# 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 ClassVar
from typing import Iterable
from numpy import array
from numpy import ndarray
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.core.dataset import Dataset
from gemseo.mlearning.core.ml_algo import DataType
from gemseo.mlearning.core.ml_algo import TransformerType
from gemseo.mlearning.regression.regression import MLRegressionAlgo
from gemseo.mlearning.transform.dimension_reduction.dimension_reduction import (
DimensionReduction,
)
from gemseo.utils.data_conversion import split_array_to_dict_of_arrays
from gemseo.utils.python_compatibility import Final
[docs]class LinearRegressor(MLRegressionAlgo):
"""Linear regression model."""
SHORT_ALGO_NAME: ClassVar[str] = "LinReg"
LIBRARY: Final[str] = "scikit-learn"
def __init__(
self,
data: Dataset,
transformer: TransformerType = MLRegressionAlgo.IDENTITY,
input_names: Iterable[str] | None = None,
output_names: Iterable[str] | None = None,
fit_intercept: bool = True,
penalty_level: float = 0.0,
l2_penalty_ratio: float = 1.0,
**parameters: float | int | str | bool | None,
) -> None:
"""
Args:
fit_intercept: Whether to fit the intercept.
penalty_level: The penalty level greater or equal to 0.
If 0, there is no penalty.
l2_penalty_ratio: The penalty ratio related to the l2 regularization.
If 1, use the Ridge penalty.
If 0, use the Lasso penalty.
Between 0 and 1, use the ElasticNet penalty.
**parameters: The parameters of the machine learning algorithm.
"""
super().__init__(
data,
transformer=transformer,
input_names=input_names,
output_names=output_names,
fit_intercept=fit_intercept,
penalty_level=penalty_level,
l2_penalty_ratio=l2_penalty_ratio,
**parameters,
)
if "degree" in parameters:
del parameters["degree"]
if penalty_level == 0.0:
self.algo = LinReg(copy_X=False, fit_intercept=fit_intercept, **parameters)
else:
if l2_penalty_ratio == 1.0:
self.algo = Ridge(
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
**parameters,
)
elif l2_penalty_ratio == 0.0:
self.algo = Lasso(
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
**parameters,
)
else:
self.algo = ElasticNet(
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
l1_ratio=1 - l2_penalty_ratio,
**parameters,
)
def _fit(
self,
input_data: ndarray,
output_data: ndarray,
) -> None:
self.algo.fit(input_data, output_data)
def _predict(
self,
input_data: ndarray,
) -> ndarray:
return self.algo.predict(input_data)
def _predict_jacobian(
self,
input_data: ndarray,
) -> ndarray:
n_samples = input_data.shape[0]
return repeat(self.algo.coef_[None], n_samples, axis=0)
@property
def coefficients(self) -> ndarray:
"""The regression coefficients of the linear model."""
return self.algo.coef_
@property
def intercept(self) -> ndarray:
"""The regression intercepts of the linear model."""
if self.parameters["fit_intercept"]:
intercept = self.algo.intercept_
else:
intercept = zeros(self.algo.coef_.shape[0])
return intercept
[docs] def get_coefficients(
self,
as_dict: bool = True,
) -> DataType:
"""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 as_dict:
if any(
[
isinstance(transformer, DimensionReduction)
for _, transformer in self.transformer.items()
]
):
raise ValueError(
"Coefficients are only representable in dictionary "
"form if the transformers do not change the "
"dimensions of the variables."
)
coefficients = self.__convert_array_to_dict(coefficients)
return coefficients
[docs] def get_intercept(
self,
as_dict: bool = True,
) -> DataType:
"""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 as_dict:
if Dataset.OUTPUT_GROUP in self.transformer:
raise ValueError(
"Intercept is only representable in dictionary "
"form if the transformers do not change the "
"dimensions of the output variables."
)
varsizes = self.learning_set.sizes
intercept = split_array_to_dict_of_arrays(
intercept, varsizes, self.output_names
)
intercept = {key: list(val) for key, val in intercept.items()}
return intercept
def __convert_array_to_dict(
self,
data: ndarray,
) -> dict[str, ndarray]:
"""Convert a data array into a dictionary.
Args:
data: The data to be converted.
Returns:
The converted data.
"""
varsizes = self.learning_set.sizes
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)
data = {key: list(val) for key, val in data.items()}
return data
