"""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
# Joel Nothman <joel.nothman@gmail.com>
# Noel Dawe <noel@dawe.me>
# Michal Karbownik <michakarbownik@gmail.com>
# License: BSD 3 clause
import warnings
from functools import partial
import numpy as np
from scipy.sparse import csr_matrix
from scipy.stats import rankdata
from ..utils import assert_all_finite
from ..utils import check_consistent_length
from ..utils.validation import _check_sample_weight
from ..utils import column_or_1d, check_array
from ..utils.multiclass import type_of_target
from ..utils.extmath import stable_cumsum
from ..utils.sparsefuncs import count_nonzero
from ..exceptions import UndefinedMetricWarning
from ..preprocessing import label_binarize
from ..utils._encode import _encode, _unique
from ._base import (
_average_binary_score,
_average_multiclass_ovo_score,
_check_pos_label_consistency,
)
def auc(x, y):
"""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`. For an alternative
way to summarize a precision-recall curve, see
:func:`average_precision_score`.
Parameters
----------
x : ndarray of shape (n,)
x coordinates. These must be either monotonic increasing or monotonic
decreasing.
y : ndarray of shape, (n,)
y coordinates.
Returns
-------
auc : float
See Also
--------
roc_auc_score : Compute the area under the ROC curve.
average_precision_score : Compute average precision from prediction scores.
precision_recall_curve : Compute precision-recall pairs for different
probability thresholds.
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
"""
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
dx = np.diff(x)
if np.any(dx < 0):
if np.all(dx <= 0):
direction = -1
else:
raise ValueError("x is neither increasing nor decreasing : {}.".format(x))
area = direction * np.trapz(y, x)
if isinstance(area, np.memmap):
# Reductions such as .sum used internally in np.trapz do not return a
# scalar by default for numpy.memmap instances contrary to
# regular numpy.ndarray instances.
area = area.dtype.type(area)
return area
def average_precision_score(
y_true, y_score, *, average="macro", pos_label=1, sample_weight=None
):
"""Compute average precision (AP) from prediction scores.
AP summarizes a precision-recall curve as the weighted mean of precisions
achieved at each threshold, with the increase in recall from the previous
threshold used as the weight:
.. math::
\\text{AP} = \\sum_n (R_n - R_{n-1}) P_n
where :math:`P_n` and :math:`R_n` are the precision and recall at the nth
threshold [1]_. This implementation is not interpolated and is different
from computing the area under the precision-recall curve with the
trapezoidal rule, which uses linear interpolation and can be too
optimistic.
Note: this implementation is restricted to the binary classification task
or multilabel classification task.
Read more in the :ref:`User Guide <precision_recall_f_measure_metrics>`.
Parameters
----------
y_true : ndarray of shape (n_samples,) or (n_samples, n_classes)
True binary labels or binary label indicators.
y_score : ndarray of shape (n_samples,) or (n_samples, n_classes)
Target scores, can either be probability estimates of the positive
class, confidence values, or non-thresholded measure of decisions
(as returned by :term:`decision_function` on some classifiers).
average : {'micro', 'samples', 'weighted', 'macro'} or None, \
default='macro'
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.
Will be ignored when ``y_true`` is binary.
pos_label : int or str, default=1
The label of the positive class. Only applied to binary ``y_true``.
For multilabel-indicator ``y_true``, ``pos_label`` is fixed to 1.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
average_precision : float
See Also
--------
roc_auc_score : Compute the area under the ROC curve.
precision_recall_curve : Compute precision-recall pairs for different
probability thresholds.
Notes
-----
.. versionchanged:: 0.19
Instead of linearly interpolating between operating points, precisions
are weighted by the change in recall since the last operating point.
References
----------
.. [1] `Wikipedia entry for the Average precision
<https://en.wikipedia.org/w/index.php?title=Information_retrieval&
oldid=793358396#Average_precision>`_
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)
0.83...
"""
def _binary_uninterpolated_average_precision(
y_true, y_score, pos_label=1, sample_weight=None
):
precision, recall, _ = precision_recall_curve(
y_true, y_score, pos_label=pos_label, sample_weight=sample_weight
)
# Return the step function integral
# The following works because the last entry of precision is
# guaranteed to be 1, as returned by precision_recall_curve
return -np.sum(np.diff(recall) * np.array(precision)[:-1])
y_type = type_of_target(y_true)
if y_type == "multilabel-indicator" and pos_label != 1:
raise ValueError(
"Parameter pos_label is fixed to 1 for "
"multilabel-indicator y_true. Do not set "
"pos_label or set pos_label to 1."
)
elif y_type == "binary":
# Convert to Python primitive type to avoid NumPy type / Python str
# comparison. See https://github.com/numpy/numpy/issues/6784
present_labels = np.unique(y_true).tolist()
if len(present_labels) == 2 and pos_label not in present_labels:
raise ValueError(
f"pos_label={pos_label} is not a valid label. It should be "
f"one of {present_labels}"
)
average_precision = partial(
_binary_uninterpolated_average_precision, pos_label=pos_label
)
return _average_binary_score(
average_precision, y_true, y_score, average, sample_weight=sample_weight
)
def det_curve(y_true, y_score, pos_label=None, sample_weight=None):
"""Compute error rates for different probability thresholds.
.. note::
This metric is used for evaluation of ranking and error tradeoffs of
a binary classification task.
Read more in the :ref:`User Guide <det_curve>`.
.. versionadded:: 0.24
Parameters
----------
y_true : ndarray of shape (n_samples,)
True binary labels. If labels are not either {-1, 1} or {0, 1}, then
pos_label should be explicitly given.
y_score : ndarray of shape of (n_samples,)
Target scores, can either be probability estimates of the positive
class, confidence values, or non-thresholded measure of decisions
(as returned by "decision_function" on some classifiers).
pos_label : int or str, default=None
The label of the positive class.
When ``pos_label=None``, if `y_true` is in {-1, 1} or {0, 1},
``pos_label`` is set to 1, otherwise an error will be raised.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
fpr : ndarray of shape (n_thresholds,)
False positive rate (FPR) such that element i is the false positive
rate of predictions with score >= thresholds[i]. This is occasionally
referred to as false acceptance propability or fall-out.
fnr : ndarray of shape (n_thresholds,)
False negative rate (FNR) such that element i is the false negative
rate of predictions with score >= thresholds[i]. This is occasionally
referred to as false rejection or miss rate.
thresholds : ndarray of shape (n_thresholds,)
Decreasing score values.
See Also
--------
DetCurveDisplay.from_estimator : Plot DET curve given an estimator and
some data.
DetCurveDisplay.from_predictions : Plot DET curve given the true and
predicted labels.
DetCurveDisplay : DET curve visualization.
roc_curve : Compute Receiver operating characteristic (ROC) curve.
precision_recall_curve : Compute precision-recall curve.
Examples
--------
>>> import numpy as np
>>> from sklearn.metrics import det_curve
>>> y_true = np.array([0, 0, 1, 1])
>>> y_scores = np.array([0.1, 0.4, 0.35, 0.8])
>>> fpr, fnr, thresholds = det_curve(y_true, y_scores)
>>> fpr
array([0.5, 0.5, 0. ])
>>> fnr
array([0. , 0.5, 0.5])
>>> thresholds
array([0.35, 0.4 , 0.8 ])
"""
fps, tps, thresholds = _binary_clf_curve(
y_true, y_score, pos_label=pos_label, sample_weight=sample_weight
)
if len(np.unique(y_true)) != 2:
raise ValueError(
"Only one class present in y_true. Detection error "
"tradeoff curve is not defined in that case."
)
fns = tps[-1] - tps
p_count = tps[-1]
n_count = fps[-1]
# start with false positives zero
first_ind = (
fps.searchsorted(fps[0], side="right") - 1
if fps.searchsorted(fps[0], side="right") > 0
else None
)
# stop with false negatives zero
last_ind = tps.searchsorted(tps[-1]) + 1
sl = slice(first_ind, last_ind)
# reverse the output such that list of false positives is decreasing
return (fps[sl][::-1] / n_count, fns[sl][::-1] / p_count, thresholds[sl][::-1])
def _binary_roc_auc_score(y_true, y_score, sample_weight=None, max_fpr=None):
"""Binary roc auc score."""
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, _ = roc_curve(y_true, y_score, sample_weight=sample_weight)
if max_fpr is None or max_fpr == 1:
return auc(fpr, tpr)
if max_fpr <= 0 or max_fpr > 1:
raise ValueError("Expected max_fpr in range (0, 1], got: %r" % max_fpr)
# Add a single point at max_fpr by linear interpolation
stop = np.searchsorted(fpr, max_fpr, "right")
x_interp = [fpr[stop - 1], fpr[stop]]
y_interp = [tpr[stop - 1], tpr[stop]]
tpr = np.append(tpr[:stop], np.interp(max_fpr, x_interp, y_interp))
fpr = np.append(fpr[:stop], max_fpr)
partial_auc = auc(fpr, tpr)
# McClish correction: standardize result to be 0.5 if non-discriminant
# and 1 if maximal
min_area = 0.5 * max_fpr ** 2
max_area = max_fpr
return 0.5 * (1 + (partial_auc - min_area) / (max_area - min_area))
[docs]def roc_auc_score(
y_true,
y_score,
*,
average="macro",
sample_weight=None,
max_fpr=None,
multi_class="raise",
labels=None,
):
"""Compute Area Under the Receiver Operating Characteristic Curve (ROC AUC)
from prediction scores.
Note: this implementation can be used with binary, multiclass and
multilabel classification, but some restrictions apply (see Parameters).
Read more in the :ref:`User Guide <roc_metrics>`.
Parameters
----------
y_true : array-like of shape (n_samples,) or (n_samples, n_classes)
True labels or binary label indicators. The binary and multiclass cases
expect labels with shape (n_samples,) while the multilabel case expects
binary label indicators with shape (n_samples, n_classes).
y_score : array-like of shape (n_samples,) or (n_samples, n_classes)
Target scores.
* In the binary case, it corresponds to an array of shape
`(n_samples,)`. Both probability estimates and non-thresholded
decision values can be provided. The probability estimates correspond
to the **probability of the class with the greater label**,
i.e. `estimator.classes_[1]` and thus
`estimator.predict_proba(X, y)[:, 1]`. The decision values
corresponds to the output of `estimator.decision_function(X, y)`.
See more information in the :ref:`User guide <roc_auc_binary>`;
* In the multiclass case, it corresponds to an array of shape
`(n_samples, n_classes)` of probability estimates provided by the
`predict_proba` method. The probability estimates **must**
sum to 1 across the possible classes. In addition, the order of the
class scores must correspond to the order of ``labels``,
if provided, or else to the numerical or lexicographical order of
the labels in ``y_true``. See more information in the
:ref:`User guide <roc_auc_multiclass>`;
* In the multilabel case, it corresponds to an array of shape
`(n_samples, n_classes)`. Probability estimates are provided by the
`predict_proba` method and the non-thresholded decision values by
the `decision_function` method. The probability estimates correspond
to the **probability of the class with the greater label for each
output** of the classifier. See more information in the
:ref:`User guide <roc_auc_multilabel>`.
average : {'micro', 'macro', 'samples', 'weighted'} or None, \
default='macro'
If ``None``, the scores for each class are returned. Otherwise,
this determines the type of averaging performed on the data:
Note: multiclass ROC AUC currently only handles the 'macro' and
'weighted' averages.
``'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.
Will be ignored when ``y_true`` is binary.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
max_fpr : float > 0 and <= 1, default=None
If not ``None``, the standardized partial AUC [2]_ over the range
[0, max_fpr] is returned. For the multiclass case, ``max_fpr``,
should be either equal to ``None`` or ``1.0`` as AUC ROC partial
computation currently is not supported for multiclass.
multi_class : {'raise', 'ovr', 'ovo'}, default='raise'
Only used for multiclass targets. Determines the type of configuration
to use. The default value raises an error, so either
``'ovr'`` or ``'ovo'`` must be passed explicitly.
``'ovr'``:
Stands for One-vs-rest. Computes the AUC of each class
against the rest [3]_ [4]_. This
treats the multiclass case in the same way as the multilabel case.
Sensitive to class imbalance even when ``average == 'macro'``,
because class imbalance affects the composition of each of the
'rest' groupings.
``'ovo'``:
Stands for One-vs-one. Computes the average AUC of all
possible pairwise combinations of classes [5]_.
Insensitive to class imbalance when
``average == 'macro'``.
labels : array-like of shape (n_classes,), default=None
Only used for multiclass targets. List of labels that index the
classes in ``y_score``. If ``None``, the numerical or lexicographical
order of the labels in ``y_true`` is used.
Returns
-------
auc : float
References
----------
.. [1] `Wikipedia entry for the Receiver operating characteristic
<https://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_
.. [2] `Analyzing a portion of the ROC curve. McClish, 1989
<https://www.ncbi.nlm.nih.gov/pubmed/2668680>`_
.. [3] Provost, F., Domingos, P. (2000). Well-trained PETs: Improving
probability estimation trees (Section 6.2), CeDER Working Paper
#IS-00-04, Stern School of Business, New York University.
.. [4] `Fawcett, T. (2006). An introduction to ROC analysis. Pattern
Recognition Letters, 27(8), 861-874.
<https://www.sciencedirect.com/science/article/pii/S016786550500303X>`_
.. [5] `Hand, D.J., Till, R.J. (2001). A Simple Generalisation of the Area
Under the ROC Curve for Multiple Class Classification Problems.
Machine Learning, 45(2), 171-186.
<http://link.springer.com/article/10.1023/A:1010920819831>`_
See Also
--------
average_precision_score : Area under the precision-recall curve.
roc_curve : Compute Receiver operating characteristic (ROC) curve.
RocCurveDisplay.from_estimator : Plot Receiver Operating Characteristic
(ROC) curve given an estimator and some data.
RocCurveDisplay.from_predictions : Plot Receiver Operating Characteristic
(ROC) curve given the true and predicted values.
Examples
--------
Binary case:
>>> from sklearn.datasets import load_breast_cancer
>>> from sklearn.linear_model import LogisticRegression
>>> from sklearn.metrics import roc_auc_score
>>> X, y = load_breast_cancer(return_X_y=True)
>>> clf = LogisticRegression(solver="liblinear", random_state=0).fit(X, y)
>>> roc_auc_score(y, clf.predict_proba(X)[:, 1])
0.99...
>>> roc_auc_score(y, clf.decision_function(X))
0.99...
Multiclass case:
>>> from sklearn.datasets import load_iris
>>> X, y = load_iris(return_X_y=True)
>>> clf = LogisticRegression(solver="liblinear").fit(X, y)
>>> roc_auc_score(y, clf.predict_proba(X), multi_class='ovr')
0.99...
Multilabel case:
>>> import numpy as np
>>> from sklearn.datasets import make_multilabel_classification
>>> from sklearn.multioutput import MultiOutputClassifier
>>> X, y = make_multilabel_classification(random_state=0)
>>> clf = MultiOutputClassifier(clf).fit(X, y)
>>> # get a list of n_output containing probability arrays of shape
>>> # (n_samples, n_classes)
>>> y_pred = clf.predict_proba(X)
>>> # extract the positive columns for each output
>>> y_pred = np.transpose([pred[:, 1] for pred in y_pred])
>>> roc_auc_score(y, y_pred, average=None)
array([0.82..., 0.86..., 0.94..., 0.85... , 0.94...])
>>> from sklearn.linear_model import RidgeClassifierCV
>>> clf = RidgeClassifierCV().fit(X, y)
>>> roc_auc_score(y, clf.decision_function(X), average=None)
array([0.81..., 0.84... , 0.93..., 0.87..., 0.94...])
"""
y_type = type_of_target(y_true)
y_true = check_array(y_true, ensure_2d=False, dtype=None)
y_score = check_array(y_score, ensure_2d=False)
if y_type == "multiclass" or (
y_type == "binary" and y_score.ndim == 2 and y_score.shape[1] > 2
):
# do not support partial ROC computation for multiclass
if max_fpr is not None and max_fpr != 1.0:
raise ValueError(
"Partial AUC computation not available in "
"multiclass setting, 'max_fpr' must be"
" set to `None`, received `max_fpr={0}` "
"instead".format(max_fpr)
)
if multi_class == "raise":
raise ValueError("multi_class must be in ('ovo', 'ovr')")
return _multiclass_roc_auc_score(
y_true, y_score, labels, multi_class, average, sample_weight
)
elif y_type == "binary":
labels = np.unique(y_true)
y_true = label_binarize(y_true, classes=labels)[:, 0]
return _average_binary_score(
partial(_binary_roc_auc_score, max_fpr=max_fpr),
y_true,
y_score,
average,
sample_weight=sample_weight,
)
else: # multilabel-indicator
return _average_binary_score(
partial(_binary_roc_auc_score, max_fpr=max_fpr),
y_true,
y_score,
average,
sample_weight=sample_weight,
)
def _multiclass_roc_auc_score(
y_true, y_score, labels, multi_class, average, sample_weight
):
"""Multiclass roc auc score.
Parameters
----------
y_true : array-like of shape (n_samples,)
True multiclass labels.
y_score : array-like of shape (n_samples, n_classes)
Target scores corresponding to probability estimates of a sample
belonging to a particular class
labels : array-like of shape (n_classes,) or None
List of labels to index ``y_score`` used for multiclass. If ``None``,
the lexical order of ``y_true`` is used to index ``y_score``.
multi_class : {'ovr', 'ovo'}
Determines the type of multiclass configuration to use.
``'ovr'``:
Calculate metrics for the multiclass case using the one-vs-rest
approach.
``'ovo'``:
Calculate metrics for the multiclass case using the one-vs-one
approach.
average : {'macro', 'weighted'}
Determines the type of averaging performed on the pairwise binary
metric scores
``'macro'``:
Calculate metrics for each label, and find their unweighted
mean. This does not take label imbalance into account. Classes
are assumed to be uniformly distributed.
``'weighted'``:
Calculate metrics for each label, taking into account the
prevalence of the classes.
sample_weight : array-like of shape (n_samples,) or None
Sample weights.
"""
# validation of the input y_score
if not np.allclose(1, y_score.sum(axis=1)):
raise ValueError(
"Target scores need to be probabilities for multiclass "
"roc_auc, i.e. they should sum up to 1.0 over classes"
)
# validation for multiclass parameter specifications
average_options = ("macro", "weighted")
if average not in average_options:
raise ValueError(
"average must be one of {0} for multiclass problems".format(average_options)
)
multiclass_options = ("ovo", "ovr")
if multi_class not in multiclass_options:
raise ValueError(
"multi_class='{0}' is not supported "
"for multiclass ROC AUC, multi_class must be "
"in {1}".format(multi_class, multiclass_options)
)
if labels is not None:
labels = column_or_1d(labels)
classes = _unique(labels)
if len(classes) != len(labels):
raise ValueError("Parameter 'labels' must be unique")
if not np.array_equal(classes, labels):
raise ValueError("Parameter 'labels' must be ordered")
if len(classes) != y_score.shape[1]:
raise ValueError(
"Number of given labels, {0}, not equal to the number "
"of columns in 'y_score', {1}".format(len(classes), y_score.shape[1])
)
if len(np.setdiff1d(y_true, classes)):
raise ValueError("'y_true' contains labels not in parameter 'labels'")
else:
classes = _unique(y_true)
if len(classes) != y_score.shape[1]:
raise ValueError(
"Number of classes in y_true not equal to the number of "
"columns in 'y_score'"
)
if multi_class == "ovo":
if sample_weight is not None:
raise ValueError(
"sample_weight is not supported "
"for multiclass one-vs-one ROC AUC, "
"'sample_weight' must be None in this case."
)
y_true_encoded = _encode(y_true, uniques=classes)
# Hand & Till (2001) implementation (ovo)
return _average_multiclass_ovo_score(
_binary_roc_auc_score, y_true_encoded, y_score, average=average
)
else:
# ovr is same as multi-label
y_true_multilabel = label_binarize(y_true, classes=classes)
return _average_binary_score(
_binary_roc_auc_score,
y_true_multilabel,
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 : ndarray of shape (n_samples,)
True targets of binary classification.
y_score : ndarray of shape (n_samples,)
Estimated probabilities or output of a decision function.
pos_label : int or str, default=None
The label of the positive class.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
fps : ndarray of 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 : ndarray of shape (n_thresholds,)
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 : ndarray of shape (n_thresholds,)
Decreasing score values.
"""
# Check to make sure y_true is valid
y_type = type_of_target(y_true)
if not (y_type == "binary" or (y_type == "multiclass" and pos_label is not None)):
raise ValueError("{0} format is not supported".format(y_type))
check_consistent_length(y_true, y_score, sample_weight)
y_true = column_or_1d(y_true)
y_score = column_or_1d(y_score)
assert_all_finite(y_true)
assert_all_finite(y_score)
# Filter out zero-weighted samples, as they should not impact the result
if sample_weight is not None:
sample_weight = column_or_1d(sample_weight)
sample_weight = _check_sample_weight(sample_weight, y_true)
nonzero_weight_mask = sample_weight != 0
y_true = y_true[nonzero_weight_mask]
y_score = y_score[nonzero_weight_mask]
sample_weight = sample_weight[nonzero_weight_mask]
pos_label = _check_pos_label_consistency(pos_label, y_true)
# 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 = 1.0
# 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.
distinct_value_indices = np.where(np.diff(y_score))[0]
threshold_idxs = np.r_[distinct_value_indices, y_true.size - 1]
# accumulate the true positives with decreasing threshold
tps = stable_cumsum(y_true * weight)[threshold_idxs]
if sample_weight is not None:
# express fps as a cumsum to ensure fps is increasing even in
# the presence of floating point errors
fps = stable_cumsum((1 - y_true) * weight)[threshold_idxs]
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
y axis.
Read more in the :ref:`User Guide <precision_recall_f_measure_metrics>`.
Parameters
----------
y_true : ndarray of shape (n_samples,)
True binary labels. If labels are not either {-1, 1} or {0, 1}, then
pos_label should be explicitly given.
probas_pred : ndarray of shape (n_samples,)
Target scores, can either be probability estimates of the positive
class, or non-thresholded measure of decisions (as returned by
`decision_function` on some classifiers).
pos_label : int or str, default=None
The label of the positive class.
When ``pos_label=None``, if y_true is in {-1, 1} or {0, 1},
``pos_label`` is set to 1, otherwise an error will be raised.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
precision : ndarray of 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 : ndarray of 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 : ndarray of shape (n_thresholds,)
Increasing thresholds on the decision function used to compute
precision and recall. n_thresholds <= len(np.unique(probas_pred)).
See Also
--------
PrecisionRecallDisplay.from_estimator : Plot Precision Recall Curve given
a binary classifier.
PrecisionRecallDisplay.from_predictions : Plot Precision Recall Curve
using predictions from a binary classifier.
average_precision_score : Compute average precision from prediction scores.
det_curve: Compute error rates for different probability thresholds.
roc_curve : Compute Receiver operating characteristic (ROC) curve.
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
array([0.66666667, 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)
precision[np.isnan(precision)] = 0
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, drop_intermediate=True
):
"""Compute Receiver operating characteristic (ROC).
Note: this implementation is restricted to the binary classification task.
Read more in the :ref:`User Guide <roc_metrics>`.
Parameters
----------
y_true : ndarray of shape (n_samples,)
True binary labels. If labels are not either {-1, 1} or {0, 1}, then
pos_label should be explicitly given.
y_score : ndarray of shape (n_samples,)
Target scores, can either be probability estimates of the positive
class, confidence values, or non-thresholded measure of decisions
(as returned by "decision_function" on some classifiers).
pos_label : int or str, default=None
The label of the positive class.
When ``pos_label=None``, if `y_true` is in {-1, 1} or {0, 1},
``pos_label`` is set to 1, otherwise an error will be raised.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
drop_intermediate : bool, default=True
Whether to drop some suboptimal thresholds which would not appear
on a plotted ROC curve. This is useful in order to create lighter
ROC curves.
.. versionadded:: 0.17
parameter *drop_intermediate*.
Returns
-------
fpr : ndarray of shape (>2,)
Increasing false positive rates such that element i is the false
positive rate of predictions with score >= `thresholds[i]`.
tpr : ndarray of shape (>2,)
Increasing true positive rates such that element `i` is the true
positive rate of predictions with score >= `thresholds[i]`.
thresholds : ndarray of 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
--------
RocCurveDisplay.from_estimator : Plot Receiver Operating Characteristic
(ROC) curve given an estimator and some data.
RocCurveDisplay.from_predictions : Plot Receiver Operating Characteristic
(ROC) curve given the true and predicted values.
det_curve: Compute error rates for different probability thresholds.
roc_auc_score : Compute the area under the ROC curve.
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
<https://en.wikipedia.org/wiki/Receiver_operating_characteristic>`_
.. [2] Fawcett T. An introduction to ROC analysis[J]. Pattern Recognition
Letters, 2006, 27(8):861-874.
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. , 0.5, 0.5, 1. ])
>>> tpr
array([0. , 0.5, 0.5, 1. , 1. ])
>>> thresholds
array([1.8 , 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
)
# Attempt to drop thresholds corresponding to points in between and
# collinear with other points. These are always suboptimal and do not
# appear on a plotted ROC curve (and thus do not affect the AUC).
# Here np.diff(_, 2) is used as a "second derivative" to tell if there
# is a corner at the point. Both fps and tps must be tested to handle
# thresholds with multiple data points (which are combined in
# _binary_clf_curve). This keeps all cases where the point should be kept,
# but does not drop more complicated cases like fps = [1, 3, 7],
# tps = [1, 2, 4]; there is no harm in keeping too many thresholds.
if drop_intermediate and len(fps) > 2:
optimal_idxs = np.where(
np.r_[True, np.logical_or(np.diff(fps, 2), np.diff(tps, 2)), True]
)[0]
fps = fps[optimal_idxs]
tps = tps[optimal_idxs]
thresholds = thresholds[optimal_idxs]
# Add an extra threshold position
# to make sure that the curve starts at (0, 0)
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, *, sample_weight=None):
"""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.
Read more in the :ref:`User Guide <label_ranking_average_precision>`.
Parameters
----------
y_true : {ndarray, sparse matrix} of shape (n_samples, n_labels)
True binary labels in binary indicator format.
y_score : ndarray of shape (n_samples, n_labels)
Target scores, can either be probability estimates of the positive
class, confidence values, or non-thresholded measure of decisions
(as returned by "decision_function" on some classifiers).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
.. versionadded:: 0.20
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)
0.416...
"""
check_consistent_length(y_true, y_score, sample_weight)
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 formatted 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 = 0.0
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.
aux = 1.0
else:
scores_i = y_score[i]
rank = rankdata(scores_i, "max")[relevant]
L = rankdata(scores_i[relevant], "max")
aux = (L / rank).mean()
if sample_weight is not None:
aux = aux * sample_weight[i]
out += aux
if sample_weight is None:
out /= n_samples
else:
out /= np.sum(sample_weight)
return out
def coverage_error(y_true, y_score, *, sample_weight=None):
"""Coverage error measure.
Compute how far we need to go through the ranked scores to cover all
true labels. The best value is equal to the average number
of labels in ``y_true`` per sample.
Ties in ``y_scores`` are broken by giving maximal rank that would have
been assigned to all tied values.
Note: Our implementation's score is 1 greater than the one given in
Tsoumakas et al., 2010. This extends it to handle the degenerate case
in which an instance has 0 true labels.
Read more in the :ref:`User Guide <coverage_error>`.
Parameters
----------
y_true : ndarray of shape (n_samples, n_labels)
True binary labels in binary indicator format.
y_score : ndarray of shape (n_samples, n_labels)
Target scores, can either be probability estimates of the positive
class, confidence values, or non-thresholded measure of decisions
(as returned by "decision_function" on some classifiers).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
coverage_error : float
References
----------
.. [1] Tsoumakas, G., Katakis, I., & Vlahavas, I. (2010).
Mining multi-label data. In Data mining and knowledge discovery
handbook (pp. 667-685). Springer US.
"""
y_true = check_array(y_true, ensure_2d=False)
y_score = check_array(y_score, ensure_2d=False)
check_consistent_length(y_true, y_score, sample_weight)
y_type = type_of_target(y_true)
if y_type != "multilabel-indicator":
raise ValueError("{0} format is not supported".format(y_type))
if y_true.shape != y_score.shape:
raise ValueError("y_true and y_score have different shape")
y_score_mask = np.ma.masked_array(y_score, mask=np.logical_not(y_true))
y_min_relevant = y_score_mask.min(axis=1).reshape((-1, 1))
coverage = (y_score >= y_min_relevant).sum(axis=1)
coverage = coverage.filled(0)
return np.average(coverage, weights=sample_weight)
def label_ranking_loss(y_true, y_score, *, sample_weight=None):
"""Compute Ranking loss measure.
Compute the average number of label pairs that are incorrectly ordered
given y_score weighted by the size of the label set and the number of
labels not in the label set.
This is similar to the error set size, but weighted by the number of
relevant and irrelevant labels. The best performance is achieved with
a ranking loss of zero.
Read more in the :ref:`User Guide <label_ranking_loss>`.
.. versionadded:: 0.17
A function *label_ranking_loss*
Parameters
----------
y_true : {ndarray, sparse matrix} of shape (n_samples, n_labels)
True binary labels in binary indicator format.
y_score : ndarray of shape (n_samples, n_labels)
Target scores, can either be probability estimates of the positive
class, confidence values, or non-thresholded measure of decisions
(as returned by "decision_function" on some classifiers).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
loss : float
References
----------
.. [1] Tsoumakas, G., Katakis, I., & Vlahavas, I. (2010).
Mining multi-label data. In Data mining and knowledge discovery
handbook (pp. 667-685). Springer US.
"""
y_true = check_array(y_true, ensure_2d=False, accept_sparse="csr")
y_score = check_array(y_score, ensure_2d=False)
check_consistent_length(y_true, y_score, sample_weight)
y_type = type_of_target(y_true)
if y_type not in ("multilabel-indicator",):
raise ValueError("{0} format is not supported".format(y_type))
if y_true.shape != y_score.shape:
raise ValueError("y_true and y_score have different shape")
n_samples, n_labels = y_true.shape
y_true = csr_matrix(y_true)
loss = np.zeros(n_samples)
for i, (start, stop) in enumerate(zip(y_true.indptr, y_true.indptr[1:])):
# Sort and bin the label scores
unique_scores, unique_inverse = np.unique(y_score[i], return_inverse=True)
true_at_reversed_rank = np.bincount(
unique_inverse[y_true.indices[start:stop]], minlength=len(unique_scores)
)
all_at_reversed_rank = np.bincount(unique_inverse, minlength=len(unique_scores))
false_at_reversed_rank = all_at_reversed_rank - true_at_reversed_rank
# if the scores are ordered, it's possible to count the number of
# incorrectly ordered paires in linear time by cumulatively counting
# how many false labels of a given score have a score higher than the
# accumulated true labels with lower score.
loss[i] = np.dot(true_at_reversed_rank.cumsum(), false_at_reversed_rank)
n_positives = count_nonzero(y_true, axis=1)
with np.errstate(divide="ignore", invalid="ignore"):
loss /= (n_labels - n_positives) * n_positives
# When there is no positive or no negative labels, those values should
# be consider as correct, i.e. the ranking doesn't matter.
loss[np.logical_or(n_positives == 0, n_positives == n_labels)] = 0.0
return np.average(loss, weights=sample_weight)
def _dcg_sample_scores(y_true, y_score, k=None, log_base=2, ignore_ties=False):
"""Compute Discounted Cumulative Gain.
Sum the true scores ranked in the order induced by the predicted scores,
after applying a logarithmic discount.
This ranking metric yields a high value if true labels are ranked high by
``y_score``.
Parameters
----------
y_true : ndarray of shape (n_samples, n_labels)
True targets of multilabel classification, or true scores of entities
to be ranked.
y_score : ndarray of shape (n_samples, n_labels)
Target scores, can either be probability estimates, confidence values,
or non-thresholded measure of decisions (as returned by
"decision_function" on some classifiers).
k : int, default=None
Only consider the highest k scores in the ranking. If `None`, use all
outputs.
log_base : float, default=2
Base of the logarithm used for the discount. A low value means a
sharper discount (top results are more important).
ignore_ties : bool, default=False
Assume that there are no ties in y_score (which is likely to be the
case if y_score is continuous) for efficiency gains.
Returns
-------
discounted_cumulative_gain : ndarray of shape (n_samples,)
The DCG score for each sample.
See Also
--------
ndcg_score : The Discounted Cumulative Gain divided by the Ideal Discounted
Cumulative Gain (the DCG obtained for a perfect ranking), in order to
have a score between 0 and 1.
"""
discount = 1 / (np.log(np.arange(y_true.shape[1]) + 2) / np.log(log_base))
if k is not None:
discount[k:] = 0
if ignore_ties:
ranking = np.argsort(y_score)[:, ::-1]
ranked = y_true[np.arange(ranking.shape[0])[:, np.newaxis], ranking]
cumulative_gains = discount.dot(ranked.T)
else:
discount_cumsum = np.cumsum(discount)
cumulative_gains = [
_tie_averaged_dcg(y_t, y_s, discount_cumsum)
for y_t, y_s in zip(y_true, y_score)
]
cumulative_gains = np.asarray(cumulative_gains)
return cumulative_gains
def _tie_averaged_dcg(y_true, y_score, discount_cumsum):
"""
Compute DCG by averaging over possible permutations of ties.
The gain (`y_true`) of an index falling inside a tied group (in the order
induced by `y_score`) is replaced by the average gain within this group.
The discounted gain for a tied group is then the average `y_true` within
this group times the sum of discounts of the corresponding ranks.
This amounts to averaging scores for all possible orderings of the tied
groups.
(note in the case of dcg@k the discount is 0 after index k)
Parameters
----------
y_true : ndarray
The true relevance scores.
y_score : ndarray
Predicted scores.
discount_cumsum : ndarray
Precomputed cumulative sum of the discounts.
Returns
-------
discounted_cumulative_gain : float
The discounted cumulative gain.
References
----------
McSherry, F., & Najork, M. (2008, March). Computing information retrieval
performance measures efficiently in the presence of tied scores. In
European conference on information retrieval (pp. 414-421). Springer,
Berlin, Heidelberg.
"""
_, inv, counts = np.unique(-y_score, return_inverse=True, return_counts=True)
ranked = np.zeros(len(counts))
np.add.at(ranked, inv, y_true)
ranked /= counts
groups = np.cumsum(counts) - 1
discount_sums = np.empty(len(counts))
discount_sums[0] = discount_cumsum[groups[0]]
discount_sums[1:] = np.diff(discount_cumsum[groups])
return (ranked * discount_sums).sum()
def _check_dcg_target_type(y_true):
y_type = type_of_target(y_true)
supported_fmt = (
"multilabel-indicator",
"continuous-multioutput",
"multiclass-multioutput",
)
if y_type not in supported_fmt:
raise ValueError(
"Only {} formats are supported. Got {} instead".format(
supported_fmt, y_type
)
)
def dcg_score(
y_true, y_score, *, k=None, log_base=2, sample_weight=None, ignore_ties=False
):
"""Compute Discounted Cumulative Gain.
Sum the true scores ranked in the order induced by the predicted scores,
after applying a logarithmic discount.
This ranking metric yields a high value if true labels are ranked high by
``y_score``.
Usually the Normalized Discounted Cumulative Gain (NDCG, computed by
ndcg_score) is preferred.
Parameters
----------
y_true : ndarray of shape (n_samples, n_labels)
True targets of multilabel classification, or true scores of entities
to be ranked.
y_score : ndarray of shape (n_samples, n_labels)
Target scores, can either be probability estimates, confidence values,
or non-thresholded measure of decisions (as returned by
"decision_function" on some classifiers).
k : int, default=None
Only consider the highest k scores in the ranking. If None, use all
outputs.
log_base : float, default=2
Base of the logarithm used for the discount. A low value means a
sharper discount (top results are more important).
sample_weight : ndarray of shape (n_samples,), default=None
Sample weights. If `None`, all samples are given the same weight.
ignore_ties : bool, default=False
Assume that there are no ties in y_score (which is likely to be the
case if y_score is continuous) for efficiency gains.
Returns
-------
discounted_cumulative_gain : float
The averaged sample DCG scores.
See Also
--------
ndcg_score : The Discounted Cumulative Gain divided by the Ideal Discounted
Cumulative Gain (the DCG obtained for a perfect ranking), in order to
have a score between 0 and 1.
References
----------
`Wikipedia entry for Discounted Cumulative Gain
<https://en.wikipedia.org/wiki/Discounted_cumulative_gain>`_.
Jarvelin, K., & Kekalainen, J. (2002).
Cumulated gain-based evaluation of IR techniques. ACM Transactions on
Information Systems (TOIS), 20(4), 422-446.
Wang, Y., Wang, L., Li, Y., He, D., Chen, W., & Liu, T. Y. (2013, May).
A theoretical analysis of NDCG ranking measures. In Proceedings of the 26th
Annual Conference on Learning Theory (COLT 2013).
McSherry, F., & Najork, M. (2008, March). Computing information retrieval
performance measures efficiently in the presence of tied scores. In
European conference on information retrieval (pp. 414-421). Springer,
Berlin, Heidelberg.
Examples
--------
>>> import numpy as np
>>> from sklearn.metrics import dcg_score
>>> # we have groud-truth relevance of some answers to a query:
>>> true_relevance = np.asarray([[10, 0, 0, 1, 5]])
>>> # we predict scores for the answers
>>> scores = np.asarray([[.1, .2, .3, 4, 70]])
>>> dcg_score(true_relevance, scores)
9.49...
>>> # we can set k to truncate the sum; only top k answers contribute
>>> dcg_score(true_relevance, scores, k=2)
5.63...
>>> # now we have some ties in our prediction
>>> scores = np.asarray([[1, 0, 0, 0, 1]])
>>> # by default ties are averaged, so here we get the average true
>>> # relevance of our top predictions: (10 + 5) / 2 = 7.5
>>> dcg_score(true_relevance, scores, k=1)
7.5
>>> # we can choose to ignore ties for faster results, but only
>>> # if we know there aren't ties in our scores, otherwise we get
>>> # wrong results:
>>> dcg_score(true_relevance,
... scores, k=1, ignore_ties=True)
5.0
"""
y_true = check_array(y_true, ensure_2d=False)
y_score = check_array(y_score, ensure_2d=False)
check_consistent_length(y_true, y_score, sample_weight)
_check_dcg_target_type(y_true)
return np.average(
_dcg_sample_scores(
y_true, y_score, k=k, log_base=log_base, ignore_ties=ignore_ties
),
weights=sample_weight,
)
def _ndcg_sample_scores(y_true, y_score, k=None, ignore_ties=False):
"""Compute Normalized Discounted Cumulative Gain.
Sum the true scores ranked in the order induced by the predicted scores,
after applying a logarithmic discount. Then divide by the best possible
score (Ideal DCG, obtained for a perfect ranking) to obtain a score between
0 and 1.
This ranking metric yields a high value if true labels are ranked high by
``y_score``.
Parameters
----------
y_true : ndarray of shape (n_samples, n_labels)
True targets of multilabel classification, or true scores of entities
to be ranked.
y_score : ndarray of shape (n_samples, n_labels)
Target scores, can either be probability estimates, confidence values,
or non-thresholded measure of decisions (as returned by
"decision_function" on some classifiers).
k : int, default=None
Only consider the highest k scores in the ranking. If None, use all
outputs.
ignore_ties : bool, default=False
Assume that there are no ties in y_score (which is likely to be the
case if y_score is continuous) for efficiency gains.
Returns
-------
normalized_discounted_cumulative_gain : ndarray of shape (n_samples,)
The NDCG score for each sample (float in [0., 1.]).
See Also
--------
dcg_score : Discounted Cumulative Gain (not normalized).
"""
gain = _dcg_sample_scores(y_true, y_score, k, ignore_ties=ignore_ties)
# Here we use the order induced by y_true so we can ignore ties since
# the gain associated to tied indices is the same (permuting ties doesn't
# change the value of the re-ordered y_true)
normalizing_gain = _dcg_sample_scores(y_true, y_true, k, ignore_ties=True)
all_irrelevant = normalizing_gain == 0
gain[all_irrelevant] = 0
gain[~all_irrelevant] /= normalizing_gain[~all_irrelevant]
return gain
def ndcg_score(y_true, y_score, *, k=None, sample_weight=None, ignore_ties=False):
"""Compute Normalized Discounted Cumulative Gain.
Sum the true scores ranked in the order induced by the predicted scores,
after applying a logarithmic discount. Then divide by the best possible
score (Ideal DCG, obtained for a perfect ranking) to obtain a score between
0 and 1.
This ranking metric yields a high value if true labels are ranked high by
``y_score``.
Parameters
----------
y_true : ndarray of shape (n_samples, n_labels)
True targets of multilabel classification, or true scores of entities
to be ranked.
y_score : ndarray of shape (n_samples, n_labels)
Target scores, can either be probability estimates, confidence values,
or non-thresholded measure of decisions (as returned by
"decision_function" on some classifiers).
k : int, default=None
Only consider the highest k scores in the ranking. If `None`, use all
outputs.
sample_weight : ndarray of shape (n_samples,), default=None
Sample weights. If `None`, all samples are given the same weight.
ignore_ties : bool, default=False
Assume that there are no ties in y_score (which is likely to be the
case if y_score is continuous) for efficiency gains.
Returns
-------
normalized_discounted_cumulative_gain : float in [0., 1.]
The averaged NDCG scores for all samples.
See Also
--------
dcg_score : Discounted Cumulative Gain (not normalized).
References
----------
`Wikipedia entry for Discounted Cumulative Gain
<https://en.wikipedia.org/wiki/Discounted_cumulative_gain>`_
Jarvelin, K., & Kekalainen, J. (2002).
Cumulated gain-based evaluation of IR techniques. ACM Transactions on
Information Systems (TOIS), 20(4), 422-446.
Wang, Y., Wang, L., Li, Y., He, D., Chen, W., & Liu, T. Y. (2013, May).
A theoretical analysis of NDCG ranking measures. In Proceedings of the 26th
Annual Conference on Learning Theory (COLT 2013)
McSherry, F., & Najork, M. (2008, March). Computing information retrieval
performance measures efficiently in the presence of tied scores. In
European conference on information retrieval (pp. 414-421). Springer,
Berlin, Heidelberg.
Examples
--------
>>> import numpy as np
>>> from sklearn.metrics import ndcg_score
>>> # we have groud-truth relevance of some answers to a query:
>>> true_relevance = np.asarray([[10, 0, 0, 1, 5]])
>>> # we predict some scores (relevance) for the answers
>>> scores = np.asarray([[.1, .2, .3, 4, 70]])
>>> ndcg_score(true_relevance, scores)
0.69...
>>> scores = np.asarray([[.05, 1.1, 1., .5, .0]])
>>> ndcg_score(true_relevance, scores)
0.49...
>>> # we can set k to truncate the sum; only top k answers contribute.
>>> ndcg_score(true_relevance, scores, k=4)
0.35...
>>> # the normalization takes k into account so a perfect answer
>>> # would still get 1.0
>>> ndcg_score(true_relevance, true_relevance, k=4)
1.0
>>> # now we have some ties in our prediction
>>> scores = np.asarray([[1, 0, 0, 0, 1]])
>>> # by default ties are averaged, so here we get the average (normalized)
>>> # true relevance of our top predictions: (10 / 10 + 5 / 10) / 2 = .75
>>> ndcg_score(true_relevance, scores, k=1)
0.75
>>> # we can choose to ignore ties for faster results, but only
>>> # if we know there aren't ties in our scores, otherwise we get
>>> # wrong results:
>>> ndcg_score(true_relevance,
... scores, k=1, ignore_ties=True)
0.5
"""
y_true = check_array(y_true, ensure_2d=False)
y_score = check_array(y_score, ensure_2d=False)
check_consistent_length(y_true, y_score, sample_weight)
_check_dcg_target_type(y_true)
gain = _ndcg_sample_scores(y_true, y_score, k=k, ignore_ties=ignore_ties)
return np.average(gain, weights=sample_weight)
def top_k_accuracy_score(
y_true, y_score, *, k=2, normalize=True, sample_weight=None, labels=None
):
"""Top-k Accuracy classification score.
This metric computes the number of times where the correct label is among
the top `k` labels predicted (ranked by predicted scores). Note that the
multilabel case isn't covered here.
Read more in the :ref:`User Guide <top_k_accuracy_score>`
Parameters
----------
y_true : array-like of shape (n_samples,)
True labels.
y_score : array-like of shape (n_samples,) or (n_samples, n_classes)
Target scores. These can be either probability estimates or
non-thresholded decision values (as returned by
:term:`decision_function` on some classifiers).
The binary case expects scores with shape (n_samples,) while the
multiclass case expects scores with shape (n_samples, n_classes).
In the multiclass case, the order of the class scores must
correspond to the order of ``labels``, if provided, or else to
the numerical or lexicographical order of the labels in ``y_true``.
If ``y_true`` does not contain all the labels, ``labels`` must be
provided.
k : int, default=2
Number of most likely outcomes considered to find the correct label.
normalize : bool, default=True
If `True`, return the fraction of correctly classified samples.
Otherwise, return the number of correctly classified samples.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If `None`, all samples are given the same weight.
labels : array-like of shape (n_classes,), default=None
Multiclass only. List of labels that index the classes in ``y_score``.
If ``None``, the numerical or lexicographical order of the labels in
``y_true`` is used. If ``y_true`` does not contain all the labels,
``labels`` must be provided.
Returns
-------
score : float
The top-k accuracy score. The best performance is 1 with
`normalize == True` and the number of samples with
`normalize == False`.
See also
--------
accuracy_score
Notes
-----
In cases where two or more labels are assigned equal predicted scores,
the labels with the highest indices will be chosen first. This might
impact the result if the correct label falls after the threshold because
of that.
Examples
--------
>>> import numpy as np
>>> from sklearn.metrics import top_k_accuracy_score
>>> y_true = np.array([0, 1, 2, 2])
>>> y_score = np.array([[0.5, 0.2, 0.2], # 0 is in top 2
... [0.3, 0.4, 0.2], # 1 is in top 2
... [0.2, 0.4, 0.3], # 2 is in top 2
... [0.7, 0.2, 0.1]]) # 2 isn't in top 2
>>> top_k_accuracy_score(y_true, y_score, k=2)
0.75
>>> # Not normalizing gives the number of "correctly" classified samples
>>> top_k_accuracy_score(y_true, y_score, k=2, normalize=False)
3
"""
y_true = check_array(y_true, ensure_2d=False, dtype=None)
y_true = column_or_1d(y_true)
y_type = type_of_target(y_true)
if y_type == "binary" and labels is not None and len(labels) > 2:
y_type = "multiclass"
y_score = check_array(y_score, ensure_2d=False)
y_score = column_or_1d(y_score) if y_type == "binary" else y_score
check_consistent_length(y_true, y_score, sample_weight)
if y_type not in {"binary", "multiclass"}:
raise ValueError(
f"y type must be 'binary' or 'multiclass', got '{y_type}' instead."
)
y_score_n_classes = y_score.shape[1] if y_score.ndim == 2 else 2
if labels is None:
classes = _unique(y_true)
n_classes = len(classes)
if n_classes != y_score_n_classes:
raise ValueError(
f"Number of classes in 'y_true' ({n_classes}) not equal "
f"to the number of classes in 'y_score' ({y_score_n_classes})."
)
else:
labels = column_or_1d(labels)
classes = _unique(labels)
n_labels = len(labels)
n_classes = len(classes)
if n_classes != n_labels:
raise ValueError("Parameter 'labels' must be unique.")
if not np.array_equal(classes, labels):
raise ValueError("Parameter 'labels' must be ordered.")
if n_classes != y_score_n_classes:
raise ValueError(
f"Number of given labels ({n_classes}) not equal to the "
f"number of classes in 'y_score' ({y_score_n_classes})."
)
if len(np.setdiff1d(y_true, classes)):
raise ValueError("'y_true' contains labels not in parameter 'labels'.")
if k >= n_classes:
warnings.warn(
f"'k' ({k}) greater than or equal to 'n_classes' ({n_classes}) "
"will result in a perfect score and is therefore meaningless.",
UndefinedMetricWarning,
)
y_true_encoded = _encode(y_true, uniques=classes)
if y_type == "binary":
if k == 1:
threshold = 0.5 if y_score.min() >= 0 and y_score.max() <= 1 else 0
y_pred = (y_score > threshold).astype(np.int64)
hits = y_pred == y_true_encoded
else:
hits = np.ones_like(y_score, dtype=np.bool_)
elif y_type == "multiclass":
sorted_pred = np.argsort(y_score, axis=1, kind="mergesort")[:, ::-1]
hits = (y_true_encoded == sorted_pred[:, :k].T).any(axis=0)
if normalize:
return np.average(hits, weights=sample_weight)
elif sample_weight is None:
return np.sum(hits)
else:
return np.dot(hits, sample_weight)