid = mid

    def __call__(self, instance, *args):
        mahalanobis_distance = 0

        mahalanobis_distance = sum(ex[self.mid].value for ex in self.nnm(instance, self.k))

        return [ Estimate(mahalanobis_distance, ABSOLUTE, MAHAL_ABSOLUTE) ]

class MahalanobisToCenter:
    """
    :rtype: :class:`Orange.evaluation.reliability.MahalanobisToCenterClassifier`
    
    Mahalanobis distance to center reliability estimate is defined as a
    `Mahalanobis distance <http://en.wikipedia.org/wiki/Mahalanobis_distance>`_
    between the predicted instance and the centroid of the data.

    
    """
    def __init__(self, name="mahalanobis to center"):
        self.name = name

    def __call__(self, instances, *args):
        dc = Orange.core.DomainContinuizer()
        dc.classTreatment = Orange.core.DomainContinuizer.Ignore
        dc.continuousTreatment = Orange.core.DomainContinuizer.NormalizeBySpan
        dc.multinomialTreatment = Orange.core.DomainContinuizer.NValues

        new_domain = dc(instances)
        new_instances = instances.translate(new_domain)

        X, _, _ = new_instances.to_numpy()
        instance_avg = numpy.average(X, 0)

        distance_constructor = Orange.distance.Mahalanobis()
        distance = distance_constructor(new_instances)

        average_instance = Orange.data.Instance(new_instances.domain, list(instance_avg) + ["?"])

        return MahalanobisToCenterClassifier(distance, average_instance, new_domain)

class MahalanobisToCenterClassifier:
    def __init__(self, distance, average_instance, new_domain):
        self.distance = distance
        self.average_instance = average_instance
        self.new_domain = new_domain

    def __call__(self, instance, *args):

        inst = Orange.data.Instance(self.new_domain, instance)

        mahalanobis_to_center = self.distance(inst, self.average_instance)

        return [ Estimate(mahalanobis_to_center, ABSOLUTE, MAHAL_TO_CENTER_ABSOLUTE) ]


class BaggingVarianceCNeighbours:
    """
    
    :param bagv: Instance of Bagging Variance estimator.
    :type bagv: :class:`BaggingVariance`
    
    :param cnk: Instance of CNK estimator.
    :type cnk: :class:`CNeighbours`
    
    :rtype: :class:`Orange.evaluation.reliability.BaggingVarianceCNeighboursClassifier`
    
    BVCK is an average of Bagging variance and local modeling of
    prediction error.
    
    """
    def __init__(self, bagv=None, cnk=None, name="bvck"):
        if bagv is None:
            bagv = BaggingVariance()
        if cnk is None:
            cnk = CNeighbours()
        self.bagv = bagv
        self.cnk = cnk
        self.name = "bvck"

    def __call__(self, instances, learner):
        bagv_classifier = self.bagv(instances, learner)
        cnk_classifier = self.cnk(instances, learner)
        return BaggingVarianceCNeighboursClassifier(bagv_classifier, cnk_classifier)

class BaggingVarianceCNeighboursClassifier:
    def __init__(self, bagv_classifier, cnk_classifier):
        self.bagv_classifier = bagv_classifier
        self.cnk_classifier = cnk_classifier

    def __call__(self, instance, predicted, probabilities):
        bagv_estimates = self.bagv_classifier(instance, predicted, probabilities)
        cnk_estimates = self.cnk_classifier(instance, predicted, probabilities)

        bvck_value = (bagv_estimates[0].estimate + cnk_estimates[1].estimate) / 2
        bvck_estimates = [ Estimate(bvck_value, ABSOLUTE, BVCK_ABSOLUTE) ]
        bvck_estimates.extend(bagv_estimates)
        bvck_estimates.extend(cnk_estimates)
        return bvck_estimates

class ErrorPredicting:
    def __init__(self, name = "ep"):
        self.name = name

    def __call__(self, instances, learner):
        res = Orange.evaluation.testing.cross_validation([learner], instances)
        prediction_errors = get_prediction_error_list(res)

        new_domain = Orange.data.Domain(instances.domain.attributes, Orange.core.FloatVariable("pe"))
        new_dataset = Orange.data.Table(new_domain, instances)

        for instance, prediction_error in izip(new_dataset, prediction_errors):
            instance.set_class(prediction_error)

        rf = Orange.ensemble.forest.RandomForestLearner()
        rf_classifier = rf(new_dataset)

        return ErrorPredictingClassification(rf_classifier, new_domain)

class ErrorPredictingClassification:
    def __init__(self, rf_classifier, new_domain):
        self.rf_classifier = rf_classifier
        self.new_domain = new_domain

    def __call__(self, instance, predicted, probabilities):
        new_instance = Orange.data.Instance(self.new_domain, instance)
        value = self.rf_classifier(new_instance, Orange.core.GetValue)

        return [Estimate(value.value, SIGNED, SABIAS_SIGNED)]

def gauss_kernel(x, sigma=1):
    return 1./(sigma*math.sqrt(2*math.pi)) * math.exp(-1./2*(x/sigma)**2)

class ParzenWindowDensityBased:
    """
    :param K: kernel function. Default: gaussian.
    :type K: function

    :param d_measure: distance measure for inter-instance distance.
    :type d_measure: :class:`Orange.distance.DistanceConstructor`

    :rtype: :class:`Orange.evaluation.reliability.ParzenWindowDensityBasedClassifier`

    Returns a value that estimates a density of problem space around the
    instance being predicted.
    """
    def __init__(self, K=gauss_kernel, d_measure=Orange.distance.Euclidean(), name="density"):
        self.K = K
        self.d_measure = d_measure
        self.name = name

    def __call__(self, instances, learner):

        self.distance = self.d_measure(instances)

        def density(x):
            l, dens = len(instances), 0
            for ex in instances:
                dens += self.K(self.distance(x,ex))
            return dens / l

        max_density = max([density(ex) for ex in instances])

        return ParzenWindowDensityBasedClassifier(density, max_density)

class ParzenWindowDensityBasedClassifier:

    def __init__(self, density, max_density):
        self.density = density
        self.max_density = max_density


    def __call__(self, instance, *args):

        DENS = self.max_density-self.density(instance)

        return [Estimate(DENS, ABSOLUTE, DENS_ABSOLUTE)]


def _normalize(data):
    dc = Orange.core.DomainContinuizer()
    dc.classTreatment = Orange.core.DomainContinuizer.Ignore
    dc.continuousTreatment = Orange.core.DomainContinuizer.NormalizeByVariance
    domain = dc(data)
    data = data.translate(domain)
    return data

class _NormalizedLearner(Orange.classification.Learner):
    """
    Wrapper for normalization.
    """
    def __init__(self, learner):
        self.learner = learner

    def __call__(self, data, *args, **kwargs):
        return self.learner(_normalize(data), *args, **kwargs)

class Stacking:
    """

    This methods develops a model that integrates reliability estimates
    from all available reliability scoring techniques (see [Wolpert1992]_ and [Dzeroski2004]_). It
    performs internal cross-validation and therefore takes roughly the same time
    as :class:`ICV`.

    :param stack_learner: a data modelling method. Default (if None): unregularized linear regression with prior normalization.
    :type stack_learner: :obj:`Orange.classification.Learner` 

    :param estimators: Reliability estimation methods to choose from. Default (if None): :class:`SensitivityAnalysis`, :class:`LocalCrossValidation`, :class:`BaggingVarianceCNeighbours`, :class:`Mahalanobis`, :class:`MahalanobisToCenter`.
    :type estimators: :obj:`list` of reliability estimators
 
    :param folds: The number of fold for cross validation (default 10).
    :type box_learner: :obj:`int`

    :param save_data: If True, save the data used for training the
        integration model into resulting classifier's .data attribute (default False).
    :type box_learner: :obj:`bool`
 
    """
 
    def __init__(self, 
        stack_learner=None, 
        estimators=None, 
        folds=10, 
        save_data=False):
        self.stack_learner = stack_learner
        self.estimators = estimators
        self.folds = folds
        self.save_data = save_data
        if self.stack_learner is None:
            self.stack_learner=_NormalizedLearner(Orange.regression.linear.LinearRegressionLearner(ridge_lambda=0.0))
        if self.estimators is None:
             self.estimators = [SensitivityAnalysis(),
                           LocalCrossValidation(),
                           BaggingVarianceCNeighbours(),
                           Mahalanobis(),
                           MahalanobisToCenter()]
    
    def __call__(self, data, learner):

        newfeatures = None
        
        if self.folds > 1:

            cvi = Orange.data.sample.SubsetIndicesCV(data, self.folds)
            data_cv = [ None ] * len(data)
            for f in set(cvi): #for each fold
                learn = data.select(cvi, f, negate=True)
                test = data.select(cvi, f)

                #learn reliability estimates for the learning set
                lf = Learner(learner, estimators=self.estimators)(learn)
                
                #pos is used to retain the order of instances
                for ex, pos in zip(test, [ i for i,n in enumerate(cvi) if n == f ]):
                    pred = lf(ex, Orange.core.GetBoth)
                    re = pred[1].reliability_estimate
                    names = [ e.method_name for e in re ]
                    assert newfeatures is None or names == newfeatures
                    newfeatures = names
                    estimates = [ abs(e.estimate) for e in re ]
                    error = ex[-1].value - pred[0].value
                    data_cv[pos] = estimates + [ abs(error) ]

        else:
 
            #use half of the data to learn reliability estimates
            #and the other half for induction of a stacking classifier
            cvi = Orange.data.sample.SubsetIndicesCV(data, 2)
            data_cv = []

            learn = data.select(cvi, 0, negate=True)
            test = data.select(cvi, 0)

            #learn reliability estimates for the learning set
            lf = Learner(learner, estimators=self.estimators)(learn)
            
            for ex in test:
                pred = lf(ex, Orange.core.GetBoth)
                re = pred[1].reliability_estimate
                names = [ e.method_name for e in re ]
                assert newfeatures is None or names == newfeatures
                newfeatures = names
                estimates = [ abs(e.estimate) for e in re ]
                error = ex[-1].value - pred[0].value
                data_cv.append(estimates + [ abs(error) ])

        lf = None

        #induce the classifier on cross-validated reliability estimates
        newfeatures = [ Orange.feature.Continuous(name=n) for n in newfeatures ]
        newdomain = Orange.data.Domain(newfeatures, Orange.feature.Continuous(name="error"))
        classifier_data = Orange.data.Table(newdomain, data_cv)
        stack_classifier = self.stack_learner(classifier_data)

        #induce reliability estimates on the whole data set
        lf = Learner(learner, estimators=self.estimators)(data)

        return StackingClassifier(stack_classifier, lf, newdomain, data=classifier_data if self.save_data else None)


class StackingClassifier:

    def __init__(self, stacking_classifier, reliability_classifier, domain, data=None):
        self.stacking_classifier = stacking_classifier
        self.domain = domain
        self.reliability_classifier = reliability_classifier
        self.data = data

    def convert(self, instance):
        """ Return example in the space of reliability estimates. """
        re = self.reliability_classifier(instance, Orange.core.GetProbabilities).reliability_estimate
        #take absolute values for all
        tex = [ abs(e.estimate) for e in re ] + [ "?" ]
        tex =  Orange.data.Instance(self.domain, tex)
        return tex

    def __call__(self, instance, *args):
        tex = self.convert(instance)
        r = self.stacking_classifier(tex)
        r = float(r)
        r = max(0., r)
        return [ Estimate(r, ABSOLUTE, STACKING) ]

class ICV:
    """ Selects the best reliability estimator for
    the given data with internal cross validation [Bosnic2010]_.

    :param estimators: reliability estimation methods to choose from. Default (if None): :class:`SensitivityAnalysis`, :class:`LocalCrossValidation`, :class:`BaggingVarianceCNeighbours`, :class:`Mahalanobis`, :class:`MahalanobisToCenter` ]
    :type estimators: :obj:`list` of reliability estimators
 
    :param folds: The number of fold for cross validation (default 10).
    :type box_learner: :obj:`int`
 
    """
  
    def __init__(self, estimators=None, folds=10):
        self.estimators = estimators
        if self.estimators is None:
             self.estimators = [SensitivityAnalysis(),
                           LocalCrossValidation(),
                           BaggingVarianceCNeighbours(),
                           Mahalanobis(),
                           MahalanobisToCenter()]
        self.folds = folds
    
    def __call__(self, data, learner):

        cvi = Orange.data.sample.SubsetIndicesCV(data, self.folds)
        sum_of_rs = defaultdict(float)
        n_rs = defaultdict(int)

        elearner = Learner(learner, estimators=self.estimators)

        #average correlations from each fold
        for f in set(cvi):
            learn = data.select(cvi, f, negate=True)
            test = data.select(cvi, f)

            res = Orange.evaluation.testing.learn_and_test_on_test_data([elearner], learn, test)
            results = get_pearson_r(res)
    
            for r, p, sa, method in results:
                if not math.isnan(r): #ignore NaN values
                    sum_of_rs[(method, sa)] += r 
                    n_rs[(method, sa)] += 1 

        avg_rs = [ (k,(sum_of_rs[k]/n_rs[k])) for k in sum_of_rs ]

        avg_rs = sorted(avg_rs, key=lambda estimate: estimate[1], reverse=True)
        chosen = avg_rs[0][0]

        lf = elearner(data)
        return ICVClassifier(chosen, lf)


class ICVClassifier:

    def __init__(self, chosen, reliability_classifier):
        self.chosen = chosen
        self.reliability_classifier = reliability_classifier

    def __call__(self, instance, *args):
        re = self.reliability_classifier(instance, Orange.core.GetProbabilities).reliability_estimate
        for e in re:
            if e.method == self.chosen[0] and e.signed_or_absolute == self.chosen[1]:
                r = e.estimate

        return [ Estimate(r, self.chosen[1], ICV_METHOD) ]

class Learner:
    """
    Adds reliability estimation to any prediction method.
    This class can be used as any other Orange learner,
    but returns the classifier wrapped into an instance of
    :class:`Orange.evaluation.reliability.Classifier`.

    :param box_learner: Learner to wrap into a reliability estimation
        classifier.
    :type box_learner: :obj:`~Orange.classification.Learner`
    
    :param estimators: List of reliability estimation methods. Default (if None): :class:`SensitivityAnalysis`, :class:`LocalCrossValidation`, :class:`BaggingVarianceCNeighbours`, :class:`Mahalanobis`, :class:`MahalanobisToCenter`.
    :type estimators: :obj:`list` of reliability estimators
    
    :param name: Name of this reliability learner.
    :type name: string
    
    :rtype: :class:`Orange.evaluation.reliability.Learner`
    """
    def __init__(self, box_learner, name="Reliability estimation",
                 estimators=None,
                 **kwds):
        self.__dict__.update(kwds)
        self.name = name
        self.estimators = estimators
        if self.estimators is None:
             self.estimators = [SensitivityAnalysis(),
                           LocalCrossValidation(),
                           BaggingVarianceCNeighbours(),
                           Mahalanobis(),
                           MahalanobisToCenter()]
 
        self.box_learner = box_learner
        self.blending = False


    def __call__(self, instances, weight=None, **kwds):
        """Construct a classifier.
        
        :param instances: Learning data.
        :type instances: Orange.data.Table
        :param weight: Id of meta attribute with weights of instances
        :type weight: int

        :rtype: :class:`Orange.evaluation.reliability.Classifier`
        """

        blending_classifier = None
        new_domain = None

#        if instances.domain.class_var.var_type != Orange.feature.Continuous.Continuous:
#            raise Exception("This method only works on data with continuous class.")

        return Classifier(instances, self.box_learner, self.estimators, self.blending, new_domain, blending_classifier)
 
class Classifier:
    """
    A reliability estimation wrapper for classifiers. 
    The returned probabilities contain an
    additional attribute :obj:`reliability_estimate`, which is a list of
    :class:`~Orange.evaluation.reliability.Estimate` (see :obj:`~Classifier.__call__`).
    """

    def __init__(self, instances, box_learner, estimators, blending, blending_domain, rf_classifier, **kwds):
        self.__dict__.update(kwds)
        self.instances = instances
        self.box_learner = box_learner
        self.estimators = estimators
        self.blending = blending
        self.blending_domain = blending_domain
        self.rf_classifier = rf_classifier

        # Train the learner with original data
        self.classifier = box_learner(instances)

        # Train all the estimators and create their classifiers
        self.estimation_classifiers = [estimator(instances, box_learner) for estimator in estimators]

    def __call__(self, instance, result_type=Orange.core.GetValue):
        """
        Classify and estimate reliability for a new instance.
        When :obj:`result_type` is set to
        :obj:`Orange.classification.Classifier.GetBoth` or
        :obj:`Orange.classification.Classifier.GetProbabilities`,
        an additional attribute :obj:`reliability_estimate`
        (a list of :class:`~Orange.evaluation.reliability.Estimate`)
        is added to the distribution object.
        
        :param instance: instance to be classified.
        :type instance: :class:`Orange.data.Instance`
        :param result_type: :class:`Orange.classification.Classifier.GetValue` or \
              :class:`Orange.classification.Classifier.GetProbabilities` or
              :class:`Orange.classification.Classifier.GetBoth`
        
        :rtype: :class:`Orange.data.Value`, 
              :class:`Orange.statistics.Distribution` or a tuple with both
        """
        predicted, probabilities = self.classifier(instance, Orange.core.GetBoth)

        # Create a place holder for estimates
        if probabilities is None:
            probabilities = Orange.statistics.distribution.Continuous()
        #with warnings.catch_warnings():
        #    warnings.simplefilter("ignore")
        probabilities.setattr('reliability_estimate', [])

        # Calculate all the estimates and add them to the results
        for estimate in self.estimation_classifiers:
            probabilities.reliability_estimate.extend(estimate(instance, predicted, probabilities))

        # Return the appropriate type of result
        if result_type == Orange.core.GetValue:
            return predicted
        elif result_type == Orange.core.GetProbabilities:
            return probabilities
        else:
            return predicted, probabilities

# Functions for testing and plotting
#TODO Document those.
def get_acc_rel(method, data, learner):
    estimators = [method]
    reliability = Orange.evaluation.reliability.Learner(learner, estimators=estimators)
    #results = Orange.evaluation.testing.leave_one_out([reliability], data)
    results = Orange.evaluation.testing.cross_validation([reliability], data)

    rels, acc = [], []

    for res in results.results:
        rels.append(res.probabilities[0].reliability_estimate[0].estimate)
        acc.append(res.probabilities[0][res.actual_class])

    return rels, acc


def rel_acc_plot(rels, acc, file_name=None, colors=None):

    import matplotlib.pylab as plt
    
    if colors is None:
        colors = "k"
    plt.scatter(rels, acc, c=colors)
    plt.xlim(0.,1.)
    plt.ylim(ymin=0.)
    plt.xlabel("Reliability")
    plt.ylabel("Accuracy")
    if file_name is None:
        plt.show()
    else:
        plt.savefig(file_name)

def rel_acc_compute_plot(method, data, learner, file_name=None, colors=None):

    plt.clf()

    rels, acc = get_acc_rel(method, data, learner)
    el_acc_plot(acc, rels, file_name=file_name, colors=colors)
    

def acc_rel_correlation(method, data, learner):
    import scipy.stats
    rels, acc = get_acc_rel(method, data, learner)
    return scipy.stats.spearmanr(acc, rels)[0]