# Source code for gemseo.mlearning.qual_measure.mse_measure

```
# 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 mean squared error to measure the quality of a regression algorithm.
The :mod:`~gemseo.mlearning.qual_measure.mse_measure` module
implements the concept of mean squared error measures
for machine learning algorithms.
This concept is implemented through the :class:`.MSEMeasure` class
and overloads the :meth:`!MLErrorMeasure._compute_measure` method.
The mean squared error (MSE) is defined by
.. math::
\\operatorname{MSE}(\\hat{y})=\\frac{1}{n}\\sum_{i=1}^n(\\hat{y}_i-y_i)^2,
where :math:`\\hat{y}` are the predictions and :math:`y` are the data points.
"""
from __future__ import annotations
from numpy import ndarray
from sklearn.metrics import mean_squared_error
from gemseo.mlearning.qual_measure.error_measure import MLErrorMeasure
from gemseo.mlearning.regression.regression import MLRegressionAlgo
[docs]class MSEMeasure(MLErrorMeasure):
"""The Mean Squared Error measure for machine learning."""
def __init__(
self,
algo: MLRegressionAlgo,
fit_transformers: bool = False,
) -> None:
"""
Args:
algo: A machine learning algorithm for regression.
"""
super().__init__(algo, fit_transformers=fit_transformers)
def _compute_measure(
self,
outputs: ndarray,
predictions: ndarray,
multioutput: bool = True,
) -> float | ndarray:
multioutput = "raw_values" if multioutput else "uniform_average"
return mean_squared_error(outputs, predictions, multioutput=multioutput)
```