# 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: Francois Gallard, Matthias De Lozzo
# OTHER AUTHORS - MACROSCOPIC CHANGES
r"""Linear regression model.
The linear regression model expresses the output variables
as a weighted sum of the input ones:
.. math::
y = w_0 + w_1x_1 + w_2x_2 + ... + w_dx_d
+ \alpha \left( \lambda \|w\|_2 + (1-\lambda) \|w\|_1 \right),
where the coefficients :math:`(w_1, w_2, ..., w_d)` and the intercept
:math:`w_0` are estimated by least square regression. They are easily
accessible via the arguments :attr:`.coefficients` and :attr:`.intercept`.
The penalty level :math:`\alpha` is a non-negative parameter intended to
prevent overfitting, while the penalty ratio :math:`\lambda\in [0, 1]`
expresses the ratio between :math:`\ell_2`- and :math:`\ell_1`-regularization.
When :math:`\lambda=1`, there is no :math:`\ell_1`-regularization, and a Ridge
regression is performed. When :math:`\lambda=0`, there is no
:math:`\ell_2`-regularization, and a Lasso regression is performed. For
:math:`\lambda` between 0 and 1, an Elastic Net regression is performed.
One may also choose not to penalize the regression at all, by setting
:math:`\alpha=0`. In this case, a simple least squares regression is performed.
Dependence
----------
The linear model relies on the ``LinearRegression``,
``Ridge``, ``Lasso`` and ``ElasticNet``
classes of the `scikit-learn library <https://scikit-learn.org/stable/modules/
linear_model.html>`_.
"""
from __future__ import annotations
from typing import TYPE_CHECKING
from typing import ClassVar
from numpy import array
from numpy import repeat
from numpy import zeros
from sklearn.linear_model import ElasticNet
from sklearn.linear_model import Lasso
from sklearn.linear_model import LinearRegression as LinReg
from sklearn.linear_model import Ridge
from gemseo.datasets.io_dataset import IODataset
from gemseo.mlearning.regression.algos.base_regressor import BaseRegressor
from gemseo.mlearning.regression.algos.linreg_settings import LinearRegressor_Settings
from gemseo.mlearning.transformers.dimension_reduction.base_dimension_reduction import (
BaseDimensionReduction,
)
from gemseo.utils.data_conversion import split_array_to_dict_of_arrays
if TYPE_CHECKING:
from gemseo.typing import RealArray
[docs]
class LinearRegressor(BaseRegressor):
"""Linear regression model."""
SHORT_ALGO_NAME: ClassVar[str] = "LinReg"
LIBRARY: ClassVar[str] = "scikit-learn"
Settings: ClassVar[type[LinearRegressor_Settings]] = LinearRegressor_Settings
def _post_init(self):
super()._post_init()
penalty_level = self._settings.penalty_level
if penalty_level == 0.0:
self.algo = LinReg(
copy_X=False,
fit_intercept=self._settings.fit_intercept,
**self._settings.parameters,
)
elif self._settings.l2_penalty_ratio == 1.0:
self.algo = Ridge(
copy_X=False,
fit_intercept=self._settings.fit_intercept,
alpha=penalty_level,
random_state=self._settings.random_state,
**self._settings.parameters,
)
elif self._settings.l2_penalty_ratio == 0.0:
self.algo = Lasso(
copy_X=False,
fit_intercept=self._settings.fit_intercept,
alpha=penalty_level,
random_state=self._settings.random_state,
**self._settings.parameters,
)
else:
self.algo = ElasticNet(
copy_X=False,
fit_intercept=self._settings.fit_intercept,
alpha=penalty_level,
l1_ratio=1 - self._settings.l2_penalty_ratio,
random_state=self._settings.random_state,
**self._settings.parameters,
)
def _fit(
self,
input_data: RealArray,
output_data: RealArray,
) -> None:
self.algo.fit(input_data, output_data)
def _predict(
self,
input_data: RealArray,
) -> RealArray:
return self.algo.predict(input_data).reshape((len(input_data), -1))
def _predict_jacobian(
self,
input_data: RealArray,
) -> RealArray:
return repeat(self.algo.coef_[None], len(input_data), axis=0)
@property
def coefficients(self) -> RealArray:
"""The regression coefficients of the linear model."""
return self.algo.coef_
@property
def intercept(self) -> RealArray:
"""The regression intercepts of the linear model."""
if self._settings.fit_intercept:
return self.algo.intercept_
return zeros(self.algo.coef_.shape[0])
[docs]
def get_coefficients(
self,
as_dict: bool = True,
) -> RealArray | dict[str, list[dict[str, list[float]]]]:
"""Return the regression coefficients of the linear model.
Args:
as_dict: If ``True``, return the coefficients as a dictionary.
Otherwise, return the coefficients as a numpy.array
Returns:
The regression coefficients of the linear model.
Raises:
ValueError: If the coefficients are required as a dictionary
even though the transformers change the variables dimensions.
"""
coefficients = self.coefficients
if not as_dict:
return coefficients
if any(
isinstance(transformer, BaseDimensionReduction)
for transformer in self.transformer.values()
):
msg = (
"Coefficients are only representable in dictionary "
"form if the transformers do not change the "
"dimensions of the variables."
)
raise ValueError(msg)
return self.__convert_array_to_dict(coefficients)
[docs]
def get_intercept(self, as_dict: bool = True) -> RealArray | dict[str, list[float]]:
"""Return the regression intercepts of the linear model.
Args:
as_dict: If ``True``, return the intercepts as a dictionary.
Otherwise, return the intercepts as a numpy.array
Returns:
The regression intercepts of the linear model.
Raises:
ValueError: If the coefficients are required as a dictionary
even though the transformers change the variables dimensions.
"""
intercept = self.intercept
if not as_dict:
return intercept
if IODataset.OUTPUT_GROUP in self.transformer:
msg = (
"Intercept is only representable in dictionary "
"form if the transformers do not change the "
"dimensions of the output variables."
)
raise ValueError(msg)
intercept = split_array_to_dict_of_arrays(
intercept,
self.learning_set.variable_names_to_n_components,
self.output_names,
)
return {key: list(val) for key, val in intercept.items()}
def __convert_array_to_dict(
self,
data: RealArray,
) -> dict[str, list[dict[str, list[float]]]]:
"""Convert a data array into a dictionary.
Args:
data: The data to be converted.
Returns:
The converted data.
"""
varsizes = self.learning_set.variable_names_to_n_components
data = [
split_array_to_dict_of_arrays(row, varsizes, self.input_names)
for row in data
]
data = [{key: list(val) for key, val in element.items()} for element in data]
data = split_array_to_dict_of_arrays(array(data), varsizes, self.output_names)
return {key: list(val) for key, val in data.items()}
