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"""Metrics to assess performance on classification task given class prediction
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>
# Jatin Shah <jatindshah@gmail.com>
# Saurabh Jha <saurabh.jhaa@gmail.com>
# Bernardo Stein <bernardovstein@gmail.com>
# Shangwu Yao <shangwuyao@gmail.com>
# License: BSD 3 clause
import warnings
import numpy as np
from scipy.sparse import coo_matrix
from scipy.sparse import csr_matrix
from ..preprocessing import LabelBinarizer
from ..preprocessing import LabelEncoder
from ..utils import assert_all_finite
from ..utils import check_array
from ..utils import check_consistent_length
from ..utils import column_or_1d
from ..utils.multiclass import unique_labels
from ..utils.multiclass import type_of_target
from ..utils.validation import _num_samples
from ..utils.sparsefuncs import count_nonzero
from ..exceptions import UndefinedMetricWarning
def _check_zero_division(zero_division):
if isinstance(zero_division, str) and zero_division == "warn":
return
elif isinstance(zero_division, (int, float)) and zero_division in [0, 1]:
return
raise ValueError('Got zero_division={0}.'
' Must be one of ["warn", 0, 1]'.format(zero_division))
def _check_targets(y_true, y_pred):
"""Check that y_true and y_pred belong to the same classification task
This converts multiclass or binary types to a common shape, and raises a
ValueError for a mix of multilabel and multiclass targets, a mix of
multilabel formats, for the presence of continuous-valued or multioutput
targets, or for targets of different lengths.
Column vectors are squeezed to 1d, while multilabel formats are returned
as CSR sparse label indicators.
Parameters
----------
y_true : array-like
y_pred : array-like
Returns
-------
type_true : one of {'multilabel-indicator', 'multiclass', 'binary'}
The type of the true target data, as output by
``utils.multiclass.type_of_target``
y_true : array or indicator matrix
y_pred : array or indicator matrix
"""
check_consistent_length(y_true, y_pred)
type_true = type_of_target(y_true)
type_pred = type_of_target(y_pred)
y_type = {type_true, type_pred}
if y_type == {"binary", "multiclass"}:
y_type = {"multiclass"}
if len(y_type) > 1:
raise ValueError("Classification metrics can't handle a mix of {0} "
"and {1} targets".format(type_true, type_pred))
# We can't have more than one value on y_type => The set is no more needed
y_type = y_type.pop()
# No metrics support "multiclass-multioutput" format
if (y_type not in ["binary", "multiclass", "multilabel-indicator"]):
raise ValueError("{0} is not supported".format(y_type))
if y_type in ["binary", "multiclass"]:
y_true = column_or_1d(y_true)
y_pred = column_or_1d(y_pred)
if y_type == "binary":
unique_values = np.union1d(y_true, y_pred)
if len(unique_values) > 2:
y_type = "multiclass"
if y_type.startswith('multilabel'):
y_true = csr_matrix(y_true)
y_pred = csr_matrix(y_pred)
y_type = 'multilabel-indicator'
return y_type, y_true, y_pred
def _weighted_sum(sample_score, sample_weight, normalize=False):
if normalize:
return np.average(sample_score, weights=sample_weight)
elif sample_weight is not None:
return np.dot(sample_score, sample_weight)
else:
return sample_score.sum()
def accuracy_score(y_true, y_pred, normalize=True, sample_weight=None):
"""Accuracy classification score.
In multilabel classification, this function computes subset accuracy:
the set of labels predicted for a sample must *exactly* match the
corresponding set of labels in y_true.
Read more in the :ref:`User Guide <accuracy_score>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) labels.
y_pred : 1d array-like, or label indicator array / sparse matrix
Predicted labels, as returned by a classifier.
normalize : bool, optional (default=True)
If ``False``, return the number of correctly classified samples.
Otherwise, return the fraction of correctly classified samples.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
score : float
If ``normalize == True``, return the fraction of correctly
classified samples (float), else returns the number of correctly
classified samples (int).
The best performance is 1 with ``normalize == True`` and the number
of samples with ``normalize == False``.
See also
--------
jaccard_score, hamming_loss, zero_one_loss
Notes
-----
In binary and multiclass classification, this function is equal
to the ``jaccard_score`` function.
Examples
--------
>>> from sklearn.metrics import accuracy_score
>>> y_pred = [0, 2, 1, 3]
>>> y_true = [0, 1, 2, 3]
>>> accuracy_score(y_true, y_pred)
0.5
>>> accuracy_score(y_true, y_pred, normalize=False)
2
In the multilabel case with binary label indicators:
>>> import numpy as np
>>> accuracy_score(np.array([[0, 1], [1, 1]]), np.ones((2, 2)))
0.5
"""
# Compute accuracy for each possible representation
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
check_consistent_length(y_true, y_pred, sample_weight)
if y_type.startswith('multilabel'):
differing_labels = count_nonzero(y_true - y_pred, axis=1)
score = differing_labels == 0
else:
score = y_true == y_pred
return _weighted_sum(score, sample_weight, normalize)
def confusion_matrix(y_true, y_pred, labels=None, sample_weight=None,
normalize=None):
"""Compute confusion matrix to evaluate the accuracy of a classification.
By definition a confusion matrix :math:`C` is such that :math:`C_{i, j}`
is equal to the number of observations known to be in group :math:`i` and
predicted to be in group :math:`j`.
Thus in binary classification, the count of true negatives is
:math:`C_{0,0}`, false negatives is :math:`C_{1,0}`, true positives is
:math:`C_{1,1}` and false positives is :math:`C_{0,1}`.
Read more in the :ref:`User Guide <confusion_matrix>`.
Parameters
----------
y_true : array-like of shape (n_samples,)
Ground truth (correct) target values.
y_pred : array-like of shape (n_samples,)
Estimated targets as returned by a classifier.
labels : array-like of shape (n_classes), default=None
List of labels to index the matrix. This may be used to reorder
or select a subset of labels.
If ``None`` is given, those that appear at least once
in ``y_true`` or ``y_pred`` are used in sorted order.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
normalize : {'true', 'pred', 'all'}, default=None
Normalizes confusion matrix over the true (rows), predicted (columns)
conditions or all the population. If None, confusion matrix will not be
normalized.
Returns
-------
C : ndarray of shape (n_classes, n_classes)
Confusion matrix.
References
----------
.. [1] `Wikipedia entry for the Confusion matrix
<https://en.wikipedia.org/wiki/Confusion_matrix>`_
(Wikipedia and other references may use a different
convention for axes)
Examples
--------
>>> from sklearn.metrics import confusion_matrix
>>> y_true = [2, 0, 2, 2, 0, 1]
>>> y_pred = [0, 0, 2, 2, 0, 2]
>>> confusion_matrix(y_true, y_pred)
array([[2, 0, 0],
[0, 0, 1],
[1, 0, 2]])
>>> y_true = ["cat", "ant", "cat", "cat", "ant", "bird"]
>>> y_pred = ["ant", "ant", "cat", "cat", "ant", "cat"]
>>> confusion_matrix(y_true, y_pred, labels=["ant", "bird", "cat"])
array([[2, 0, 0],
[0, 0, 1],
[1, 0, 2]])
In the binary case, we can extract true positives, etc as follows:
>>> tn, fp, fn, tp = confusion_matrix([0, 1, 0, 1], [1, 1, 1, 0]).ravel()
>>> (tn, fp, fn, tp)
(0, 2, 1, 1)
"""
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
if y_type not in ("binary", "multiclass"):
raise ValueError("%s is not supported" % y_type)
if labels is None:
labels = unique_labels(y_true, y_pred)
else:
labels = np.asarray(labels)
if np.all([l not in y_true for l in labels]):
raise ValueError("At least one label specified must be in y_true")
if sample_weight is None:
sample_weight = np.ones(y_true.shape[0], dtype=np.int64)
else:
sample_weight = np.asarray(sample_weight)
check_consistent_length(y_true, y_pred, sample_weight)
if normalize not in ['true', 'pred', 'all', None]:
raise ValueError("normalize must be one of {'true', 'pred', "
"'all', None}")
n_labels = labels.size
label_to_ind = {y: x for x, y in enumerate(labels)}
# convert yt, yp into index
y_pred = np.array([label_to_ind.get(x, n_labels + 1) for x in y_pred])
y_true = np.array([label_to_ind.get(x, n_labels + 1) for x in y_true])
# intersect y_pred, y_true with labels, eliminate items not in labels
ind = np.logical_and(y_pred < n_labels, y_true < n_labels)
y_pred = y_pred[ind]
y_true = y_true[ind]
# also eliminate weights of eliminated items
sample_weight = sample_weight[ind]
# Choose the accumulator dtype to always have high precision
if sample_weight.dtype.kind in {'i', 'u', 'b'}:
dtype = np.int64
else:
dtype = np.float64
cm = coo_matrix((sample_weight, (y_true, y_pred)),
shape=(n_labels, n_labels), dtype=dtype,
).toarray()
with np.errstate(all='ignore'):
if normalize == 'true':
cm = cm / cm.sum(axis=1, keepdims=True)
elif normalize == 'pred':
cm = cm / cm.sum(axis=0, keepdims=True)
elif normalize == 'all':
cm = cm / cm.sum()
cm = np.nan_to_num(cm)
return cm
def multilabel_confusion_matrix(y_true, y_pred, sample_weight=None,
labels=None, samplewise=False):
"""Compute a confusion matrix for each class or sample
.. versionadded:: 0.21
Compute class-wise (default) or sample-wise (samplewise=True) multilabel
confusion matrix to evaluate the accuracy of a classification, and output
confusion matrices for each class or sample.
In multilabel confusion matrix :math:`MCM`, the count of true negatives
is :math:`MCM_{:,0,0}`, false negatives is :math:`MCM_{:,1,0}`,
true positives is :math:`MCM_{:,1,1}` and false positives is
:math:`MCM_{:,0,1}`.
Multiclass data will be treated as if binarized under a one-vs-rest
transformation. Returned confusion matrices will be in the order of
sorted unique labels in the union of (y_true, y_pred).
Read more in the :ref:`User Guide <multilabel_confusion_matrix>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
of shape (n_samples, n_outputs) or (n_samples,)
Ground truth (correct) target values.
y_pred : 1d array-like, or label indicator array / sparse matrix
of shape (n_samples, n_outputs) or (n_samples,)
Estimated targets as returned by a classifier
sample_weight : array-like of shape (n_samples,), default=None
Sample weights
labels : array-like
A list of classes or column indices to select some (or to force
inclusion of classes absent from the data)
samplewise : bool, default=False
In the multilabel case, this calculates a confusion matrix per sample
Returns
-------
multi_confusion : array, shape (n_outputs, 2, 2)
A 2x2 confusion matrix corresponding to each output in the input.
When calculating class-wise multi_confusion (default), then
n_outputs = n_labels; when calculating sample-wise multi_confusion
(samplewise=True), n_outputs = n_samples. If ``labels`` is defined,
the results will be returned in the order specified in ``labels``,
otherwise the results will be returned in sorted order by default.
See also
--------
confusion_matrix
Notes
-----
The multilabel_confusion_matrix calculates class-wise or sample-wise
multilabel confusion matrices, and in multiclass tasks, labels are
binarized under a one-vs-rest way; while confusion_matrix calculates
one confusion matrix for confusion between every two classes.
Examples
--------
Multilabel-indicator case:
>>> import numpy as np
>>> from sklearn.metrics import multilabel_confusion_matrix
>>> y_true = np.array([[1, 0, 1],
... [0, 1, 0]])
>>> y_pred = np.array([[1, 0, 0],
... [0, 1, 1]])
>>> multilabel_confusion_matrix(y_true, y_pred)
array([[[1, 0],
[0, 1]],
<BLANKLINE>
[[1, 0],
[0, 1]],
<BLANKLINE>
[[0, 1],
[1, 0]]])
Multiclass case:
>>> y_true = ["cat", "ant", "cat", "cat", "ant", "bird"]
>>> y_pred = ["ant", "ant", "cat", "cat", "ant", "cat"]
>>> multilabel_confusion_matrix(y_true, y_pred,
... labels=["ant", "bird", "cat"])
array([[[3, 1],
[0, 2]],
<BLANKLINE>
[[5, 0],
[1, 0]],
<BLANKLINE>
[[2, 1],
[1, 2]]])
"""
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
if sample_weight is not None:
sample_weight = column_or_1d(sample_weight)
check_consistent_length(y_true, y_pred, sample_weight)
if y_type not in ("binary", "multiclass", "multilabel-indicator"):
raise ValueError("%s is not supported" % y_type)
present_labels = unique_labels(y_true, y_pred)
if labels is None:
labels = present_labels
n_labels = None
else:
n_labels = len(labels)
labels = np.hstack([labels, np.setdiff1d(present_labels, labels,
assume_unique=True)])
if y_true.ndim == 1:
if samplewise:
raise ValueError("Samplewise metrics are not available outside of "
"multilabel classification.")
le = LabelEncoder()
le.fit(labels)
y_true = le.transform(y_true)
y_pred = le.transform(y_pred)
sorted_labels = le.classes_
# labels are now from 0 to len(labels) - 1 -> use bincount
tp = y_true == y_pred
tp_bins = y_true[tp]
if sample_weight is not None:
tp_bins_weights = np.asarray(sample_weight)[tp]
else:
tp_bins_weights = None
if len(tp_bins):
tp_sum = np.bincount(tp_bins, weights=tp_bins_weights,
minlength=len(labels))
else:
# Pathological case
true_sum = pred_sum = tp_sum = np.zeros(len(labels))
if len(y_pred):
pred_sum = np.bincount(y_pred, weights=sample_weight,
minlength=len(labels))
if len(y_true):
true_sum = np.bincount(y_true, weights=sample_weight,
minlength=len(labels))
# Retain only selected labels
indices = np.searchsorted(sorted_labels, labels[:n_labels])
tp_sum = tp_sum[indices]
true_sum = true_sum[indices]
pred_sum = pred_sum[indices]
else:
sum_axis = 1 if samplewise else 0
# All labels are index integers for multilabel.
# Select labels:
if not np.array_equal(labels, present_labels):
if np.max(labels) > np.max(present_labels):
raise ValueError('All labels must be in [0, n labels) for '
'multilabel targets. '
'Got %d > %d' %
(np.max(labels), np.max(present_labels)))
if np.min(labels) < 0:
raise ValueError('All labels must be in [0, n labels) for '
'multilabel targets. '
'Got %d < 0' % np.min(labels))
if n_labels is not None:
y_true = y_true[:, labels[:n_labels]]
y_pred = y_pred[:, labels[:n_labels]]
# calculate weighted counts
true_and_pred = y_true.multiply(y_pred)
tp_sum = count_nonzero(true_and_pred, axis=sum_axis,
sample_weight=sample_weight)
pred_sum = count_nonzero(y_pred, axis=sum_axis,
sample_weight=sample_weight)
true_sum = count_nonzero(y_true, axis=sum_axis,
sample_weight=sample_weight)
fp = pred_sum - tp_sum
fn = true_sum - tp_sum
tp = tp_sum
if sample_weight is not None and samplewise:
sample_weight = np.array(sample_weight)
tp = np.array(tp)
fp = np.array(fp)
fn = np.array(fn)
tn = sample_weight * y_true.shape[1] - tp - fp - fn
elif sample_weight is not None:
tn = sum(sample_weight) - tp - fp - fn
elif samplewise:
tn = y_true.shape[1] - tp - fp - fn
else:
tn = y_true.shape[0] - tp - fp - fn
return np.array([tn, fp, fn, tp]).T.reshape(-1, 2, 2)
def cohen_kappa_score(y1, y2, labels=None, weights=None, sample_weight=None):
r"""Cohen's kappa: a statistic that measures inter-annotator agreement.
This function computes Cohen's kappa [1]_, a score that expresses the level
of agreement between two annotators on a classification problem. It is
defined as
.. math::
\kappa = (p_o - p_e) / (1 - p_e)
where :math:`p_o` is the empirical probability of agreement on the label
assigned to any sample (the observed agreement ratio), and :math:`p_e` is
the expected agreement when both annotators assign labels randomly.
:math:`p_e` is estimated using a per-annotator empirical prior over the
class labels [2]_.
Read more in the :ref:`User Guide <cohen_kappa>`.
Parameters
----------
y1 : array, shape = [n_samples]
Labels assigned by the first annotator.
y2 : array, shape = [n_samples]
Labels assigned by the second annotator. The kappa statistic is
symmetric, so swapping ``y1`` and ``y2`` doesn't change the value.
labels : array, shape = [n_classes], optional
List of labels to index the matrix. This may be used to select a
subset of labels. If None, all labels that appear at least once in
``y1`` or ``y2`` are used.
weights : str, optional
Weighting type to calculate the score. None means no weighted;
"linear" means linear weighted; "quadratic" means quadratic weighted.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
kappa : float
The kappa statistic, which is a number between -1 and 1. The maximum
value means complete agreement; zero or lower means chance agreement.
References
----------
.. [1] J. Cohen (1960). "A coefficient of agreement for nominal scales".
Educational and Psychological Measurement 20(1):37-46.
doi:10.1177/001316446002000104.
.. [2] `R. Artstein and M. Poesio (2008). "Inter-coder agreement for
computational linguistics". Computational Linguistics 34(4):555-596.
<https://www.mitpressjournals.org/doi/pdf/10.1162/coli.07-034-R2>`_
.. [3] `Wikipedia entry for the Cohen's kappa.
<https://en.wikipedia.org/wiki/Cohen%27s_kappa>`_
"""
confusion = confusion_matrix(y1, y2, labels=labels,
sample_weight=sample_weight)
n_classes = confusion.shape[0]
sum0 = np.sum(confusion, axis=0)
sum1 = np.sum(confusion, axis=1)
expected = np.outer(sum0, sum1) / np.sum(sum0)
if weights is None:
w_mat = np.ones([n_classes, n_classes], dtype=np.int)
w_mat.flat[:: n_classes + 1] = 0
elif weights == "linear" or weights == "quadratic":
w_mat = np.zeros([n_classes, n_classes], dtype=np.int)
w_mat += np.arange(n_classes)
if weights == "linear":
w_mat = np.abs(w_mat - w_mat.T)
else:
w_mat = (w_mat - w_mat.T) ** 2
else:
raise ValueError("Unknown kappa weighting type.")
k = np.sum(w_mat * confusion) / np.sum(w_mat * expected)
return 1 - k
def jaccard_similarity_score(y_true, y_pred, normalize=True,
sample_weight=None):
"""Jaccard similarity coefficient score
.. deprecated:: 0.21
This is deprecated to be removed in 0.23, since its handling of
binary and multiclass inputs was broken. `jaccard_score` has an API
that is consistent with precision_score, f_score, etc.
Read more in the :ref:`User Guide <jaccard_similarity_score>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) labels.
y_pred : 1d array-like, or label indicator array / sparse matrix
Predicted labels, as returned by a classifier.
normalize : bool, optional (default=True)
If ``False``, return the sum of the Jaccard similarity coefficient
over the sample set. Otherwise, return the average of Jaccard
similarity coefficient.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
score : float
If ``normalize == True``, return the average Jaccard similarity
coefficient, else it returns the sum of the Jaccard similarity
coefficient over the sample set.
The best performance is 1 with ``normalize == True`` and the number
of samples with ``normalize == False``.
See also
--------
accuracy_score, hamming_loss, zero_one_loss
Notes
-----
In binary and multiclass classification, this function is equivalent
to the ``accuracy_score``. It differs in the multilabel classification
problem.
References
----------
.. [1] `Wikipedia entry for the Jaccard index
<https://en.wikipedia.org/wiki/Jaccard_index>`_
"""
warnings.warn('jaccard_similarity_score has been deprecated and replaced '
'with jaccard_score. It will be removed in version 0.23. '
'This implementation has surprising behavior for binary '
'and multiclass classification tasks.',
FutureWarning)
# Compute accuracy for each possible representation
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
check_consistent_length(y_true, y_pred, sample_weight)
if y_type.startswith('multilabel'):
with np.errstate(divide='ignore', invalid='ignore'):
# oddly, we may get an "invalid" rather than a "divide" error here
pred_or_true = count_nonzero(y_true + y_pred, axis=1)
pred_and_true = count_nonzero(y_true.multiply(y_pred), axis=1)
score = pred_and_true / pred_or_true
score[pred_or_true == 0.0] = 1.0
else:
score = y_true == y_pred
return _weighted_sum(score, sample_weight, normalize)
def jaccard_score(y_true, y_pred, labels=None, pos_label=1,
average='binary', sample_weight=None):
"""Jaccard similarity coefficient score
The Jaccard index [1], or Jaccard similarity coefficient, defined as
the size of the intersection divided by the size of the union of two label
sets, is used to compare set of predicted labels for a sample to the
corresponding set of labels in ``y_true``.
Read more in the :ref:`User Guide <jaccard_similarity_score>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) labels.
y_pred : 1d array-like, or label indicator array / sparse matrix
Predicted labels, as returned by a classifier.
labels : list, optional
The set of labels to include when ``average != 'binary'``, and their
order if ``average is None``. Labels present in the data can be
excluded, for example to calculate a multiclass average ignoring a
majority negative class, while labels not present in the data will
result in 0 components in a macro average. For multilabel targets,
labels are column indices. By default, all labels in ``y_true`` and
``y_pred`` are used in sorted order.
pos_label : str or int, 1 by default
The class to report if ``average='binary'`` and the data is binary.
If the data are multiclass or multilabel, this will be ignored;
setting ``labels=[pos_label]`` and ``average != 'binary'`` will report
scores for that label only.
average : string, [None, 'binary' (default), 'micro', 'macro', 'samples', \
'weighted']
If ``None``, the scores for each class are returned. Otherwise, this
determines the type of averaging performed on the data:
``'binary'``:
Only report results for the class specified by ``pos_label``.
This is applicable only if targets (``y_{true,pred}``) are binary.
``'micro'``:
Calculate metrics globally by counting the total true positives,
false negatives and false positives.
``'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). This
alters 'macro' to account for label imbalance.
``'samples'``:
Calculate metrics for each instance, and find their average (only
meaningful for multilabel classification).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
score : float (if average is not None) or array of floats, shape =\
[n_unique_labels]
See also
--------
accuracy_score, f_score, multilabel_confusion_matrix
Notes
-----
:func:`jaccard_score` may be a poor metric if there are no
positives for some samples or classes. Jaccard is undefined if there are
no true or predicted labels, and our implementation will return a score
of 0 with a warning.
References
----------
.. [1] `Wikipedia entry for the Jaccard index
<https://en.wikipedia.org/wiki/Jaccard_index>`_
Examples
--------
>>> import numpy as np
>>> from sklearn.metrics import jaccard_score
>>> y_true = np.array([[0, 1, 1],
... [1, 1, 0]])
>>> y_pred = np.array([[1, 1, 1],
... [1, 0, 0]])
In the binary case:
>>> jaccard_score(y_true[0], y_pred[0])
0.6666...
In the multilabel case:
>>> jaccard_score(y_true, y_pred, average='samples')
0.5833...
>>> jaccard_score(y_true, y_pred, average='macro')
0.6666...
>>> jaccard_score(y_true, y_pred, average=None)
array([0.5, 0.5, 1. ])
In the multiclass case:
>>> y_pred = [0, 2, 1, 2]
>>> y_true = [0, 1, 2, 2]
>>> jaccard_score(y_true, y_pred, average=None)
array([1. , 0. , 0.33...])
"""
labels = _check_set_wise_labels(y_true, y_pred, average, labels,
pos_label)
samplewise = average == 'samples'
MCM = multilabel_confusion_matrix(y_true, y_pred,
sample_weight=sample_weight,
labels=labels, samplewise=samplewise)
numerator = MCM[:, 1, 1]
denominator = MCM[:, 1, 1] + MCM[:, 0, 1] + MCM[:, 1, 0]
if average == 'micro':
numerator = np.array([numerator.sum()])
denominator = np.array([denominator.sum()])
jaccard = _prf_divide(numerator, denominator, 'jaccard',
'true or predicted', average, ('jaccard',))
if average is None:
return jaccard
if average == 'weighted':
weights = MCM[:, 1, 0] + MCM[:, 1, 1]
if not np.any(weights):
# numerator is 0, and warning should have already been issued
weights = None
elif average == 'samples' and sample_weight is not None:
weights = sample_weight
else:
weights = None
return np.average(jaccard, weights=weights)
def matthews_corrcoef(y_true, y_pred, sample_weight=None):
"""Compute the Matthews correlation coefficient (MCC)
The Matthews correlation coefficient is used in machine learning as a
measure of the quality of binary and multiclass classifications. It takes
into account true and false positives and negatives and is generally
regarded as a balanced measure which can be used even if the classes are of
very different sizes. The MCC is in essence a correlation coefficient value
between -1 and +1. A coefficient of +1 represents a perfect prediction, 0
an average random prediction and -1 an inverse prediction. The statistic
is also known as the phi coefficient. [source: Wikipedia]
Binary and multiclass labels are supported. Only in the binary case does
this relate to information about true and false positives and negatives.
See references below.
Read more in the :ref:`User Guide <matthews_corrcoef>`.
Parameters
----------
y_true : array, shape = [n_samples]
Ground truth (correct) target values.
y_pred : array, shape = [n_samples]
Estimated targets as returned by a classifier.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
mcc : float
The Matthews correlation coefficient (+1 represents a perfect
prediction, 0 an average random prediction and -1 and inverse
prediction).
References
----------
.. [1] `Baldi, Brunak, Chauvin, Andersen and Nielsen, (2000). Assessing the
accuracy of prediction algorithms for classification: an overview
<https://doi.org/10.1093/bioinformatics/16.5.412>`_
.. [2] `Wikipedia entry for the Matthews Correlation Coefficient
<https://en.wikipedia.org/wiki/Matthews_correlation_coefficient>`_
.. [3] `Gorodkin, (2004). Comparing two K-category assignments by a
K-category correlation coefficient
<https://www.sciencedirect.com/science/article/pii/S1476927104000799>`_
.. [4] `Jurman, Riccadonna, Furlanello, (2012). A Comparison of MCC and CEN
Error Measures in MultiClass Prediction
<https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0041882>`_
Examples
--------
>>> from sklearn.metrics import matthews_corrcoef
>>> y_true = [+1, +1, +1, -1]
>>> y_pred = [+1, -1, +1, +1]
>>> matthews_corrcoef(y_true, y_pred)
-0.33...
"""
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
check_consistent_length(y_true, y_pred, sample_weight)
if y_type not in {"binary", "multiclass"}:
raise ValueError("%s is not supported" % y_type)
lb = LabelEncoder()
lb.fit(np.hstack([y_true, y_pred]))
y_true = lb.transform(y_true)
y_pred = lb.transform(y_pred)
C = confusion_matrix(y_true, y_pred, sample_weight=sample_weight)
t_sum = C.sum(axis=1, dtype=np.float64)
p_sum = C.sum(axis=0, dtype=np.float64)
n_correct = np.trace(C, dtype=np.float64)
n_samples = p_sum.sum()
cov_ytyp = n_correct * n_samples - np.dot(t_sum, p_sum)
cov_ypyp = n_samples ** 2 - np.dot(p_sum, p_sum)
cov_ytyt = n_samples ** 2 - np.dot(t_sum, t_sum)
mcc = cov_ytyp / np.sqrt(cov_ytyt * cov_ypyp)
if np.isnan(mcc):
return 0.
else:
return mcc
def zero_one_loss(y_true, y_pred, normalize=True, sample_weight=None):
"""Zero-one classification loss.
If normalize is ``True``, return the fraction of misclassifications
(float), else it returns the number of misclassifications (int). The best
performance is 0.
Read more in the :ref:`User Guide <zero_one_loss>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) labels.
y_pred : 1d array-like, or label indicator array / sparse matrix
Predicted labels, as returned by a classifier.
normalize : bool, optional (default=True)
If ``False``, return the number of misclassifications.
Otherwise, return the fraction of misclassifications.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
loss : float or int,
If ``normalize == True``, return the fraction of misclassifications
(float), else it returns the number of misclassifications (int).
Notes
-----
In multilabel classification, the zero_one_loss function corresponds to
the subset zero-one loss: for each sample, the entire set of labels must be
correctly predicted, otherwise the loss for that sample is equal to one.
See also
--------
accuracy_score, hamming_loss, jaccard_score
Examples
--------
>>> from sklearn.metrics import zero_one_loss
>>> y_pred = [1, 2, 3, 4]
>>> y_true = [2, 2, 3, 4]
>>> zero_one_loss(y_true, y_pred)
0.25
>>> zero_one_loss(y_true, y_pred, normalize=False)
1
In the multilabel case with binary label indicators:
>>> import numpy as np
>>> zero_one_loss(np.array([[0, 1], [1, 1]]), np.ones((2, 2)))
0.5
"""
score = accuracy_score(y_true, y_pred,
normalize=normalize,
sample_weight=sample_weight)
if normalize:
return 1 - score
else:
if sample_weight is not None:
n_samples = np.sum(sample_weight)
else:
n_samples = _num_samples(y_true)
return n_samples - score
def f1_score(y_true, y_pred, labels=None, pos_label=1, average='binary',
sample_weight=None, zero_division="warn"):
"""Compute the F1 score, also known as balanced F-score or F-measure
The F1 score can be interpreted as a weighted average of the precision and
recall, where an F1 score reaches its best value at 1 and worst score at 0.
The relative contribution of precision and recall to the F1 score are
equal. The formula for the F1 score is::
F1 = 2 * (precision * recall) / (precision + recall)
In the multi-class and multi-label case, this is the average of
the F1 score of each class with weighting depending on the ``average``
parameter.
Read more in the :ref:`User Guide <precision_recall_f_measure_metrics>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) target values.
y_pred : 1d array-like, or label indicator array / sparse matrix
Estimated targets as returned by a classifier.
labels : list, optional
The set of labels to include when ``average != 'binary'``, and their
order if ``average is None``. Labels present in the data can be
excluded, for example to calculate a multiclass average ignoring a
majority negative class, while labels not present in the data will
result in 0 components in a macro average. For multilabel targets,
labels are column indices. By default, all labels in ``y_true`` and
``y_pred`` are used in sorted order.
.. versionchanged:: 0.17
parameter *labels* improved for multiclass problem.
pos_label : str or int, 1 by default
The class to report if ``average='binary'`` and the data is binary.
If the data are multiclass or multilabel, this will be ignored;
setting ``labels=[pos_label]`` and ``average != 'binary'`` will report
scores for that label only.
average : string, [None, 'binary' (default), 'micro', 'macro', 'samples', \
'weighted']
This parameter is required for multiclass/multilabel targets.
If ``None``, the scores for each class are returned. Otherwise, this
determines the type of averaging performed on the data:
``'binary'``:
Only report results for the class specified by ``pos_label``.
This is applicable only if targets (``y_{true,pred}``) are binary.
``'micro'``:
Calculate metrics globally by counting the total true positives,
false negatives and false positives.
``'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). This
alters 'macro' to account for label imbalance; it can result in an
F-score that is not between precision and recall.
``'samples'``:
Calculate metrics for each instance, and find their average (only
meaningful for multilabel classification where this differs from
:func:`accuracy_score`).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
zero_division : "warn", 0 or 1, default="warn"
Sets the value to return when there is a zero division, i.e. when all
predictions and labels are negative. If set to "warn", this acts as 0,
but warnings are also raised.
Returns
-------
f1_score : float or array of float, shape = [n_unique_labels]
F1 score of the positive class in binary classification or weighted
average of the F1 scores of each class for the multiclass task.
See also
--------
fbeta_score, precision_recall_fscore_support, jaccard_score,
multilabel_confusion_matrix
References
----------
.. [1] `Wikipedia entry for the F1-score
<https://en.wikipedia.org/wiki/F1_score>`_
Examples
--------
>>> from sklearn.metrics import f1_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> f1_score(y_true, y_pred, average='macro')
0.26...
>>> f1_score(y_true, y_pred, average='micro')
0.33...
>>> f1_score(y_true, y_pred, average='weighted')
0.26...
>>> f1_score(y_true, y_pred, average=None)
array([0.8, 0. , 0. ])
>>> y_true = [0, 0, 0, 0, 0, 0]
>>> y_pred = [0, 0, 0, 0, 0, 0]
>>> f1_score(y_true, y_pred, zero_division=1)
1.0...
Notes
-----
When ``true positive + false positive == 0``, precision is undefined;
When ``true positive + false negative == 0``, recall is undefined.
In such cases, by default the metric will be set to 0, as will f-score,
and ``UndefinedMetricWarning`` will be raised. This behavior can be
modified with ``zero_division``.
"""
return fbeta_score(y_true, y_pred, 1, labels=labels,
pos_label=pos_label, average=average,
sample_weight=sample_weight,
zero_division=zero_division)
def fbeta_score(y_true, y_pred, beta, labels=None, pos_label=1,
average='binary', sample_weight=None, zero_division="warn"):
"""Compute the F-beta score
The F-beta score is the weighted harmonic mean of precision and recall,
reaching its optimal value at 1 and its worst value at 0.
The `beta` parameter determines the weight of recall in the combined
score. ``beta < 1`` lends more weight to precision, while ``beta > 1``
favors recall (``beta -> 0`` considers only precision, ``beta -> +inf``
only recall).
Read more in the :ref:`User Guide <precision_recall_f_measure_metrics>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) target values.
y_pred : 1d array-like, or label indicator array / sparse matrix
Estimated targets as returned by a classifier.
beta : float
Determines the weight of recall in the combined score.
labels : list, optional
The set of labels to include when ``average != 'binary'``, and their
order if ``average is None``. Labels present in the data can be
excluded, for example to calculate a multiclass average ignoring a
majority negative class, while labels not present in the data will
result in 0 components in a macro average. For multilabel targets,
labels are column indices. By default, all labels in ``y_true`` and
``y_pred`` are used in sorted order.
.. versionchanged:: 0.17
parameter *labels* improved for multiclass problem.
pos_label : str or int, 1 by default
The class to report if ``average='binary'`` and the data is binary.
If the data are multiclass or multilabel, this will be ignored;
setting ``labels=[pos_label]`` and ``average != 'binary'`` will report
scores for that label only.
average : string, [None, 'binary' (default), 'micro', 'macro', 'samples', \
'weighted']
This parameter is required for multiclass/multilabel targets.
If ``None``, the scores for each class are returned. Otherwise, this
determines the type of averaging performed on the data:
``'binary'``:
Only report results for the class specified by ``pos_label``.
This is applicable only if targets (``y_{true,pred}``) are binary.
``'micro'``:
Calculate metrics globally by counting the total true positives,
false negatives and false positives.
``'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). This
alters 'macro' to account for label imbalance; it can result in an
F-score that is not between precision and recall.
``'samples'``:
Calculate metrics for each instance, and find their average (only
meaningful for multilabel classification where this differs from
:func:`accuracy_score`).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
zero_division : "warn", 0 or 1, default="warn"
Sets the value to return when there is a zero division, i.e. when all
predictions and labels are negative. If set to "warn", this acts as 0,
but warnings are also raised.
Returns
-------
fbeta_score : float (if average is not None) or array of float, shape =\
[n_unique_labels]
F-beta score of the positive class in binary classification or weighted
average of the F-beta score of each class for the multiclass task.
See also
--------
precision_recall_fscore_support, multilabel_confusion_matrix
References
----------
.. [1] R. Baeza-Yates and B. Ribeiro-Neto (2011).
Modern Information Retrieval. Addison Wesley, pp. 327-328.
.. [2] `Wikipedia entry for the F1-score
<https://en.wikipedia.org/wiki/F1_score>`_
Examples
--------
>>> from sklearn.metrics import fbeta_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> fbeta_score(y_true, y_pred, average='macro', beta=0.5)
0.23...
>>> fbeta_score(y_true, y_pred, average='micro', beta=0.5)
0.33...
>>> fbeta_score(y_true, y_pred, average='weighted', beta=0.5)
0.23...
>>> fbeta_score(y_true, y_pred, average=None, beta=0.5)
array([0.71..., 0. , 0. ])
Notes
-----
When ``true positive + false positive == 0`` or
``true positive + false negative == 0``, f-score returns 0 and raises
``UndefinedMetricWarning``. This behavior can be
modified with ``zero_division``.
"""
_, _, f, _ = precision_recall_fscore_support(y_true, y_pred,
beta=beta,
labels=labels,
pos_label=pos_label,
average=average,
warn_for=('f-score',),
sample_weight=sample_weight,
zero_division=zero_division)
return f
def _prf_divide(numerator, denominator, metric,
modifier, average, warn_for, zero_division="warn"):
"""Performs division and handles divide-by-zero.
On zero-division, sets the corresponding result elements equal to
0 or 1 (according to ``zero_division``). Plus, if
``zero_division != "warn"`` raises a warning.
The metric, modifier and average arguments are used only for determining
an appropriate warning.
"""
mask = denominator == 0.0
denominator = denominator.copy()
denominator[mask] = 1 # avoid infs/nans
result = numerator / denominator
if not np.any(mask):
return result
# if ``zero_division=1``, set those with denominator == 0 equal to 1
result[mask] = 0.0 if zero_division in ["warn", 0] else 1.0
# the user will be removing warnings if zero_division is set to something
# different than its default value. If we are computing only f-score
# the warning will be raised only if precision and recall are ill-defined
if zero_division != "warn" or metric not in warn_for:
return result
# build appropriate warning
# E.g. "Precision and F-score are ill-defined and being set to 0.0 in
# labels with no predicted samples. Use ``zero_division`` parameter to
# control this behavior."
if metric in warn_for and 'f-score' in warn_for:
msg_start = '{0} and F-score are'.format(metric.title())
elif metric in warn_for:
msg_start = '{0} is'.format(metric.title())
elif 'f-score' in warn_for:
msg_start = 'F-score is'
else:
return result
_warn_prf(average, modifier, msg_start, len(result))
return result
def _warn_prf(average, modifier, msg_start, result_size):
axis0, axis1 = 'sample', 'label'
if average == 'samples':
axis0, axis1 = axis1, axis0
msg = ('{0} ill-defined and being set to 0.0 {{0}} '
'no {1} {2}s. Use `zero_division` parameter to control'
' this behavior.'.format(msg_start, modifier, axis0))
if result_size == 1:
msg = msg.format('due to')
else:
msg = msg.format('in {0}s with'.format(axis1))
warnings.warn(msg, UndefinedMetricWarning, stacklevel=2)
def _check_set_wise_labels(y_true, y_pred, average, labels, pos_label):
"""Validation associated with set-wise metrics
Returns identified labels
"""
average_options = (None, 'micro', 'macro', 'weighted', 'samples')
if average not in average_options and average != 'binary':
raise ValueError('average has to be one of ' +
str(average_options))
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
present_labels = unique_labels(y_true, y_pred)
if average == 'binary':
if y_type == 'binary':
if pos_label not in present_labels:
if len(present_labels) >= 2:
raise ValueError("pos_label=%r is not a valid label: "
"%r" % (pos_label, present_labels))
labels = [pos_label]
else:
average_options = list(average_options)
if y_type == 'multiclass':
average_options.remove('samples')
raise ValueError("Target is %s but average='binary'. Please "
"choose another average setting, one of %r."
% (y_type, average_options))
elif pos_label not in (None, 1):
warnings.warn("Note that pos_label (set to %r) is ignored when "
"average != 'binary' (got %r). You may use "
"labels=[pos_label] to specify a single positive class."
% (pos_label, average), UserWarning)
return labels
def precision_recall_fscore_support(y_true, y_pred, beta=1.0, labels=None,
pos_label=1, average=None,
warn_for=('precision', 'recall',
'f-score'),
sample_weight=None,
zero_division="warn"):
"""Compute precision, recall, F-measure and support for each class
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 F-beta score can be interpreted as a weighted harmonic mean of
the precision and recall, where an F-beta score reaches its best
value at 1 and worst score at 0.
The F-beta score weights recall more than precision by a factor of
``beta``. ``beta == 1.0`` means recall and precision are equally important.
The support is the number of occurrences of each class in ``y_true``.
If ``pos_label is None`` and in binary classification, this function
returns the average precision, recall and F-measure if ``average``
is one of ``'micro'``, ``'macro'``, ``'weighted'`` or ``'samples'``.
Read more in the :ref:`User Guide <precision_recall_f_measure_metrics>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) target values.
y_pred : 1d array-like, or label indicator array / sparse matrix
Estimated targets as returned by a classifier.
beta : float, 1.0 by default
The strength of recall versus precision in the F-score.
labels : list, optional
The set of labels to include when ``average != 'binary'``, and their
order if ``average is None``. Labels present in the data can be
excluded, for example to calculate a multiclass average ignoring a
majority negative class, while labels not present in the data will
result in 0 components in a macro average. For multilabel targets,
labels are column indices. By default, all labels in ``y_true`` and
``y_pred`` are used in sorted order.
pos_label : str or int, 1 by default
The class to report if ``average='binary'`` and the data is binary.
If the data are multiclass or multilabel, this will be ignored;
setting ``labels=[pos_label]`` and ``average != 'binary'`` will report
scores for that label only.
average : string, [None (default), 'binary', 'micro', 'macro', 'samples', \
'weighted']
If ``None``, the scores for each class are returned. Otherwise, this
determines the type of averaging performed on the data:
``'binary'``:
Only report results for the class specified by ``pos_label``.
This is applicable only if targets (``y_{true,pred}``) are binary.
``'micro'``:
Calculate metrics globally by counting the total true positives,
false negatives and false positives.
``'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). This
alters 'macro' to account for label imbalance; it can result in an
F-score that is not between precision and recall.
``'samples'``:
Calculate metrics for each instance, and find their average (only
meaningful for multilabel classification where this differs from
:func:`accuracy_score`).
warn_for : tuple or set, for internal use
This determines which warnings will be made in the case that this
function is being used to return only one of its metrics.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
zero_division : "warn", 0 or 1, default="warn"
Sets the value to return when there is a zero division:
- recall: when there are no positive labels
- precision: when there are no positive predictions
- f-score: both
If set to "warn", this acts as 0, but warnings are also raised.
Returns
-------
precision : float (if average is not None) or array of float, shape =\
[n_unique_labels]
recall : float (if average is not None) or array of float, , shape =\
[n_unique_labels]
fbeta_score : float (if average is not None) or array of float, shape =\
[n_unique_labels]
support : None (if average is not None) or array of int, shape =\
[n_unique_labels]
The number of occurrences of each label in ``y_true``.
References
----------
.. [1] `Wikipedia entry for the Precision and recall
<https://en.wikipedia.org/wiki/Precision_and_recall>`_
.. [2] `Wikipedia entry for the F1-score
<https://en.wikipedia.org/wiki/F1_score>`_
.. [3] `Discriminative Methods for Multi-labeled Classification Advances
in Knowledge Discovery and Data Mining (2004), pp. 22-30 by Shantanu
Godbole, Sunita Sarawagi
<http://www.godbole.net/shantanu/pubs/multilabelsvm-pakdd04.pdf>`_
Examples
--------
>>> import numpy as np
>>> from sklearn.metrics import precision_recall_fscore_support
>>> y_true = np.array(['cat', 'dog', 'pig', 'cat', 'dog', 'pig'])
>>> y_pred = np.array(['cat', 'pig', 'dog', 'cat', 'cat', 'dog'])
>>> precision_recall_fscore_support(y_true, y_pred, average='macro')
(0.22..., 0.33..., 0.26..., None)
>>> precision_recall_fscore_support(y_true, y_pred, average='micro')
(0.33..., 0.33..., 0.33..., None)
>>> precision_recall_fscore_support(y_true, y_pred, average='weighted')
(0.22..., 0.33..., 0.26..., None)
It is possible to compute per-label precisions, recalls, F1-scores and
supports instead of averaging:
>>> precision_recall_fscore_support(y_true, y_pred, average=None,
... labels=['pig', 'dog', 'cat'])
(array([0. , 0. , 0.66...]),
array([0., 0., 1.]), array([0. , 0. , 0.8]),
array([2, 2, 2]))
Notes
-----
When ``true positive + false positive == 0``, precision is undefined;
When ``true positive + false negative == 0``, recall is undefined.
In such cases, by default the metric will be set to 0, as will f-score,
and ``UndefinedMetricWarning`` will be raised. This behavior can be
modified with ``zero_division``.
"""
_check_zero_division(zero_division)
if beta < 0:
raise ValueError("beta should be >=0 in the F-beta score")
labels = _check_set_wise_labels(y_true, y_pred, average, labels,
pos_label)
# Calculate tp_sum, pred_sum, true_sum ###
samplewise = average == 'samples'
MCM = multilabel_confusion_matrix(y_true, y_pred,
sample_weight=sample_weight,
labels=labels, samplewise=samplewise)
tp_sum = MCM[:, 1, 1]
pred_sum = tp_sum + MCM[:, 0, 1]
true_sum = tp_sum + MCM[:, 1, 0]
if average == 'micro':
tp_sum = np.array([tp_sum.sum()])
pred_sum = np.array([pred_sum.sum()])
true_sum = np.array([true_sum.sum()])
# Finally, we have all our sufficient statistics. Divide! #
beta2 = beta ** 2
# Divide, and on zero-division, set scores and/or warn according to
# zero_division:
precision = _prf_divide(tp_sum, pred_sum, 'precision',
'predicted', average, warn_for, zero_division)
recall = _prf_divide(tp_sum, true_sum, 'recall',
'true', average, warn_for, zero_division)
# warn for f-score only if zero_division is warn, it is in warn_for
# and BOTH prec and rec are ill-defined
if zero_division == "warn" and ("f-score",) == warn_for:
if (pred_sum[true_sum == 0] == 0).any():
_warn_prf(
average, "true nor predicted", 'F-score is', len(true_sum)
)
# if tp == 0 F will be 1 only if all predictions are zero, all labels are
# zero, and zero_division=1. In all other case, 0
if np.isposinf(beta):
f_score = recall
else:
denom = beta2 * precision + recall
denom[denom == 0.] = 1 # avoid division by 0
f_score = (1 + beta2) * precision * recall / denom
# Average the results
if average == 'weighted':
weights = true_sum
if weights.sum() == 0:
zero_division_value = 0.0 if zero_division in ["warn", 0] else 1.0
# precision is zero_division if there are no positive predictions
# recall is zero_division if there are no positive labels
# fscore is zero_division if all labels AND predictions are
# negative
return (zero_division_value if pred_sum.sum() == 0 else 0,
zero_division_value,
zero_division_value if pred_sum.sum() == 0 else 0,
None)
elif average == 'samples':
weights = sample_weight
else:
weights = None
if average is not None:
assert average != 'binary' or len(precision) == 1
precision = np.average(precision, weights=weights)
recall = np.average(recall, weights=weights)
f_score = np.average(f_score, weights=weights)
true_sum = None # return no support
return precision, recall, f_score, true_sum
def precision_score(y_true, y_pred, labels=None, pos_label=1,
average='binary', sample_weight=None,
zero_division="warn"):
"""Compute the precision
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 best value is 1 and the worst value is 0.
Read more in the :ref:`User Guide <precision_recall_f_measure_metrics>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) target values.
y_pred : 1d array-like, or label indicator array / sparse matrix
Estimated targets as returned by a classifier.
labels : list, optional
The set of labels to include when ``average != 'binary'``, and their
order if ``average is None``. Labels present in the data can be
excluded, for example to calculate a multiclass average ignoring a
majority negative class, while labels not present in the data will
result in 0 components in a macro average. For multilabel targets,
labels are column indices. By default, all labels in ``y_true`` and
``y_pred`` are used in sorted order.
.. versionchanged:: 0.17
parameter *labels* improved for multiclass problem.
pos_label : str or int, 1 by default
The class to report if ``average='binary'`` and the data is binary.
If the data are multiclass or multilabel, this will be ignored;
setting ``labels=[pos_label]`` and ``average != 'binary'`` will report
scores for that label only.
average : string, [None, 'binary' (default), 'micro', 'macro', 'samples', \
'weighted']
This parameter is required for multiclass/multilabel targets.
If ``None``, the scores for each class are returned. Otherwise, this
determines the type of averaging performed on the data:
``'binary'``:
Only report results for the class specified by ``pos_label``.
This is applicable only if targets (``y_{true,pred}``) are binary.
``'micro'``:
Calculate metrics globally by counting the total true positives,
false negatives and false positives.
``'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). This
alters 'macro' to account for label imbalance; it can result in an
F-score that is not between precision and recall.
``'samples'``:
Calculate metrics for each instance, and find their average (only
meaningful for multilabel classification where this differs from
:func:`accuracy_score`).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
zero_division : "warn", 0 or 1, default="warn"
Sets the value to return when there is a zero division. If set to
"warn", this acts as 0, but warnings are also raised.
Returns
-------
precision : float (if average is not None) or array of float, shape =\
[n_unique_labels]
Precision of the positive class in binary classification or weighted
average of the precision of each class for the multiclass task.
See also
--------
precision_recall_fscore_support, multilabel_confusion_matrix
Examples
--------
>>> from sklearn.metrics import precision_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> precision_score(y_true, y_pred, average='macro')
0.22...
>>> precision_score(y_true, y_pred, average='micro')
0.33...
>>> precision_score(y_true, y_pred, average='weighted')
0.22...
>>> precision_score(y_true, y_pred, average=None)
array([0.66..., 0. , 0. ])
>>> y_pred = [0, 0, 0, 0, 0, 0]
>>> precision_score(y_true, y_pred, average=None)
array([0.33..., 0. , 0. ])
>>> precision_score(y_true, y_pred, average=None, zero_division=1)
array([0.33..., 1. , 1. ])
Notes
-----
When ``true positive + false positive == 0``, precision returns 0 and
raises ``UndefinedMetricWarning``. This behavior can be
modified with ``zero_division``.
"""
p, _, _, _ = precision_recall_fscore_support(y_true, y_pred,
labels=labels,
pos_label=pos_label,
average=average,
warn_for=('precision',),
sample_weight=sample_weight,
zero_division=zero_division)
return p
def recall_score(y_true, y_pred, labels=None, pos_label=1, average='binary',
sample_weight=None, zero_division="warn"):
"""Compute the recall
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 best value is 1 and the worst value is 0.
Read more in the :ref:`User Guide <precision_recall_f_measure_metrics>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) target values.
y_pred : 1d array-like, or label indicator array / sparse matrix
Estimated targets as returned by a classifier.
labels : list, optional
The set of labels to include when ``average != 'binary'``, and their
order if ``average is None``. Labels present in the data can be
excluded, for example to calculate a multiclass average ignoring a
majority negative class, while labels not present in the data will
result in 0 components in a macro average. For multilabel targets,
labels are column indices. By default, all labels in ``y_true`` and
``y_pred`` are used in sorted order.
.. versionchanged:: 0.17
parameter *labels* improved for multiclass problem.
pos_label : str or int, 1 by default
The class to report if ``average='binary'`` and the data is binary.
If the data are multiclass or multilabel, this will be ignored;
setting ``labels=[pos_label]`` and ``average != 'binary'`` will report
scores for that label only.
average : string, [None, 'binary' (default), 'micro', 'macro', 'samples', \
'weighted']
This parameter is required for multiclass/multilabel targets.
If ``None``, the scores for each class are returned. Otherwise, this
determines the type of averaging performed on the data:
``'binary'``:
Only report results for the class specified by ``pos_label``.
This is applicable only if targets (``y_{true,pred}``) are binary.
``'micro'``:
Calculate metrics globally by counting the total true positives,
false negatives and false positives.
``'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). This
alters 'macro' to account for label imbalance; it can result in an
F-score that is not between precision and recall.
``'samples'``:
Calculate metrics for each instance, and find their average (only
meaningful for multilabel classification where this differs from
:func:`accuracy_score`).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
zero_division : "warn", 0 or 1, default="warn"
Sets the value to return when there is a zero division. If set to
"warn", this acts as 0, but warnings are also raised.
Returns
-------
recall : float (if average is not None) or array of float, shape =\
[n_unique_labels]
Recall of the positive class in binary classification or weighted
average of the recall of each class for the multiclass task.
See also
--------
precision_recall_fscore_support, balanced_accuracy_score,
multilabel_confusion_matrix
Examples
--------
>>> from sklearn.metrics import recall_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> recall_score(y_true, y_pred, average='macro')
0.33...
>>> recall_score(y_true, y_pred, average='micro')
0.33...
>>> recall_score(y_true, y_pred, average='weighted')
0.33...
>>> recall_score(y_true, y_pred, average=None)
array([1., 0., 0.])
>>> y_true = [0, 0, 0, 0, 0, 0]
>>> recall_score(y_true, y_pred, average=None)
array([0.5, 0. , 0. ])
>>> recall_score(y_true, y_pred, average=None, zero_division=1)
array([0.5, 1. , 1. ])
Notes
-----
When ``true positive + false negative == 0``, recall returns 0 and raises
``UndefinedMetricWarning``. This behavior can be modified with
``zero_division``.
"""
_, r, _, _ = precision_recall_fscore_support(y_true, y_pred,
labels=labels,
pos_label=pos_label,
average=average,
warn_for=('recall',),
sample_weight=sample_weight,
zero_division=zero_division)
return r
def balanced_accuracy_score(y_true, y_pred, sample_weight=None,
adjusted=False):
"""Compute the balanced accuracy
The balanced accuracy in binary and multiclass classification problems to
deal with imbalanced datasets. It is defined as the average of recall
obtained on each class.
The best value is 1 and the worst value is 0 when ``adjusted=False``.
Read more in the :ref:`User Guide <balanced_accuracy_score>`.
Parameters
----------
y_true : 1d array-like
Ground truth (correct) target values.
y_pred : 1d array-like
Estimated targets as returned by a classifier.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
adjusted : bool, default=False
When true, the result is adjusted for chance, so that random
performance would score 0, and perfect performance scores 1.
Returns
-------
balanced_accuracy : float
See also
--------
recall_score, roc_auc_score
Notes
-----
Some literature promotes alternative definitions of balanced accuracy. Our
definition is equivalent to :func:`accuracy_score` with class-balanced
sample weights, and shares desirable properties with the binary case.
See the :ref:`User Guide <balanced_accuracy_score>`.
References
----------
.. [1] Brodersen, K.H.; Ong, C.S.; Stephan, K.E.; Buhmann, J.M. (2010).
The balanced accuracy and its posterior distribution.
Proceedings of the 20th International Conference on Pattern
Recognition, 3121-24.
.. [2] John. D. Kelleher, Brian Mac Namee, Aoife D'Arcy, (2015).
`Fundamentals of Machine Learning for Predictive Data Analytics:
Algorithms, Worked Examples, and Case Studies
<https://mitpress.mit.edu/books/fundamentals-machine-learning-predictive-data-analytics>`_.
Examples
--------
>>> from sklearn.metrics import balanced_accuracy_score
>>> y_true = [0, 1, 0, 0, 1, 0]
>>> y_pred = [0, 1, 0, 0, 0, 1]
>>> balanced_accuracy_score(y_true, y_pred)
0.625
"""
C = confusion_matrix(y_true, y_pred, sample_weight=sample_weight)
with np.errstate(divide='ignore', invalid='ignore'):
per_class = np.diag(C) / C.sum(axis=1)
if np.any(np.isnan(per_class)):
warnings.warn('y_pred contains classes not in y_true')
per_class = per_class[~np.isnan(per_class)]
score = np.mean(per_class)
if adjusted:
n_classes = len(per_class)
chance = 1 / n_classes
score -= chance
score /= 1 - chance
return score
def classification_report(y_true, y_pred, labels=None, target_names=None,
sample_weight=None, digits=2, output_dict=False,
zero_division="warn"):
"""Build a text report showing the main classification metrics
Read more in the :ref:`User Guide <classification_report>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) target values.
y_pred : 1d array-like, or label indicator array / sparse matrix
Estimated targets as returned by a classifier.
labels : array, shape = [n_labels]
Optional list of label indices to include in the report.
target_names : list of strings
Optional display names matching the labels (same order).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
digits : int
Number of digits for formatting output floating point values.
When ``output_dict`` is ``True``, this will be ignored and the
returned values will not be rounded.
output_dict : bool (default = False)
If True, return output as dict
zero_division : "warn", 0 or 1, default="warn"
Sets the value to return when there is a zero division. If set to
"warn", this acts as 0, but warnings are also raised.
Returns
-------
report : string / dict
Text summary of the precision, recall, F1 score for each class.
Dictionary returned if output_dict is True. Dictionary has the
following structure::
{'label 1': {'precision':0.5,
'recall':1.0,
'f1-score':0.67,
'support':1},
'label 2': { ... },
...
}
The reported averages include macro average (averaging the unweighted
mean per label), weighted average (averaging the support-weighted mean
per label), and sample average (only for multilabel classification).
Micro average (averaging the total true positives, false negatives and
false positives) is only shown for multi-label or multi-class
with a subset of classes, because it corresponds to accuracy otherwise.
See also :func:`precision_recall_fscore_support` for more details
on averages.
Note that in binary classification, recall of the positive class
is also known as "sensitivity"; recall of the negative class is
"specificity".
See also
--------
precision_recall_fscore_support, confusion_matrix,
multilabel_confusion_matrix
Examples
--------
>>> from sklearn.metrics import classification_report
>>> y_true = [0, 1, 2, 2, 2]
>>> y_pred = [0, 0, 2, 2, 1]
>>> target_names = ['class 0', 'class 1', 'class 2']
>>> print(classification_report(y_true, y_pred, target_names=target_names))
precision recall f1-score support
<BLANKLINE>
class 0 0.50 1.00 0.67 1
class 1 0.00 0.00 0.00 1
class 2 1.00 0.67 0.80 3
<BLANKLINE>
accuracy 0.60 5
macro avg 0.50 0.56 0.49 5
weighted avg 0.70 0.60 0.61 5
<BLANKLINE>
>>> y_pred = [1, 1, 0]
>>> y_true = [1, 1, 1]
>>> print(classification_report(y_true, y_pred, labels=[1, 2, 3]))
precision recall f1-score support
<BLANKLINE>
1 1.00 0.67 0.80 3
2 0.00 0.00 0.00 0
3 0.00 0.00 0.00 0
<BLANKLINE>
micro avg 1.00 0.67 0.80 3
macro avg 0.33 0.22 0.27 3
weighted avg 1.00 0.67 0.80 3
<BLANKLINE>
"""
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
labels_given = True
if labels is None:
labels = unique_labels(y_true, y_pred)
labels_given = False
else:
labels = np.asarray(labels)
# labelled micro average
micro_is_accuracy = ((y_type == 'multiclass' or y_type == 'binary') and
(not labels_given or
(set(labels) == set(unique_labels(y_true, y_pred)))))
if target_names is not None and len(labels) != len(target_names):
if labels_given:
warnings.warn(
"labels size, {0}, does not match size of target_names, {1}"
.format(len(labels), len(target_names))
)
else:
raise ValueError(
"Number of classes, {0}, does not match size of "
"target_names, {1}. Try specifying the labels "
"parameter".format(len(labels), len(target_names))
)
if target_names is None:
target_names = ['%s' % l for l in labels]
headers = ["precision", "recall", "f1-score", "support"]
# compute per-class results without averaging
p, r, f1, s = precision_recall_fscore_support(y_true, y_pred,
labels=labels,
average=None,
sample_weight=sample_weight,
zero_division=zero_division)
rows = zip(target_names, p, r, f1, s)
if y_type.startswith('multilabel'):
average_options = ('micro', 'macro', 'weighted', 'samples')
else:
average_options = ('micro', 'macro', 'weighted')
if output_dict:
report_dict = {label[0]: label[1:] for label in rows}
for label, scores in report_dict.items():
report_dict[label] = dict(zip(headers,
[i.item() for i in scores]))
else:
longest_last_line_heading = 'weighted avg'
name_width = max(len(cn) for cn in target_names)
width = max(name_width, len(longest_last_line_heading), digits)
head_fmt = '{:>{width}s} ' + ' {:>9}' * len(headers)
report = head_fmt.format('', *headers, width=width)
report += '\n\n'
row_fmt = '{:>{width}s} ' + ' {:>9.{digits}f}' * 3 + ' {:>9}\n'
for row in rows:
report += row_fmt.format(*row, width=width, digits=digits)
report += '\n'
# compute all applicable averages
for average in average_options:
if average.startswith('micro') and micro_is_accuracy:
line_heading = 'accuracy'
else:
line_heading = average + ' avg'
# compute averages with specified averaging method
avg_p, avg_r, avg_f1, _ = precision_recall_fscore_support(
y_true, y_pred, labels=labels,
average=average, sample_weight=sample_weight,
zero_division=zero_division)
avg = [avg_p, avg_r, avg_f1, np.sum(s)]
if output_dict:
report_dict[line_heading] = dict(
zip(headers, [i.item() for i in avg]))
else:
if line_heading == 'accuracy':
row_fmt_accuracy = '{:>{width}s} ' + \
' {:>9.{digits}}' * 2 + ' {:>9.{digits}f}' + \
' {:>9}\n'
report += row_fmt_accuracy.format(line_heading, '', '',
*avg[2:], width=width,
digits=digits)
else:
report += row_fmt.format(line_heading, *avg,
width=width, digits=digits)
if output_dict:
if 'accuracy' in report_dict.keys():
report_dict['accuracy'] = report_dict['accuracy']['precision']
return report_dict
else:
return report
def hamming_loss(y_true, y_pred, labels=None, sample_weight=None):
"""Compute the average Hamming loss.
The Hamming loss is the fraction of labels that are incorrectly predicted.
Read more in the :ref:`User Guide <hamming_loss>`.
Parameters
----------
y_true : 1d array-like, or label indicator array / sparse matrix
Ground truth (correct) labels.
y_pred : 1d array-like, or label indicator array / sparse matrix
Predicted labels, as returned by a classifier.
labels : array, shape = [n_labels], optional (default='deprecated')
Integer array of labels. If not provided, labels will be inferred
from y_true and y_pred.
.. versionadded:: 0.18
.. deprecated:: 0.21
This parameter ``labels`` is deprecated in version 0.21 and will
be removed in version 0.23. Hamming loss uses ``y_true.shape[1]``
for the number of labels when y_true is binary label indicators,
so it is unnecessary for the user to specify.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
.. versionadded:: 0.18
Returns
-------
loss : float or int,
Return the average Hamming loss between element of ``y_true`` and
``y_pred``.
See Also
--------
accuracy_score, jaccard_score, zero_one_loss
Notes
-----
In multiclass classification, the Hamming loss corresponds to the Hamming
distance between ``y_true`` and ``y_pred`` which is equivalent to the
subset ``zero_one_loss`` function, when `normalize` parameter is set to
True.
In multilabel classification, the Hamming loss is different from the
subset zero-one loss. The zero-one loss considers the entire set of labels
for a given sample incorrect if it does not entirely match the true set of
labels. Hamming loss is more forgiving in that it penalizes only the
individual labels.
The Hamming loss is upperbounded by the subset zero-one loss, when
`normalize` parameter is set to True. It is always between 0 and 1,
lower being better.
References
----------
.. [1] Grigorios Tsoumakas, Ioannis Katakis. Multi-Label Classification:
An Overview. International Journal of Data Warehousing & Mining,
3(3), 1-13, July-September 2007.
.. [2] `Wikipedia entry on the Hamming distance
<https://en.wikipedia.org/wiki/Hamming_distance>`_
Examples
--------
>>> from sklearn.metrics import hamming_loss
>>> y_pred = [1, 2, 3, 4]
>>> y_true = [2, 2, 3, 4]
>>> hamming_loss(y_true, y_pred)
0.25
In the multilabel case with binary label indicators:
>>> import numpy as np
>>> hamming_loss(np.array([[0, 1], [1, 1]]), np.zeros((2, 2)))
0.75
"""
y_type, y_true, y_pred = _check_targets(y_true, y_pred)
check_consistent_length(y_true, y_pred, sample_weight)
if labels is not None:
warnings.warn("The labels parameter is unused. It was"
" deprecated in version 0.21 and"
" will be removed in version 0.23",
FutureWarning)
if sample_weight is None:
weight_average = 1.
else:
weight_average = np.mean(sample_weight)
if y_type.startswith('multilabel'):
n_differences = count_nonzero(y_true - y_pred,
sample_weight=sample_weight)
return (n_differences /
(y_true.shape[0] * y_true.shape[1] * weight_average))
elif y_type in ["binary", "multiclass"]:
return _weighted_sum(y_true != y_pred, sample_weight, normalize=True)
else:
raise ValueError("{0} is not supported".format(y_type))
def log_loss(y_true, y_pred, eps=1e-15, normalize=True, sample_weight=None,
labels=None):
"""Log loss, aka logistic loss or cross-entropy loss.
This is the loss function used in (multinomial) logistic regression
and extensions of it such as neural networks, defined as the negative
log-likelihood of the true labels given a probabilistic classifier's
predictions. The log loss is only defined for two or more labels.
For a single sample with true label yt in {0,1} and
estimated probability yp that yt = 1, the log loss is
-log P(yt|yp) = -(yt log(yp) + (1 - yt) log(1 - yp))
Read more in the :ref:`User Guide <log_loss>`.
Parameters
----------
y_true : array-like or label indicator matrix
Ground truth (correct) labels for n_samples samples.
y_pred : array-like of float, shape = (n_samples, n_classes) or (n_samples,)
Predicted probabilities, as returned by a classifier's
predict_proba method. If ``y_pred.shape = (n_samples,)``
the probabilities provided are assumed to be that of the
positive class. The labels in ``y_pred`` are assumed to be
ordered alphabetically, as done by
:class:`preprocessing.LabelBinarizer`.
eps : float
Log loss is undefined for p=0 or p=1, so probabilities are
clipped to max(eps, min(1 - eps, p)).
normalize : bool, optional (default=True)
If true, return the mean loss per sample.
Otherwise, return the sum of the per-sample losses.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
labels : array-like, optional (default=None)
If not provided, labels will be inferred from y_true. If ``labels``
is ``None`` and ``y_pred`` has shape (n_samples,) the labels are
assumed to be binary and are inferred from ``y_true``.
.. versionadded:: 0.18
Returns
-------
loss : float
Examples
--------
>>> from sklearn.metrics import log_loss
>>> log_loss(["spam", "ham", "ham", "spam"],
... [[.1, .9], [.9, .1], [.8, .2], [.35, .65]])
0.21616...
References
----------
C.M. Bishop (2006). Pattern Recognition and Machine Learning. Springer,
p. 209.
Notes
-----
The logarithm used is the natural logarithm (base-e).
"""
y_pred = check_array(y_pred, ensure_2d=False)
check_consistent_length(y_pred, y_true, sample_weight)
lb = LabelBinarizer()
if labels is not None:
lb.fit(labels)
else:
lb.fit(y_true)
if len(lb.classes_) == 1:
if labels is None:
raise ValueError('y_true contains only one label ({0}). Please '
'provide the true labels explicitly through the '
'labels argument.'.format(lb.classes_[0]))
else:
raise ValueError('The labels array needs to contain at least two '
'labels for log_loss, '
'got {0}.'.format(lb.classes_))
transformed_labels = lb.transform(y_true)
if transformed_labels.shape[1] == 1:
transformed_labels = np.append(1 - transformed_labels,
transformed_labels, axis=1)
# Clipping
y_pred = np.clip(y_pred, eps, 1 - eps)
# If y_pred is of single dimension, assume y_true to be binary
# and then check.
if y_pred.ndim == 1:
y_pred = y_pred[:, np.newaxis]
if y_pred.shape[1] == 1:
y_pred = np.append(1 - y_pred, y_pred, axis=1)
# Check if dimensions are consistent.
transformed_labels = check_array(transformed_labels)
if len(lb.classes_) != y_pred.shape[1]:
if labels is None:
raise ValueError("y_true and y_pred contain different number of "
"classes {0}, {1}. Please provide the true "
"labels explicitly through the labels argument. "
"Classes found in "
"y_true: {2}".format(transformed_labels.shape[1],
y_pred.shape[1],
lb.classes_))
else:
raise ValueError('The number of classes in labels is different '
'from that in y_pred. Classes found in '
'labels: {0}'.format(lb.classes_))
# Renormalize
y_pred /= y_pred.sum(axis=1)[:, np.newaxis]
loss = -(transformed_labels * np.log(y_pred)).sum(axis=1)
return _weighted_sum(loss, sample_weight, normalize)
def hinge_loss(y_true, pred_decision, labels=None, sample_weight=None):
"""Average hinge loss (non-regularized)
In binary class case, assuming labels in y_true are encoded with +1 and -1,
when a prediction mistake is made, ``margin = y_true * pred_decision`` is
always negative (since the signs disagree), implying ``1 - margin`` is
always greater than 1. The cumulated hinge loss is therefore an upper
bound of the number of mistakes made by the classifier.
In multiclass case, the function expects that either all the labels are
included in y_true or an optional labels argument is provided which
contains all the labels. The multilabel margin is calculated according
to Crammer-Singer's method. As in the binary case, the cumulated hinge loss
is an upper bound of the number of mistakes made by the classifier.
Read more in the :ref:`User Guide <hinge_loss>`.
Parameters
----------
y_true : array, shape = [n_samples]
True target, consisting of integers of two values. The positive label
must be greater than the negative label.
pred_decision : array, shape = [n_samples] or [n_samples, n_classes]
Predicted decisions, as output by decision_function (floats).
labels : array, optional, default None
Contains all the labels for the problem. Used in multiclass hinge loss.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
loss : float
References
----------
.. [1] `Wikipedia entry on the Hinge loss
<https://en.wikipedia.org/wiki/Hinge_loss>`_
.. [2] Koby Crammer, Yoram Singer. On the Algorithmic
Implementation of Multiclass Kernel-based Vector
Machines. Journal of Machine Learning Research 2,
(2001), 265-292
.. [3] `L1 AND L2 Regularization for Multiclass Hinge Loss Models
by Robert C. Moore, John DeNero.
<http://www.ttic.edu/sigml/symposium2011/papers/
Moore+DeNero_Regularization.pdf>`_
Examples
--------
>>> from sklearn import svm
>>> from sklearn.metrics import hinge_loss
>>> X = [[0], [1]]
>>> y = [-1, 1]
>>> est = svm.LinearSVC(random_state=0)
>>> est.fit(X, y)
LinearSVC(random_state=0)
>>> pred_decision = est.decision_function([[-2], [3], [0.5]])
>>> pred_decision
array([-2.18..., 2.36..., 0.09...])
>>> hinge_loss([-1, 1, 1], pred_decision)
0.30...
In the multiclass case:
>>> import numpy as np
>>> X = np.array([[0], [1], [2], [3]])
>>> Y = np.array([0, 1, 2, 3])
>>> labels = np.array([0, 1, 2, 3])
>>> est = svm.LinearSVC()
>>> est.fit(X, Y)
LinearSVC()
>>> pred_decision = est.decision_function([[-1], [2], [3]])
>>> y_true = [0, 2, 3]
>>> hinge_loss(y_true, pred_decision, labels)
0.56...
"""
check_consistent_length(y_true, pred_decision, sample_weight)
pred_decision = check_array(pred_decision, ensure_2d=False)
y_true = column_or_1d(y_true)
y_true_unique = np.unique(y_true)
if y_true_unique.size > 2:
if (labels is None and pred_decision.ndim > 1 and
(np.size(y_true_unique) != pred_decision.shape[1])):
raise ValueError("Please include all labels in y_true "
"or pass labels as third argument")
if labels is None:
labels = y_true_unique
le = LabelEncoder()
le.fit(labels)
y_true = le.transform(y_true)
mask = np.ones_like(pred_decision, dtype=bool)
mask[np.arange(y_true.shape[0]), y_true] = False
margin = pred_decision[~mask]
margin -= np.max(pred_decision[mask].reshape(y_true.shape[0], -1),
axis=1)
else:
# Handles binary class case
# this code assumes that positive and negative labels
# are encoded as +1 and -1 respectively
pred_decision = column_or_1d(pred_decision)
pred_decision = np.ravel(pred_decision)
lbin = LabelBinarizer(neg_label=-1)
y_true = lbin.fit_transform(y_true)[:, 0]
try:
margin = y_true * pred_decision
except TypeError:
raise TypeError("pred_decision should be an array of floats.")
losses = 1 - margin
# The hinge_loss doesn't penalize good enough predictions.
np.clip(losses, 0, None, out=losses)
return np.average(losses, weights=sample_weight)
def brier_score_loss(y_true, y_prob, sample_weight=None, pos_label=None):
"""Compute the Brier score.
The smaller the Brier score, the better, hence the naming with "loss".
Across all items in a set N predictions, the Brier score measures the
mean squared difference between (1) the predicted probability assigned
to the possible outcomes for item i, and (2) the actual outcome.
Therefore, the lower the Brier score is for a set of predictions, the
better the predictions are calibrated. Note that the Brier score always
takes on a value between zero and one, since this is the largest
possible difference between a predicted probability (which must be
between zero and one) and the actual outcome (which can take on values
of only 0 and 1). The Brier loss is composed of refinement loss and
calibration loss.
The Brier score is appropriate for binary and categorical outcomes that
can be structured as true or false, but is inappropriate for ordinal
variables which can take on three or more values (this is because the
Brier score assumes that all possible outcomes are equivalently
"distant" from one another). Which label is considered to be the positive
label is controlled via the parameter pos_label, which defaults to 1.
Read more in the :ref:`User Guide <calibration>`.
Parameters
----------
y_true : array, shape (n_samples,)
True targets.
y_prob : array, shape (n_samples,)
Probabilities of the positive class.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
pos_label : int or str, default=None
Label of the positive class.
Defaults to the greater label unless y_true is all 0 or all -1
in which case pos_label defaults to 1.
Returns
-------
score : float
Brier score
Examples
--------
>>> import numpy as np
>>> from sklearn.metrics import brier_score_loss
>>> y_true = np.array([0, 1, 1, 0])
>>> y_true_categorical = np.array(["spam", "ham", "ham", "spam"])
>>> y_prob = np.array([0.1, 0.9, 0.8, 0.3])
>>> brier_score_loss(y_true, y_prob)
0.037...
>>> brier_score_loss(y_true, 1-y_prob, pos_label=0)
0.037...
>>> brier_score_loss(y_true_categorical, y_prob, pos_label="ham")
0.037...
>>> brier_score_loss(y_true, np.array(y_prob) > 0.5)
0.0
References
----------
.. [1] `Wikipedia entry for the Brier score.
<https://en.wikipedia.org/wiki/Brier_score>`_
"""
y_true = column_or_1d(y_true)
y_prob = column_or_1d(y_prob)
assert_all_finite(y_true)
assert_all_finite(y_prob)
check_consistent_length(y_true, y_prob, sample_weight)
labels = np.unique(y_true)
if len(labels) > 2:
raise ValueError("Only binary classification is supported. "
"Labels in y_true: %s." % labels)
if y_prob.max() > 1:
raise ValueError("y_prob contains values greater than 1.")
if y_prob.min() < 0:
raise ValueError("y_prob contains values less than 0.")
# if pos_label=None, when y_true is in {-1, 1} or {0, 1},
# pos_label is set to 1 (consistent with precision_recall_curve/roc_curve),
# otherwise pos_label is set to the greater label
# (different from precision_recall_curve/roc_curve,
# the purpose is to keep backward compatibility).
if pos_label is None:
if (np.array_equal(labels, [0]) or
np.array_equal(labels, [-1])):
pos_label = 1
else:
pos_label = y_true.max()
y_true = np.array(y_true == pos_label, int)
return np.average((y_true - y_prob) ** 2, weights=sample_weight)
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