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# coding: utf-8
# pylint: disable=no-member, too-many-lines
"""Online evaluation metric module."""
from __future__ import absolute_import
import math
from collections import OrderedDict
import numpy
from .base import numeric_types, string_types
from . import ndarray
from . import registry
[docs]def check_label_shapes(labels, preds, wrap=False, shape=False):
"""Helper function for checking shape of label and prediction
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
wrap : boolean
If True, wrap labels/preds in a list if they are single NDArray
shape : boolean
If True, check the shape of labels and preds;
Otherwise only check their length.
"""
if not shape:
label_shape, pred_shape = len(labels), len(preds)
else:
label_shape, pred_shape = labels.shape, preds.shape
if label_shape != pred_shape:
raise ValueError("Shape of labels {} does not match shape of "
"predictions {}".format(label_shape, pred_shape))
if wrap:
if isinstance(labels, ndarray.ndarray.NDArray):
labels = [labels]
if isinstance(preds, ndarray.ndarray.NDArray):
preds = [preds]
return labels, preds
[docs]class EvalMetric(object):
"""Base class for all evaluation metrics.
.. note::
This is a base class that provides common metric interfaces.
One should not use this class directly, but instead create new metric
classes that extend it.
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
"""
def __init__(self, name, output_names=None,
label_names=None, **kwargs):
self.name = str(name)
self.output_names = output_names
self.label_names = label_names
self._has_global_stats = kwargs.pop("has_global_stats", False)
self._kwargs = kwargs
self.reset()
def __str__(self):
return "EvalMetric: {}".format(dict(self.get_name_value()))
[docs] def get_config(self):
"""Save configurations of metric. Can be recreated
from configs with metric.create(``**config``)
"""
config = self._kwargs.copy()
config.update({
'metric': self.__class__.__name__,
'name': self.name,
'output_names': self.output_names,
'label_names': self.label_names})
return config
[docs] def update_dict(self, label, pred):
"""Update the internal evaluation with named label and pred
Parameters
----------
labels : OrderedDict of str -> NDArray
name to array mapping for labels.
preds : OrderedDict of str -> NDArray
name to array mapping of predicted outputs.
"""
if self.output_names is not None:
pred = [pred[name] for name in self.output_names]
else:
pred = list(pred.values())
if self.label_names is not None:
label = [label[name] for name in self.label_names]
else:
label = list(label.values())
self.update(label, pred)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
raise NotImplementedError()
[docs] def reset(self):
"""Resets the internal evaluation result to initial state."""
self.num_inst = 0
self.sum_metric = 0.0
self.global_num_inst = 0
self.global_sum_metric = 0.0
[docs] def reset_local(self):
"""Resets the local portion of the internal evaluation results
to initial state."""
self.num_inst = 0
self.sum_metric = 0.0
[docs] def get(self):
"""Gets the current evaluation result.
Returns
-------
names : list of str
Name of the metrics.
values : list of float
Value of the evaluations.
"""
if self.num_inst == 0:
return (self.name, float('nan'))
else:
return (self.name, self.sum_metric / self.num_inst)
[docs] def get_global(self):
"""Gets the current global evaluation result.
Returns
-------
names : list of str
Name of the metrics.
values : list of float
Value of the evaluations.
"""
if self._has_global_stats:
if self.global_num_inst == 0:
return (self.name, float('nan'))
else:
return (self.name, self.global_sum_metric / self.global_num_inst)
else:
return self.get()
[docs] def get_name_value(self):
"""Returns zipped name and value pairs.
Returns
-------
list of tuples
A (name, value) tuple list.
"""
name, value = self.get()
if not isinstance(name, list):
name = [name]
if not isinstance(value, list):
value = [value]
return list(zip(name, value))
[docs] def get_global_name_value(self):
"""Returns zipped name and value pairs for global results.
Returns
-------
list of tuples
A (name, value) tuple list.
"""
if self._has_global_stats:
name, value = self.get_global()
if not isinstance(name, list):
name = [name]
if not isinstance(value, list):
value = [value]
return list(zip(name, value))
else:
return self.get_name_value()
# pylint: disable=invalid-name
register = registry.get_register_func(EvalMetric, 'metric')
alias = registry.get_alias_func(EvalMetric, 'metric')
_create = registry.get_create_func(EvalMetric, 'metric')
# pylint: enable=invalid-name
[docs]def create(metric, *args, **kwargs):
"""Creates evaluation metric from metric names or instances of EvalMetric
or a custom metric function.
Parameters
----------
metric : str or callable
Specifies the metric to create.
This argument must be one of the below:
- Name of a metric.
- An instance of `EvalMetric`.
- A list, each element of which is a metric or a metric name.
- An evaluation function that computes custom metric for a given batch of
labels and predictions.
*args : list
Additional arguments to metric constructor.
Only used when metric is str.
**kwargs : dict
Additional arguments to metric constructor.
Only used when metric is str
Examples
--------
>>> def custom_metric(label, pred):
... return np.mean(np.abs(label - pred))
...
>>> metric1 = mx.metric.create('acc')
>>> metric2 = mx.metric.create(custom_metric)
>>> metric3 = mx.metric.create([metric1, metric2, 'rmse'])
"""
if callable(metric):
return CustomMetric(metric, *args, **kwargs)
elif isinstance(metric, list):
composite_metric = CompositeEvalMetric()
for child_metric in metric:
composite_metric.add(create(child_metric, *args, **kwargs))
return composite_metric
return _create(metric, *args, **kwargs)
@register
@alias('composite')
[docs]class CompositeEvalMetric(EvalMetric):
"""Manages multiple evaluation metrics.
Parameters
----------
metrics : list of EvalMetric
List of child metrics.
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array([[0.3, 0.7], [0, 1.], [0.4, 0.6]])]
>>> labels = [mx.nd.array([0, 1, 1])]
>>> eval_metrics_1 = mx.metric.Accuracy()
>>> eval_metrics_2 = mx.metric.F1()
>>> eval_metrics = mx.metric.CompositeEvalMetric()
>>> for child_metric in [eval_metrics_1, eval_metrics_2]:
>>> eval_metrics.add(child_metric)
>>> eval_metrics.update(labels = labels, preds = predicts)
>>> print eval_metrics.get()
(['accuracy', 'f1'], [0.6666666666666666, 0.8])
"""
def __init__(self, metrics=None, name='composite',
output_names=None, label_names=None):
super(CompositeEvalMetric, self).__init__(
name, output_names=output_names, label_names=label_names,
has_global_stats=True)
if metrics is None:
metrics = []
self.metrics = [create(i) for i in metrics]
[docs] def add(self, metric):
"""Adds a child metric.
Parameters
----------
metric
A metric instance.
"""
self.metrics.append(create(metric))
[docs] def get_metric(self, index):
"""Returns a child metric.
Parameters
----------
index : int
Index of child metric in the list of metrics.
"""
try:
return self.metrics[index]
except IndexError:
return ValueError("Metric index {} is out of range 0 and {}".format(
index, len(self.metrics)))
def update_dict(self, labels, preds): # pylint: disable=arguments-differ
if self.label_names is not None:
labels = OrderedDict([i for i in labels.items()
if i[0] in self.label_names])
if self.output_names is not None:
preds = OrderedDict([i for i in preds.items()
if i[0] in self.output_names])
for metric in self.metrics:
metric.update_dict(labels, preds)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
for metric in self.metrics:
metric.update(labels, preds)
[docs] def reset(self):
"""Resets the internal evaluation result to initial state."""
try:
for metric in self.metrics:
metric.reset()
except AttributeError:
pass
[docs] def reset_local(self):
"""Resets the local portion of the internal evaluation results
to initial state."""
try:
for metric in self.metrics:
metric.reset_local()
except AttributeError:
pass
[docs] def get(self):
"""Returns the current evaluation result.
Returns
-------
names : list of str
Name of the metrics.
values : list of float
Value of the evaluations.
"""
names = []
values = []
for metric in self.metrics:
name, value = metric.get()
if isinstance(name, string_types):
name = [name]
if isinstance(value, numeric_types):
value = [value]
names.extend(name)
values.extend(value)
return (names, values)
[docs] def get_global(self):
"""Returns the current evaluation result.
Returns
-------
names : list of str
Name of the metrics.
values : list of float
Value of the evaluations.
"""
names = []
values = []
for metric in self.metrics:
name, value = metric.get_global()
if isinstance(name, string_types):
name = [name]
if isinstance(value, numeric_types):
value = [value]
names.extend(name)
values.extend(value)
return (names, values)
def get_config(self):
config = super(CompositeEvalMetric, self).get_config()
config.update({'metrics': [i.get_config() for i in self.metrics]})
return config
########################
# CLASSIFICATION METRICS
########################
@register
@alias('acc')
[docs]class Accuracy(EvalMetric):
"""Computes accuracy classification score.
The accuracy score is defined as
.. math::
\\text{accuracy}(y, \\hat{y}) = \\frac{1}{n} \\sum_{i=0}^{n-1}
\\text{1}(\\hat{y_i} == y_i)
Parameters
----------
axis : int, default=1
The axis that represents classes
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array([[0.3, 0.7], [0, 1.], [0.4, 0.6]])]
>>> labels = [mx.nd.array([0, 1, 1])]
>>> acc = mx.metric.Accuracy()
>>> acc.update(preds = predicts, labels = labels)
>>> print acc.get()
('accuracy', 0.6666666666666666)
"""
def __init__(self, axis=1, name='accuracy',
output_names=None, label_names=None):
super(Accuracy, self).__init__(
name, axis=axis,
output_names=output_names, label_names=label_names,
has_global_stats=True)
self.axis = axis
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data with class indices as values, one per sample.
preds : list of `NDArray`
Prediction values for samples. Each prediction value can either be the class index,
or a vector of likelihoods for all classes.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred_label in zip(labels, preds):
if pred_label.shape != label.shape:
pred_label = ndarray.argmax(pred_label, axis=self.axis)
pred_label = pred_label.asnumpy().astype('int32')
label = label.asnumpy().astype('int32')
# flatten before checking shapes to avoid shape miss match
label = label.flat
pred_label = pred_label.flat
check_label_shapes(label, pred_label)
num_correct = (pred_label == label).sum()
self.sum_metric += num_correct
self.global_sum_metric += num_correct
self.num_inst += len(pred_label)
self.global_num_inst += len(pred_label)
@register
@alias('top_k_accuracy', 'top_k_acc')
[docs]class TopKAccuracy(EvalMetric):
"""Computes top k predictions accuracy.
`TopKAccuracy` differs from Accuracy in that it considers the prediction
to be ``True`` as long as the ground truth label is in the top K
predicated labels.
If `top_k` = ``1``, then `TopKAccuracy` is identical to `Accuracy`.
Parameters
----------
top_k : int
Whether targets are in top k predictions.
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> np.random.seed(999)
>>> top_k = 3
>>> labels = [mx.nd.array([2, 6, 9, 2, 3, 4, 7, 8, 9, 6])]
>>> predicts = [mx.nd.array(np.random.rand(10, 10))]
>>> acc = mx.metric.TopKAccuracy(top_k=top_k)
>>> acc.update(labels, predicts)
>>> print acc.get()
('top_k_accuracy', 0.3)
"""
def __init__(self, top_k=1, name='top_k_accuracy',
output_names=None, label_names=None):
super(TopKAccuracy, self).__init__(
name, top_k=top_k,
output_names=output_names, label_names=label_names,
has_global_stats=True)
self.top_k = top_k
assert(self.top_k > 1), 'Please use Accuracy if top_k is no more than 1'
self.name += '_%d' % self.top_k
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred_label in zip(labels, preds):
assert(len(pred_label.shape) <= 2), 'Predictions should be no more than 2 dims'
# Using argpartition here instead of argsort is safe because
# we do not care about the order of top k elements. It is
# much faster, which is important since that computation is
# single-threaded due to Python GIL.
pred_label = numpy.argpartition(pred_label.asnumpy().astype('float32'), -self.top_k)
label = label.asnumpy().astype('int32')
check_label_shapes(label, pred_label)
num_samples = pred_label.shape[0]
num_dims = len(pred_label.shape)
if num_dims == 1:
self.sum_metric += (pred_label.flat == label.flat).sum()
elif num_dims == 2:
num_classes = pred_label.shape[1]
top_k = min(num_classes, self.top_k)
for j in range(top_k):
num_correct = (pred_label[:, num_classes - 1 - j].flat == label.flat).sum()
self.sum_metric += num_correct
self.global_sum_metric += num_correct
self.num_inst += num_samples
self.global_num_inst += num_samples
class _BinaryClassificationMetrics(object):
"""
Private container class for classification metric statistics. True/false positive and
true/false negative counts are sufficient statistics for various classification metrics.
This class provides the machinery to track those statistics across mini-batches of
(label, prediction) pairs.
"""
def __init__(self):
self.true_positives = 0
self.false_negatives = 0
self.false_positives = 0
self.true_negatives = 0
self.global_true_positives = 0
self.global_false_negatives = 0
self.global_false_positives = 0
self.global_true_negatives = 0
def update_binary_stats(self, label, pred):
"""
Update various binary classification counts for a single (label, pred)
pair.
Parameters
----------
label : `NDArray`
The labels of the data.
pred : `NDArray`
Predicted values.
"""
pred = pred.asnumpy()
label = label.asnumpy().astype('int32')
pred_label = numpy.argmax(pred, axis=1)
check_label_shapes(label, pred)
if len(numpy.unique(label)) > 2:
raise ValueError("%s currently only supports binary classification."
% self.__class__.__name__)
pred_true = (pred_label == 1)
pred_false = 1 - pred_true
label_true = (label == 1)
label_false = 1 - label_true
true_pos = (pred_true * label_true).sum()
false_pos = (pred_true * label_false).sum()
false_neg = (pred_false * label_true).sum()
true_neg = (pred_false * label_false).sum()
self.true_positives += true_pos
self.global_true_positives += true_pos
self.false_positives += false_pos
self.global_false_positives += false_pos
self.false_negatives += false_neg
self.global_false_negatives += false_neg
self.true_negatives += true_neg
self.global_true_negatives += true_neg
@property
def precision(self):
if self.true_positives + self.false_positives > 0:
return float(self.true_positives) / (self.true_positives + self.false_positives)
else:
return 0.
@property
def global_precision(self):
if self.global_true_positives + self.global_false_positives > 0:
return float(self.global_true_positives) / (self.global_true_positives + self.global_false_positives)
else:
return 0.
@property
def recall(self):
if self.true_positives + self.false_negatives > 0:
return float(self.true_positives) / (self.true_positives + self.false_negatives)
else:
return 0.
@property
def global_recall(self):
if self.global_true_positives + self.global_false_negatives > 0:
return float(self.global_true_positives) / (self.global_true_positives + self.global_false_negatives)
else:
return 0.
@property
def fscore(self):
if self.precision + self.recall > 0:
return 2 * self.precision * self.recall / (self.precision + self.recall)
else:
return 0.
@property
def global_fscore(self):
if self.global_precision + self.global_recall > 0:
return 2 * self.global_precision * self.global_recall / (self.global_precision + self.global_recall)
else:
return 0.
def matthewscc(self, use_global=False):
"""
Calculate the Matthew's Correlation Coefficent
"""
if use_global:
if not self.global_total_examples:
return 0.
true_pos = float(self.global_true_positives)
false_pos = float(self.global_false_positives)
false_neg = float(self.global_false_negatives)
true_neg = float(self.global_true_negatives)
else:
if not self.total_examples:
return 0.
true_pos = float(self.true_positives)
false_pos = float(self.false_positives)
false_neg = float(self.false_negatives)
true_neg = float(self.true_negatives)
terms = [(true_pos + false_pos),
(true_pos + false_neg),
(true_neg + false_pos),
(true_neg + false_neg)]
denom = 1.
for t in filter(lambda t: t != 0., terms):
denom *= t
return ((true_pos * true_neg) - (false_pos * false_neg)) / math.sqrt(denom)
@property
def total_examples(self):
return self.false_negatives + self.false_positives + \
self.true_negatives + self.true_positives
@property
def global_total_examples(self):
return self.global_false_negatives + self.global_false_positives + \
self.global_true_negatives + self.global_true_positives
def local_reset_stats(self):
self.false_positives = 0
self.false_negatives = 0
self.true_positives = 0
self.true_negatives = 0
def reset_stats(self):
self.false_positives = 0
self.false_negatives = 0
self.true_positives = 0
self.true_negatives = 0
self.global_false_positives = 0
self.global_false_negatives = 0
self.global_true_positives = 0
self.global_true_negatives = 0
@register
[docs]class F1(EvalMetric):
"""Computes the F1 score of a binary classification problem.
The F1 score is equivalent to harmonic mean of the precision and recall,
where the best value is 1.0 and the worst value is 0.0. The formula for F1 score is::
F1 = 2 * (precision * recall) / (precision + recall)
The formula for precision and recall is::
precision = true_positives / (true_positives + false_positives)
recall = true_positives / (true_positives + false_negatives)
.. note::
This F1 score only supports binary classification.
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
average : str, default 'macro'
Strategy to be used for aggregating across mini-batches.
"macro": average the F1 scores for each batch.
"micro": compute a single F1 score across all batches.
Examples
--------
>>> predicts = [mx.nd.array([[0.3, 0.7], [0., 1.], [0.4, 0.6]])]
>>> labels = [mx.nd.array([0., 1., 1.])]
>>> f1 = mx.metric.F1()
>>> f1.update(preds = predicts, labels = labels)
>>> print f1.get()
('f1', 0.8)
"""
def __init__(self, name='f1',
output_names=None, label_names=None, average="macro"):
self.average = average
self.metrics = _BinaryClassificationMetrics()
EvalMetric.__init__(self, name=name,
output_names=output_names, label_names=label_names,
has_global_stats=True)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
self.metrics.update_binary_stats(label, pred)
if self.average == "macro":
self.sum_metric += self.metrics.fscore
self.global_sum_metric += self.metrics.global_fscore
self.num_inst += 1
self.global_num_inst += 1
self.metrics.reset_stats()
else:
self.sum_metric = self.metrics.fscore * self.metrics.total_examples
self.global_sum_metric = self.metrics.global_fscore * self.metrics.global_total_examples
self.num_inst = self.metrics.total_examples
self.global_num_inst = self.metrics.global_total_examples
[docs] def reset(self):
"""Resets the internal evaluation result to initial state."""
self.sum_metric = 0.
self.num_inst = 0
self.global_num_inst = 0
self.global_sum_metric = 0.0
self.metrics.reset_stats()
[docs] def reset_local(self):
"""Resets the internal evaluation result to initial state."""
self.sum_metric = 0.
self.num_inst = 0
self.metrics.local_reset_stats()
@register
[docs]class MCC(EvalMetric):
"""Computes the Matthews Correlation Coefficient of a binary classification problem.
While slower to compute than F1 the MCC can give insight that F1 or Accuracy cannot.
For instance, if the network always predicts the same result
then the MCC will immeadiately show this. The MCC is also symetric with respect
to positive and negative categorization, however, there needs to be both
positive and negative examples in the labels or it will always return 0.
MCC of 0 is uncorrelated, 1 is completely correlated, and -1 is negatively correlated.
.. math::
\\text{MCC} = \\frac{ TP \\times TN - FP \\times FN }
{\\sqrt{ (TP + FP) ( TP + FN ) ( TN + FP ) ( TN + FN ) } }
where 0 terms in the denominator are replaced by 1.
.. note::
This version of MCC only supports binary classification. See PCC.
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
average : str, default 'macro'
Strategy to be used for aggregating across mini-batches.
"macro": average the MCC for each batch.
"micro": compute a single MCC across all batches.
Examples
--------
>>> # In this example the network almost always predicts positive
>>> false_positives = 1000
>>> false_negatives = 1
>>> true_positives = 10000
>>> true_negatives = 1
>>> predicts = [mx.nd.array(
[[.3, .7]]*false_positives +
[[.7, .3]]*true_negatives +
[[.7, .3]]*false_negatives +
[[.3, .7]]*true_positives
)]
>>> labels = [mx.nd.array(
[0.]*(false_positives + true_negatives) +
[1.]*(false_negatives + true_positives)
)]
>>> f1 = mx.metric.F1()
>>> f1.update(preds = predicts, labels = labels)
>>> mcc = mx.metric.MCC()
>>> mcc.update(preds = predicts, labels = labels)
>>> print f1.get()
('f1', 0.95233560306652054)
>>> print mcc.get()
('mcc', 0.01917751877733392)
"""
def __init__(self, name='mcc',
output_names=None, label_names=None, average="macro"):
self._average = average
self._metrics = _BinaryClassificationMetrics()
EvalMetric.__init__(self, name=name,
output_names=output_names, label_names=label_names,
has_global_stats=True)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
self._metrics.update_binary_stats(label, pred)
if self._average == "macro":
self.sum_metric += self._metrics.matthewscc()
self.global_sum_metric += self._metrics.matthewscc(use_global=True)
self.num_inst += 1
self.global_num_inst += 1
self._metrics.reset_stats()
else:
self.sum_metric = self._metrics.matthewscc() * self._metrics.total_examples
self.global_sum_metric = self._metrics.matthewscc(use_global=True) * \
self._metrics.global_total_examples
self.num_inst = self._metrics.total_examples
self.global_num_inst = self._metrics.global_total_examples
[docs] def reset(self):
"""Resets the internal evaluation result to initial state."""
self.sum_metric = 0.
self.num_inst = 0.
self.global_sum_metric = 0.
self.global_num_inst = 0.
self._metrics.reset_stats()
[docs] def reset_local(self):
"""Resets the internal evaluation result to initial state."""
self.sum_metric = 0.
self.num_inst = 0.
self._metrics.local_reset_stats()
@register
[docs]class Perplexity(EvalMetric):
"""Computes perplexity.
Perplexity is a measurement of how well a probability distribution
or model predicts a sample. A low perplexity indicates the model
is good at predicting the sample.
The perplexity of a model q is defined as
.. math::
b^{\\big(-\\frac{1}{N} \\sum_{i=1}^N \\log_b q(x_i) \\big)}
= \\exp \\big(-\\frac{1}{N} \\sum_{i=1}^N \\log q(x_i)\\big)
where we let `b = e`.
:math:`q(x_i)` is the predicted value of its ground truth
label on sample :math:`x_i`.
For example, we have three samples :math:`x_1, x_2, x_3` and their labels
are :math:`[0, 1, 1]`.
Suppose our model predicts :math:`q(x_1) = p(y_1 = 0 | x_1) = 0.3`
and :math:`q(x_2) = 1.0`,
:math:`q(x_3) = 0.6`. The perplexity of model q is
:math:`exp\\big(-(\\log 0.3 + \\log 1.0 + \\log 0.6) / 3\\big) = 1.77109762852`.
Parameters
----------
ignore_label : int or None
Index of invalid label to ignore when
counting. By default, sets to -1.
If set to `None`, it will include all entries.
axis : int (default -1)
The axis from prediction that was used to
compute softmax. By default use the last
axis.
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array([[0.3, 0.7], [0, 1.], [0.4, 0.6]])]
>>> labels = [mx.nd.array([0, 1, 1])]
>>> perp = mx.metric.Perplexity(ignore_label=None)
>>> perp.update(labels, predicts)
>>> print perp.get()
('Perplexity', 1.7710976285155853)
"""
def __init__(self, ignore_label, axis=-1, name='perplexity',
output_names=None, label_names=None):
super(Perplexity, self).__init__(
name, ignore_label=ignore_label,
output_names=output_names, label_names=label_names,
has_global_stats=True)
self.ignore_label = ignore_label
self.axis = axis
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
assert len(labels) == len(preds)
loss = 0.
num = 0
for label, pred in zip(labels, preds):
assert label.size == pred.size/pred.shape[-1], \
"shape mismatch: %s vs. %s"%(label.shape, pred.shape)
label = label.as_in_context(pred.context).reshape((label.size,))
pred = ndarray.pick(pred, label.astype(dtype='int32'), axis=self.axis)
if self.ignore_label is not None:
ignore = (label == self.ignore_label).astype(pred.dtype)
num -= ndarray.sum(ignore).asscalar()
pred = pred*(1-ignore) + ignore
loss -= ndarray.sum(ndarray.log(ndarray.maximum(1e-10, pred))).asscalar()
num += pred.size
self.sum_metric += loss
self.global_sum_metric += loss
self.num_inst += num
self.global_num_inst += num
[docs] def get(self):
"""Returns the current evaluation result.
Returns
-------
Tuple of (str, float)
Representing name of the metric and evaluation result.
"""
if self.num_inst == 0:
return (self.name, float('nan'))
else:
return (self.name, math.exp(self.sum_metric/self.num_inst))
[docs] def get_global(self):
"""Returns the current global evaluation result.
Returns
-------
Tuple of (str, float)
Representing name of the metric and evaluation result.
"""
if self.global_num_inst == 0:
return (self.name, float('nan'))
else:
return (self.name, math.exp(self.global_sum_metric/self.global_num_inst))
####################
# REGRESSION METRICS
####################
@register
[docs]class MAE(EvalMetric):
"""Computes Mean Absolute Error (MAE) loss.
The mean absolute error is given by
.. math::
\\frac{\\sum_i^n |y_i - \\hat{y}_i|}{n}
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array(np.array([3, -0.5, 2, 7]).reshape(4,1))]
>>> labels = [mx.nd.array(np.array([2.5, 0.0, 2, 8]).reshape(4,1))]
>>> mean_absolute_error = mx.metric.MAE()
>>> mean_absolute_error.update(labels = labels, preds = predicts)
>>> print mean_absolute_error.get()
('mae', 0.5)
"""
def __init__(self, name='mae',
output_names=None, label_names=None):
super(MAE, self).__init__(
name, output_names=output_names, label_names=label_names,
has_global_stats=True)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
label = label.asnumpy()
pred = pred.asnumpy()
if len(label.shape) == 1:
label = label.reshape(label.shape[0], 1)
if len(pred.shape) == 1:
pred = pred.reshape(pred.shape[0], 1)
mae = numpy.abs(label - pred).mean()
self.sum_metric += mae
self.global_sum_metric += mae
self.num_inst += 1 # numpy.prod(label.shape)
self.global_num_inst += 1 # numpy.prod(label.shape)
@register
[docs]class MSE(EvalMetric):
"""Computes Mean Squared Error (MSE) loss.
The mean squared error is given by
.. math::
\\frac{\\sum_i^n (y_i - \\hat{y}_i)^2}{n}
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array(np.array([3, -0.5, 2, 7]).reshape(4,1))]
>>> labels = [mx.nd.array(np.array([2.5, 0.0, 2, 8]).reshape(4,1))]
>>> mean_squared_error = mx.metric.MSE()
>>> mean_squared_error.update(labels = labels, preds = predicts)
>>> print mean_squared_error.get()
('mse', 0.375)
"""
def __init__(self, name='mse',
output_names=None, label_names=None):
super(MSE, self).__init__(
name, output_names=output_names, label_names=label_names,
has_global_stats=True)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
label = label.asnumpy()
pred = pred.asnumpy()
if len(label.shape) == 1:
label = label.reshape(label.shape[0], 1)
if len(pred.shape) == 1:
pred = pred.reshape(pred.shape[0], 1)
mse = ((label - pred)**2.0).mean()
self.sum_metric += mse
self.global_sum_metric += mse
self.num_inst += 1 # numpy.prod(label.shape)
self.global_num_inst += 1 # numpy.prod(label.shape)
@register
[docs]class RMSE(EvalMetric):
"""Computes Root Mean Squred Error (RMSE) loss.
The root mean squared error is given by
.. math::
\\sqrt{\\frac{\\sum_i^n (y_i - \\hat{y}_i)^2}{n}}
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array(np.array([3, -0.5, 2, 7]).reshape(4,1))]
>>> labels = [mx.nd.array(np.array([2.5, 0.0, 2, 8]).reshape(4,1))]
>>> root_mean_squared_error = mx.metric.RMSE()
>>> root_mean_squared_error.update(labels = labels, preds = predicts)
>>> print root_mean_squared_error.get()
('rmse', 0.612372457981)
"""
def __init__(self, name='rmse',
output_names=None, label_names=None):
super(RMSE, self).__init__(
name, output_names=output_names, label_names=label_names,
has_global_stats=True)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
label = label.asnumpy()
pred = pred.asnumpy()
if len(label.shape) == 1:
label = label.reshape(label.shape[0], 1)
if len(pred.shape) == 1:
pred = pred.reshape(pred.shape[0], 1)
rmse = numpy.sqrt(((label - pred)**2.0).mean())
self.sum_metric += rmse
self.global_sum_metric += rmse
self.num_inst += 1
self.global_num_inst += 1
@register
@alias('ce')
[docs]class CrossEntropy(EvalMetric):
"""Computes Cross Entropy loss.
The cross entropy over a batch of sample size :math:`N` is given by
.. math::
-\\sum_{n=1}^{N}\\sum_{k=1}^{K}t_{nk}\\log (y_{nk}),
where :math:`t_{nk}=1` if and only if sample :math:`n` belongs to class :math:`k`.
:math:`y_{nk}` denotes the probability of sample :math:`n` belonging to
class :math:`k`.
Parameters
----------
eps : float
Cross Entropy loss is undefined for predicted value is 0 or 1,
so predicted values are added with the small constant.
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array([[0.3, 0.7], [0, 1.], [0.4, 0.6]])]
>>> labels = [mx.nd.array([0, 1, 1])]
>>> ce = mx.metric.CrossEntropy()
>>> ce.update(labels, predicts)
>>> print ce.get()
('cross-entropy', 0.57159948348999023)
"""
def __init__(self, eps=1e-12, name='cross-entropy',
output_names=None, label_names=None):
super(CrossEntropy, self).__init__(
name, eps=eps,
output_names=output_names, label_names=label_names,
has_global_stats=True)
self.eps = eps
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
label = label.asnumpy()
pred = pred.asnumpy()
label = label.ravel()
assert label.shape[0] == pred.shape[0]
prob = pred[numpy.arange(label.shape[0]), numpy.int64(label)]
cross_entropy = (-numpy.log(prob + self.eps)).sum()
self.sum_metric += cross_entropy
self.global_sum_metric += cross_entropy
self.num_inst += label.shape[0]
self.global_num_inst += label.shape[0]
@register
@alias('nll_loss')
[docs]class NegativeLogLikelihood(EvalMetric):
"""Computes the negative log-likelihood loss.
The negative log-likelihoodd loss over a batch of sample size :math:`N` is given by
.. math::
-\\sum_{n=1}^{N}\\sum_{k=1}^{K}t_{nk}\\log (y_{nk}),
where :math:`K` is the number of classes, :math:`y_{nk}` is the prediceted probability for
:math:`k`-th class for :math:`n`-th sample. :math:`t_{nk}=1` if and only if sample
:math:`n` belongs to class :math:`k`.
Parameters
----------
eps : float
Negative log-likelihood loss is undefined for predicted value is 0,
so predicted values are added with the small constant.
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array([[0.3, 0.7], [0, 1.], [0.4, 0.6]])]
>>> labels = [mx.nd.array([0, 1, 1])]
>>> nll_loss = mx.metric.NegativeLogLikelihood()
>>> nll_loss.update(labels, predicts)
>>> print nll_loss.get()
('nll-loss', 0.57159948348999023)
"""
def __init__(self, eps=1e-12, name='nll-loss',
output_names=None, label_names=None):
super(NegativeLogLikelihood, self).__init__(
name, eps=eps,
output_names=output_names, label_names=label_names,
has_global_stats=True)
self.eps = eps
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
label = label.asnumpy()
pred = pred.asnumpy()
label = label.ravel()
num_examples = pred.shape[0]
assert label.shape[0] == num_examples, (label.shape[0], num_examples)
prob = pred[numpy.arange(num_examples, dtype=numpy.int64), numpy.int64(label)]
nll = (-numpy.log(prob + self.eps)).sum()
self.sum_metric += nll
self.global_sum_metric += nll
self.num_inst += num_examples
self.global_num_inst += num_examples
@register
@alias('pearsonr')
[docs]class PearsonCorrelation(EvalMetric):
"""Computes Pearson correlation.
The pearson correlation is given by
.. math::
\\frac{cov(y, \\hat{y})}{\\sigma{y}\\sigma{\\hat{y}}}
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array([[0.3, 0.7], [0, 1.], [0.4, 0.6]])]
>>> labels = [mx.nd.array([[1, 0], [0, 1], [0, 1]])]
>>> pr = mx.metric.PearsonCorrelation()
>>> pr.update(labels, predicts)
>>> print pr.get()
('pearson-correlation', 0.42163704544016178)
"""
def __init__(self, name='pearsonr',
output_names=None, label_names=None):
super(PearsonCorrelation, self).__init__(
name, output_names=output_names, label_names=label_names,
has_global_stats=True)
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
for label, pred in zip(labels, preds):
check_label_shapes(label, pred, False, True)
label = label.asnumpy()
pred = pred.asnumpy()
pearson_corr = numpy.corrcoef(pred.ravel(), label.ravel())[0, 1]
self.sum_metric += pearson_corr
self.global_sum_metric += pearson_corr
self.num_inst += 1
self.global_num_inst += 1
@register
[docs]class PCC(EvalMetric):
"""PCC is a multiclass equivalent for the Matthews correlation coefficient derived
from a discrete solution to the Pearson correlation coefficient.
.. math::
\\text{PCC} = \\frac {\\sum _{k}\\sum _{l}\\sum _{m}C_{kk}C_{lm}-C_{kl}C_{mk}}
{{\\sqrt {\\sum _{k}(\\sum _{l}C_{kl})(\\sum _{k'|k'\\neq k}\\sum _{l'}C_{k'l'})}}
{\\sqrt {\\sum _{k}(\\sum _{l}C_{lk})(\\sum _{k'|k'\\neq k}\\sum _{l'}C_{l'k'})}}}
defined in terms of a K x K confusion matrix C.
When there are more than two labels the PCC will no longer range between -1 and +1.
Instead the minimum value will be between -1 and 0 depending on the true distribution.
The maximum value is always +1.
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> # In this example the network almost always predicts positive
>>> false_positives = 1000
>>> false_negatives = 1
>>> true_positives = 10000
>>> true_negatives = 1
>>> predicts = [mx.nd.array(
[[.3, .7]]*false_positives +
[[.7, .3]]*true_negatives +
[[.7, .3]]*false_negatives +
[[.3, .7]]*true_positives
)]
>>> labels = [mx.nd.array(
[0]*(false_positives + true_negatives) +
[1]*(false_negatives + true_positives)
)]
>>> f1 = mx.metric.F1()
>>> f1.update(preds = predicts, labels = labels)
>>> pcc = mx.metric.PCC()
>>> pcc.update(preds = predicts, labels = labels)
>>> print f1.get()
('f1', 0.95233560306652054)
>>> print pcc.get()
('pcc', 0.01917751877733392)
"""
def __init__(self, name='pcc',
output_names=None, label_names=None,
has_global_stats=True):
self.k = 2
super(PCC, self).__init__(
name=name, output_names=output_names, label_names=label_names,
has_global_stats=has_global_stats)
def _grow(self, inc):
self.lcm = numpy.pad(
self.lcm, ((0, inc), (0, inc)), 'constant', constant_values=(0))
self.gcm = numpy.pad(
self.gcm, ((0, inc), (0, inc)), 'constant', constant_values=(0))
self.k += inc
def _calc_mcc(self, cmat):
n = cmat.sum()
x = cmat.sum(axis=1)
y = cmat.sum(axis=0)
cov_xx = numpy.sum(x * (n - x))
cov_yy = numpy.sum(y * (n - y))
if cov_xx == 0 or cov_yy == 0:
return float('nan')
i = cmat.diagonal()
cov_xy = numpy.sum(i * n - x * y)
return cov_xy / (cov_xx * cov_yy) ** 0.5
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
labels, preds = check_label_shapes(labels, preds, True)
# update the confusion matrix
for label, pred in zip(labels, preds):
label = label.astype('int32', copy=False).asnumpy()
pred = pred.asnumpy().argmax(axis=1)
n = max(pred.max(), label.max())
if n >= self.k:
self._grow(n + 1 - self.k)
bcm = numpy.zeros((self.k, self.k))
for i, j in zip(pred, label):
bcm[i, j] += 1
self.lcm += bcm
self.gcm += bcm
self.num_inst += 1
self.global_num_inst += 1
@property
def sum_metric(self):
return self._calc_mcc(self.lcm) * self.num_inst
@property
def global_sum_metric(self):
return self._calc_mcc(self.gcm) * self.global_num_inst
[docs] def reset(self):
"""Resets the internal evaluation result to initial state."""
self.global_num_inst = 0.
self.gcm = numpy.zeros((self.k, self.k))
self.reset_local()
[docs] def reset_local(self):
"""Resets the local portion of the internal evaluation results
to initial state."""
self.num_inst = 0.
self.lcm = numpy.zeros((self.k, self.k))
@register
[docs]class Loss(EvalMetric):
"""Dummy metric for directly printing loss.
Parameters
----------
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
"""
def __init__(self, name='loss',
output_names=None, label_names=None):
super(Loss, self).__init__(
name, output_names=output_names, label_names=label_names,
has_global_stats=True)
def update(self, _, preds):
if isinstance(preds, ndarray.ndarray.NDArray):
preds = [preds]
for pred in preds:
loss = ndarray.sum(pred).asscalar()
self.sum_metric += loss
self.global_sum_metric += loss
self.num_inst += pred.size
self.global_num_inst += pred.size
@register
[docs]class Torch(Loss):
"""Dummy metric for torch criterions."""
def __init__(self, name='torch',
output_names=None, label_names=None):
super(Torch, self).__init__(
name, output_names=output_names, label_names=label_names)
@register
[docs]class Caffe(Loss):
"""Dummy metric for caffe criterions."""
def __init__(self, name='caffe',
output_names=None, label_names=None):
super(Caffe, self).__init__(
name, output_names=output_names, label_names=label_names)
@register
[docs]class CustomMetric(EvalMetric):
"""Computes a customized evaluation metric.
The `feval` function can return a `tuple` of (sum_metric, num_inst) or return
an `int` sum_metric.
Parameters
----------
feval : callable(label, pred)
Customized evaluation function.
name : str, optional
The name of the metric. (the default is None).
allow_extra_outputs : bool, optional
If true, the prediction outputs can have extra outputs.
This is useful in RNN, where the states are also produced
in outputs for forwarding. (the default is False).
name : str
Name of this metric instance for display.
output_names : list of str, or None
Name of predictions that should be used when updating with update_dict.
By default include all predictions.
label_names : list of str, or None
Name of labels that should be used when updating with update_dict.
By default include all labels.
Examples
--------
>>> predicts = [mx.nd.array(np.array([3, -0.5, 2, 7]).reshape(4,1))]
>>> labels = [mx.nd.array(np.array([2.5, 0.0, 2, 8]).reshape(4,1))]
>>> feval = lambda x, y : (x + y).mean()
>>> eval_metrics = mx.metric.CustomMetric(feval=feval)
>>> eval_metrics.update(labels, predicts)
>>> print eval_metrics.get()
('custom()', 6.0)
"""
def __init__(self, feval, name=None, allow_extra_outputs=False,
output_names=None, label_names=None):
if name is None:
name = feval.__name__
if name.find('<') != -1:
name = 'custom(%s)' % name
super(CustomMetric, self).__init__(
name, feval=feval,
allow_extra_outputs=allow_extra_outputs,
output_names=output_names, label_names=label_names,
has_global_stats=True)
self._feval = feval
self._allow_extra_outputs = allow_extra_outputs
[docs] def update(self, labels, preds):
"""Updates the internal evaluation result.
Parameters
----------
labels : list of `NDArray`
The labels of the data.
preds : list of `NDArray`
Predicted values.
"""
if not self._allow_extra_outputs:
labels, preds = check_label_shapes(labels, preds, True)
for pred, label in zip(preds, labels):
label = label.asnumpy()
pred = pred.asnumpy()
reval = self._feval(label, pred)
if isinstance(reval, tuple):
(sum_metric, num_inst) = reval
self.sum_metric += sum_metric
self.global_sum_metric += sum_metric
self.num_inst += num_inst
self.global_num_inst += num_inst
else:
self.sum_metric += reval
self.global_sum_metric += reval
self.num_inst += 1
self.global_num_inst += 1
def get_config(self):
raise NotImplementedError("CustomMetric cannot be serialized")
# pylint: disable=invalid-name
[docs]def np(numpy_feval, name=None, allow_extra_outputs=False):
"""Creates a custom evaluation metric that receives its inputs as numpy arrays.
Parameters
----------
numpy_feval : callable(label, pred)
Custom evaluation function that receives labels and predictions for a minibatch
as numpy arrays and returns the corresponding custom metric as a floating point number.
name : str, optional
Name of the custom metric.
allow_extra_outputs : bool, optional
Whether prediction output is allowed to have extra outputs. This is useful in cases
like RNN where states are also part of output which can then be fed back to the RNN
in the next step. By default, extra outputs are not allowed.
Returns
-------
float
Custom metric corresponding to the provided labels and predictions.
Example
-------
>>> def custom_metric(label, pred):
... return np.mean(np.abs(label-pred))
...
>>> metric = mx.metric.np(custom_metric)
"""
def feval(label, pred):
"""Internal eval function."""
return numpy_feval(label, pred)
feval.__name__ = numpy_feval.__name__
return CustomMetric(feval, name, allow_extra_outputs)
# pylint: enable=invalid-name
