# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# Contributors:
# INITIAL AUTHORS - initial API and implementation and/or initial
# documentation
# :author: Syver Doving Agdestein
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""The R2 to measure the quality of a regression algorithm.
The :mod:`~gemseo.mlearning.qual_measure.r2_measure` module
implements the concept of R2 measures for machine learning algorithms.
This concept is implemented through the :class:`.R2Measure` class
and overloads the :meth:`!MLErrorMeasure._compute_measure` method.
The R2 is defined by
.. math::
R_2(\\hat{y}) = 1 - \\frac{\\sum_i (\\hat{y}_i - y_i)^2}
{\\sum_i (y_i-\\bar{y})^2},
where
:math:`\\hat{y}` are the predictions,
:math:`y` are the data points and
:math:`\\bar{y}` is the mean of :math:`y`.
"""
from __future__ import division, unicode_literals
from copy import deepcopy
from typing import List, NoReturn, Optional, Union
from numpy import atleast_2d
from numpy import delete as npdelete
from numpy import mean, ndarray, repeat
from sklearn.metrics import mean_squared_error, r2_score
from gemseo.mlearning.qual_measure.error_measure import MLErrorMeasure
from gemseo.mlearning.regression.regression import MLRegressionAlgo
[docs]class R2Measure(MLErrorMeasure):
"""The R2 measure for machine learning."""
SMALLER_IS_BETTER = False
def __init__(
self,
algo, # type: MLRegressionAlgo
): # type: (...) -> None
"""
Args:
algo: A machine learning algorithm for regression.
"""
super(R2Measure, self).__init__(algo)
def _compute_measure(
self,
outputs, # type: ndarray
predictions, # type: ndarray
multioutput=True, # type: bool
): # type: (...) -> Union[float,ndarray]
multioutput = "raw_values" if multioutput else "uniform_average"
return r2_score(outputs, predictions, multioutput=multioutput)
[docs] def evaluate_kfolds(
self,
n_folds=5, # type: int
samples=None, # type: Optional[List[int]]
multioutput=True, # type: bool
randomize=False, # type:bool
): # type: (...) -> Union[float,ndarray]
folds, samples = self._compute_folds(samples, n_folds, randomize)
in_grp = self.algo.learning_set.INPUT_GROUP
out_grp = self.algo.learning_set.OUTPUT_GROUP
inputs = self.algo.learning_set.get_data_by_group(in_grp)
outputs = self.algo.learning_set.get_data_by_group(out_grp)
multiout = "raw_values" if multioutput else "uniform_average"
algo = deepcopy(self.algo)
num = 0
ymean = mean(outputs, axis=0)
ymean = atleast_2d(ymean)
ymean = repeat(ymean, outputs.shape[0], axis=0)
den = mean_squared_error(outputs, ymean, multioutput=multiout) * len(ymean)
for n_fold in range(n_folds):
fold = folds[n_fold]
train = npdelete(samples, fold)
algo.learn(samples=train)
expected = outputs[fold]
predicted = algo.predict(inputs[fold])
tmp = mean_squared_error(expected, predicted, multioutput=multiout)
num += tmp * len(fold)
quality = 1 - num / den
return quality
[docs] def evaluate_bootstrap(
self,
n_replicates=100, # type: int
samples=None, # type: Optional[List[int]]
multioutput=True, # type: bool
): # type: (...) -> NoReturn
raise NotImplementedError
