ranking.py

"""Metrics to assess performance on classification task given scores

Functions named as ``*_score`` return a scalar value to maximize: the higher
the better

Function named as ``*_error`` or ``*_loss`` return a scalar value to minimize:
the lower the better
"""

# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#          Mathieu Blondel <mathieu@mblondel.org>
#          Olivier Grisel <olivier.grisel@ensta.org>
#          Arnaud Joly <a.joly@ulg.ac.be>
#          Jochen Wersdorfer <jochen@wersdoerfer.de>
#          Lars Buitinck <L.J.Buitinck@uva.nl>
#          Joel Nothman <joel.nothman@gmail.com>
#          Noel Dawe <noel@dawe.me>
# License: BSD 3 clause

from __future__ import division

import warnings
import numpy as np
from scipy.sparse import csr_matrix

from ..preprocessing import LabelBinarizer
from ..utils import check_consistent_length
from ..utils import deprecated
from ..utils import column_or_1d, check_array
from ..utils.multiclass import type_of_target
from ..utils.fixes import isclose
from ..utils.stats import rankdata

from .base import _average_binary_score
from .base import UndefinedMetricWarning


def auc(x, y, reorder=False):
    """Compute Area Under the Curve (AUC) using the trapezoidal rule

    This is a general function, given points on a curve.  For computing the
    area under the ROC-curve, see :func:`roc_auc_score`.

    Parameters
    ----------
    x : array, shape = [n]
        x coordinates.

    y : array, shape = [n]
        y coordinates.

    reorder : boolean, optional (default=False)
        If True, assume that the curve is ascending in the case of ties, as for
        an ROC curve. If the curve is non-ascending, the result will be wrong.

    Returns
    -------
    auc : float

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn import metrics
    >>> y = np.array([1, 1, 2, 2])
    >>> pred = np.array([0.1, 0.4, 0.35, 0.8])
    >>> fpr, tpr, thresholds = metrics.roc_curve(y, pred, pos_label=2)
    >>> metrics.auc(fpr, tpr)
    0.75

    See also
    --------
    roc_auc_score : Computes the area under the ROC curve

    precision_recall_curve :
        Compute precision-recall pairs for different probability thresholds

    """
    check_consistent_length(x, y)
    x = column_or_1d(x)
    y = column_or_1d(y)

    if x.shape[0] < 2:
        raise ValueError('At least 2 points are needed to compute'
                         ' area under curve, but x.shape = %s' % x.shape)

    direction = 1
    if reorder:
        # reorder the data points according to the x axis and using y to
        # break ties
        order = np.lexsort((y, x))
        x, y = x[order], y[order]
    else:
        dx = np.diff(x)
        if np.any(dx < 0):
            if np.all(dx <= 0):
                direction = -1
            else:
                raise ValueError("Reordering is not turned on, and "
                                 "the x array is not increasing: %s" % x)

    area = direction * np.trapz(y, x)

    return area


def average_precision_score(y_true, y_score, average="macro",
                            sample_weight=None):
    """Compute average precision (AP) from prediction scores

    This score corresponds to the area under the precision-recall curve.

    Note: this implementation is restricted to the binary classification task
    or multilabel classification task.

    Parameters
    ----------
    y_true : array, shape = [n_samples] or [n_samples, n_classes]
        True binary labels in binary label indicators.

    y_score : array, shape = [n_samples] or [n_samples, n_classes]
        Target scores, can either be probability estimates of the positive
        class, confidence values, or binary decisions.

    average : string, [None, 'micro', 'macro' (default), 'samples', 'weighted']
        If ``None``, the scores for each class are returned. Otherwise,
        this determines the type of averaging performed on the data:

        ``'micro'``:
            Calculate metrics globally by considering each element of the label
            indicator matrix as a label.
        ``'macro'``:
            Calculate metrics for each label, and find their unweighted
            mean.  This does not take label imbalance into account.
        ``'weighted'``:
            Calculate metrics for each label, and find their average, weighted
            by support (the number of true instances for each label).
        ``'samples'``:
            Calculate metrics for each instance, and find their average.

    sample_weight : array-like of shape = [n_samples], optional
        Sample weights.

    Returns
    -------
    average_precision : float

    References
    ----------
    .. [1] `Wikipedia entry for the Average precision
           <http://en.wikipedia.org/wiki/Average_precision>`_

    See also
    --------
    roc_auc_score : Area under the ROC curve

    precision_recall_curve :
        Compute precision-recall pairs for different probability thresholds

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.metrics import average_precision_score
    >>> y_true = np.array([0, 0, 1, 1])
    >>> y_scores = np.array([0.1, 0.4, 0.35, 0.8])
    >>> average_precision_score(y_true, y_scores)  # doctest: +ELLIPSIS
    0.79...

    """
    def _binary_average_precision(y_true, y_score, sample_weight=None):
        precision, recall, thresholds = precision_recall_curve(
            y_true, y_score, sample_weight=sample_weight)
        return auc(recall, precision)

    return _average_binary_score(_binary_average_precision, y_true, y_score,
                                 average, sample_weight=sample_weight)


@deprecated("Function 'auc_score' has been renamed to "
            "'roc_auc_score' and will be removed in release 0.16.")
def auc_score(y_true, y_score):
    """Compute Area Under the Curve (AUC) from prediction scores

    Note: this implementation is restricted to the binary classification task.

    Parameters
    ----------

    y_true : array, shape = [n_samples]
        True binary labels.

    y_score : array, shape = [n_samples]
        Target scores, can either be probability estimates of the positive
        class, confidence values, or binary decisions.

    Returns
    -------
    auc : float

    References
    ----------
    .. [1] `Wikipedia entry for the Receiver operating characteristic
            <http://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_

    See also
    --------
    average_precision_score : Area under the precision-recall curve

    roc_curve : Compute Receiver operating characteristic (ROC)

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.metrics import auc_score
    >>> y_true = np.array([0, 0, 1, 1])
    >>> y_scores = np.array([0.1, 0.4, 0.35, 0.8])
    >>> auc_score(y_true, y_scores)
    0.75

    """
    return roc_auc_score(y_true, y_score)


def roc_auc_score(y_true, y_score, average="macro", sample_weight=None):
    """Compute Area Under the Curve (AUC) from prediction scores

    Note: this implementation is restricted to the binary classification task
    or multilabel classification task in label indicator format.

    Parameters
    ----------
    y_true : array, shape = [n_samples] or [n_samples, n_classes]
        True binary labels in binary label indicators.

    y_score : array, shape = [n_samples] or [n_samples, n_classes]
        Target scores, can either be probability estimates of the positive
        class, confidence values, or binary decisions.

    average : string, [None, 'micro', 'macro' (default), 'samples', 'weighted']
        If ``None``, the scores for each class are returned. Otherwise,
        this determines the type of averaging performed on the data:

        ``'micro'``:
            Calculate metrics globally by considering each element of the label
            indicator matrix as a label.
        ``'macro'``:
            Calculate metrics for each label, and find their unweighted
            mean.  This does not take label imbalance into account.
        ``'weighted'``:
            Calculate metrics for each label, and find their average, weighted
            by support (the number of true instances for each label).
        ``'samples'``:
            Calculate metrics for each instance, and find their average.

    sample_weight : array-like of shape = [n_samples], optional
        Sample weights.

    Returns
    -------
    auc : float

    References
    ----------
    .. [1] `Wikipedia entry for the Receiver operating characteristic
            <http://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_

    See also
    --------
    average_precision_score : Area under the precision-recall curve

    roc_curve : Compute Receiver operating characteristic (ROC)

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.metrics import roc_auc_score
    >>> y_true = np.array([0, 0, 1, 1])
    >>> y_scores = np.array([0.1, 0.4, 0.35, 0.8])
    >>> roc_auc_score(y_true, y_scores)
    0.75

    """
    def _binary_roc_auc_score(y_true, y_score, sample_weight=None):
        if len(np.unique(y_true)) != 2:
            raise ValueError("Only one class present in y_true. ROC AUC score "
                             "is not defined in that case.")

        fpr, tpr, tresholds = roc_curve(y_true, y_score,
                                        sample_weight=sample_weight)
        return auc(fpr, tpr, reorder=True)

    return _average_binary_score(
        _binary_roc_auc_score, y_true, y_score, average,
        sample_weight=sample_weight)


def _binary_clf_curve(y_true, y_score, pos_label=None, sample_weight=None):
    """Calculate true and false positives per binary classification threshold.

    Parameters
    ----------
    y_true : array, shape = [n_samples]
        True targets of binary classification

    y_score : array, shape = [n_samples]
        Estimated probabilities or decision function

    pos_label : int, optional (default=None)
        The label of the positive class

    sample_weight : array-like of shape = [n_samples], optional
        Sample weights.

    Returns
    -------
    fps : array, shape = [n_thresholds]
        A count of false positives, at index i being the number of negative
        samples assigned a score >= thresholds[i]. The total number of
        negative samples is equal to fps[-1] (thus true negatives are given by
        fps[-1] - fps).

    tps : array, shape = [n_thresholds := len(np.unique(y_score))]
        An increasing count of true positives, at index i being the number
        of positive samples assigned a score >= thresholds[i]. The total
        number of positive samples is equal to tps[-1] (thus false negatives
        are given by tps[-1] - tps).

    thresholds : array, shape = [n_thresholds]
        Decreasing score values.
    """
    check_consistent_length(y_true, y_score)
    y_true = column_or_1d(y_true)
    y_score = column_or_1d(y_score)
    if sample_weight is not None:
        sample_weight = column_or_1d(sample_weight)

    # ensure binary classification if pos_label is not specified
    classes = np.unique(y_true)
    if (pos_label is None and
        not (np.all(classes == [0, 1]) or
             np.all(classes == [-1, 1]) or
             np.all(classes == [0]) or
             np.all(classes == [-1]) or
             np.all(classes == [1]))):
        raise ValueError("Data is not binary and pos_label is not specified")
    elif pos_label is None:
        pos_label = 1.

    # make y_true a boolean vector
    y_true = (y_true == pos_label)

    # sort scores and corresponding truth values
    desc_score_indices = np.argsort(y_score, kind="mergesort")[::-1]
    y_score = y_score[desc_score_indices]
    y_true = y_true[desc_score_indices]
    if sample_weight is not None:
        weight = sample_weight[desc_score_indices]
    else:
        weight = 1.

    # y_score typically has many tied values. Here we extract
    # the indices associated with the distinct values. We also
    # concatenate a value for the end of the curve.
    # We need to use isclose to avoid spurious repeated thresholds
    # stemming from floating point roundoff errors.
    distinct_value_indices = np.where(np.logical_not(isclose(
        np.diff(y_score), 0)))[0]
    threshold_idxs = np.r_[distinct_value_indices, y_true.size - 1]

    # accumulate the true positives with decreasing threshold
    tps = (y_true * weight).cumsum()[threshold_idxs]
    if sample_weight is not None:
        fps = weight.cumsum()[threshold_idxs] - tps
    else:
        fps = 1 + threshold_idxs - tps
    return fps, tps, y_score[threshold_idxs]


def precision_recall_curve(y_true, probas_pred, pos_label=None,
                           sample_weight=None):
    """Compute precision-recall pairs for different probability thresholds

    Note: this implementation is restricted to the binary classification task.

    The precision is the ratio ``tp / (tp + fp)`` where ``tp`` is the number of
    true positives and ``fp`` the number of false positives. The precision is
    intuitively the ability of the classifier not to label as positive a sample
    that is negative.

    The recall is the ratio ``tp / (tp + fn)`` where ``tp`` is the number of
    true positives and ``fn`` the number of false negatives. The recall is
    intuitively the ability of the classifier to find all the positive samples.

    The last precision and recall values are 1. and 0. respectively and do not
    have a corresponding threshold.  This ensures that the graph starts on the
    x axis.

    Parameters
    ----------
    y_true : array, shape = [n_samples]
        True targets of binary classification in range {-1, 1} or {0, 1}.

    probas_pred : array, shape = [n_samples]
        Estimated probabilities or decision function.

    pos_label : int, optional (default=None)
        The label of the positive class

    sample_weight : array-like of shape = [n_samples], optional
        Sample weights.

    Returns
    -------
    precision : array, shape = [n_thresholds + 1]
        Precision values such that element i is the precision of
        predictions with score >= thresholds[i] and the last element is 1.

    recall : array, shape = [n_thresholds + 1]
        Decreasing recall values such that element i is the recall of
        predictions with score >= thresholds[i] and the last element is 0.

    thresholds : array, shape = [n_thresholds := len(np.unique(probas_pred))]
        Increasing thresholds on the decision function used to compute
        precision and recall.

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.metrics import precision_recall_curve
    >>> y_true = np.array([0, 0, 1, 1])
    >>> y_scores = np.array([0.1, 0.4, 0.35, 0.8])
    >>> precision, recall, thresholds = precision_recall_curve(
    ...     y_true, y_scores)
    >>> precision  # doctest: +ELLIPSIS
    array([ 0.66...,  0.5       ,  1.        ,  1.        ])
    >>> recall
    array([ 1. ,  0.5,  0.5,  0. ])
    >>> thresholds
    array([ 0.35,  0.4 ,  0.8 ])

    """
    fps, tps, thresholds = _binary_clf_curve(y_true, probas_pred,
                                             pos_label=pos_label,
                                             sample_weight=sample_weight)

    precision = tps / (tps + fps)
    recall = tps / tps[-1]

    # stop when full recall attained
    # and reverse the outputs so recall is decreasing
    last_ind = tps.searchsorted(tps[-1])
    sl = slice(last_ind, None, -1)
    return np.r_[precision[sl], 1], np.r_[recall[sl], 0], thresholds[sl]


def roc_curve(y_true, y_score, pos_label=None, sample_weight=None):
    """Compute Receiver operating characteristic (ROC)

    Note: this implementation is restricted to the binary classification task.

    Parameters
    ----------

    y_true : array, shape = [n_samples]
        True binary labels in range {0, 1} or {-1, 1}.  If labels are not
        binary, pos_label should be explicitly given.

    y_score : array, shape = [n_samples]
        Target scores, can either be probability estimates of the positive
        class or confidence values.

    pos_label : int
        Label considered as positive and others are considered negative.

    sample_weight : array-like of shape = [n_samples], optional
        Sample weights.

    Returns
    -------
    fpr : array, shape = [>2]
        Increasing false positive rates such that element i is the false
        positive rate of predictions with score >= thresholds[i].

    tpr : array, shape = [>2]
        Increasing true positive rates such that element i is the true
        positive rate of predictions with score >= thresholds[i].

    thresholds : array, shape = [n_thresholds]
        Decreasing thresholds on the decision function used to compute
        fpr and tpr. `thresholds[0]` represents no instances being predicted
        and is arbitrarily set to `max(y_score) + 1`.

    See also
    --------
    roc_auc_score : Compute Area Under the Curve (AUC) from prediction scores

    Notes
    -----
    Since the thresholds are sorted from low to high values, they
    are reversed upon returning them to ensure they correspond to both ``fpr``
    and ``tpr``, which are sorted in reversed order during their calculation.

    References
    ----------
    .. [1] `Wikipedia entry for the Receiver operating characteristic
            <http://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_


    Examples
    --------
    >>> import numpy as np
    >>> from sklearn import metrics
    >>> y = np.array([1, 1, 2, 2])
    >>> scores = np.array([0.1, 0.4, 0.35, 0.8])
    >>> fpr, tpr, thresholds = metrics.roc_curve(y, scores, pos_label=2)
    >>> fpr
    array([ 0. ,  0.5,  0.5,  1. ])
    >>> tpr
    array([ 0.5,  0.5,  1. ,  1. ])
    >>> thresholds
    array([ 0.8 ,  0.4 ,  0.35,  0.1 ])

    """
    fps, tps, thresholds = _binary_clf_curve(
        y_true, y_score, pos_label=pos_label, sample_weight=sample_weight)

    if tps.size == 0 or fps[0] != 0:
        # Add an extra threshold position if necessary
        tps = np.r_[0, tps]
        fps = np.r_[0, fps]
        thresholds = np.r_[thresholds[0] + 1, thresholds]

    if fps[-1] <= 0:
        warnings.warn("No negative samples in y_true, "
                      "false positive value should be meaningless",
                      UndefinedMetricWarning)
        fpr = np.repeat(np.nan, fps.shape)
    else:
        fpr = fps / fps[-1]

    if tps[-1] <= 0:
        warnings.warn("No positive samples in y_true, "
                      "true positive value should be meaningless",
                      UndefinedMetricWarning)
        tpr = np.repeat(np.nan, tps.shape)
    else:
        tpr = tps / tps[-1]

    return fpr, tpr, thresholds


def label_ranking_average_precision_score(y_true, y_score):
    """Compute ranking-based average precision

    Label ranking average precision (LRAP) is the average over each ground
    truth label assigned to each sample, of the ratio of true vs. total
    labels with lower score.

    This metric is used in multilabel ranking problem, where the goal
    is to give better rank to the labels associated to each sample.

    The obtained score is always strictly greater than 0 and
    the best value is 1.

    Parameters
    ----------
    y_true : array or sparse matrix, shape = [n_samples, n_labels]
        True binary labels in binary indicator format.

    y_score : array, shape = [n_samples, n_labels]
        Target scores, can either be probability estimates of the positive
        class, confidence values, or binary decisions.

    Returns
    -------
    score : float

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.metrics import label_ranking_average_precision_score
    >>> y_true = np.array([[1, 0, 0], [0, 0, 1]])
    >>> y_score = np.array([[0.75, 0.5, 1], [1, 0.2, 0.1]])
    >>> label_ranking_average_precision_score(y_true, y_score) \
        # doctest: +ELLIPSIS
    0.416...

    """
    check_consistent_length(y_true, y_score)
    y_true = check_array(y_true, ensure_2d=False)
    y_score = check_array(y_score, ensure_2d=False)

    if y_true.shape != y_score.shape:
        raise ValueError("y_true and y_score have different shape")

    # Handle badly formated array and the degenerate case with one label
    y_type = type_of_target(y_true)
    if (y_type != "multilabel-indicator"
            and not (y_type == "binary" and y_true.ndim == 2)):
        raise ValueError("{0} format is not supported".format(y_type))

    y_true = csr_matrix(y_true)
    y_score = -y_score

    n_samples, n_labels = y_true.shape

    out = 0.
    for i, (start, stop) in enumerate(zip(y_true.indptr, y_true.indptr[1:])):
        relevant = y_true.indices[start:stop]

        if (relevant.size == 0 or relevant.size == n_labels):
            # If all labels are relevant or unrelevant, the score is also
            # equal to 1. The label ranking has no meaning.
            out += 1.
            continue

        scores_i = y_score[i]
        rank = rankdata(scores_i, 'max')[relevant]
        L = rankdata(scores_i[relevant], 'max')
        out += np.divide(L, rank, dtype=float).mean()

    return out / n_samples