Table Of Contents
Table Of Contents

Source code for mxnet.metric

# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements.  See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership.  The ASF licenses this file
# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License.  You may obtain a copy of the License at
#
#   http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
# KIND, either express or implied.  See the License for the
# specific language governing permissions and limitations
# under the License.

# 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. """
[docs] 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())) 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 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) 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() 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 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 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) 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() 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)) 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)
[docs]@register @alias('composite') 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]) """
[docs] 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]
def add(self, metric): """Adds a child metric. Parameters ---------- metric A metric instance. """ self.metrics.append(create(metric)) 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) 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) def reset(self): """Resets the internal evaluation result to initial state.""" try: for metric in self.metrics: metric.reset() except AttributeError: pass 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 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) 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 ########################
[docs]@register @alias('acc') 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) """
[docs] 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
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)
[docs]@register @alias('top_k_accuracy', 'top_k_acc') 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) """
[docs] 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
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
[docs]@register 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) """
[docs] 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)
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 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() 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()
[docs]@register 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. 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) """
[docs] 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)
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 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() 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()
[docs]@register 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) """
[docs] 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
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 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)) 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 ####################
[docs]@register 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) """
[docs] 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)
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)
[docs]@register 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) """
[docs] 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)
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)
[docs]@register 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) """
[docs] 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)
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
[docs]@register @alias('ce') 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) """
[docs] 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
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]
[docs]@register @alias('nll_loss') 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) """
[docs] 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
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
[docs]@register @alias('pearsonr') 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) """
[docs] 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)
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
[docs]@register 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. """
[docs] 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
[docs]@register class Torch(Loss): """Dummy metric for torch criterions."""
[docs] def __init__(self, name='torch', output_names=None, label_names=None): super(Torch, self).__init__( name, output_names=output_names, label_names=label_names)
[docs]@register class Caffe(Loss): """Dummy metric for caffe criterions."""
[docs] def __init__(self, name='caffe', output_names=None, label_names=None): super(Caffe, self).__init__( name, output_names=output_names, label_names=label_names)
[docs]@register 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(<lambda>)', 6.0) """
[docs] 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
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