# -*- 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: Francois Gallard, Matthias De Lozzo
# OTHER AUTHORS - MACROSCOPIC CHANGES
r"""
Linear regression
=================
The linear regression surrogate discipline expresses the model output
as a weighted sum of the model inputs:
.. 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 are easily
accessible via the arguments *coefficients* and *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.
This concept is implemented through the :class:`.LinearRegression` class which
inherits from the :class:`.MLRegressionAlgo` class.
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 absolute_import, division, unicode_literals
from future import standard_library
from numpy import array, repeat, zeros
from sklearn.linear_model import ElasticNet, Lasso
from sklearn.linear_model import LinearRegression as LinReg
from sklearn.linear_model import Ridge
from gemseo.core.dataset import Dataset
from gemseo.mlearning.regression.regression import MLRegressionAlgo
from gemseo.mlearning.transform.dimension_reduction.dimension_reduction import (
DimensionReduction,
)
from gemseo.utils.data_conversion import DataConversion
standard_library.install_aliases()
from gemseo import LOGGER
[docs]class LinearRegression(MLRegressionAlgo):
""" Linear regression """
LIBRARY = "scikit-learn"
ABBR = "LinReg"
def __init__(
self,
data,
transformer=None,
input_names=None,
output_names=None,
fit_intercept=True,
penalty_level=0.0,
l2_penalty_ratio=1.0,
**parameters
):
"""Constructor.
:param data: learning dataset.
:type data: Dataset
:param transformer: transformation strategy for data groups.
If None, do not transform data. Default: None.
:type transformer: dict(str)
:param input_names: names of the input variables.
:type input_names: list(str)
:param output_names: names of the output variables.
:type output_names: list(str)
:param fit_intercept: if True, fit intercept. Default: True.
:type fit_intercept: bool
:param penalty_level: penalty level greater or equal to 0.
If 0, there is no penalty. Default: 0.
:type penalty_level: float
:param l2_penalty_ratio: penalty ratio related to the l2
regularization. If 1, the penalty is the Ridge penalty. If 0,
this is the Lasso penalty. Between 0 and 1, the penalty is the
ElasticNet penalty. Default: None.
:type l2_penalty_ratio: float
"""
super(LinearRegression, self).__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 penalty_level == 0.0:
self.algo = LinReg(
normalize=False, copy_X=False, fit_intercept=fit_intercept, **parameters
)
else:
if l2_penalty_ratio == 1.0:
self.algo = Ridge(
normalize=False,
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
**parameters
)
elif l2_penalty_ratio == 0.0:
self.algo = Lasso(
normalize=False,
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
**parameters
)
else:
self.algo = ElasticNet(
normalize=False,
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
l1_ratio=1 - l2_penalty_ratio,
**parameters
)
def _fit(self, input_data, output_data):
"""Fit the regression model.
:param ndarray input_data: input data (2D).
:param ndarray output_data: output data (2D).
"""
self.algo.fit(input_data, output_data)
def _predict(self, input_data):
"""Predict output for given input data.
:param ndarray input_data: input data (2D).
:return: output prediction (2D).
:rtype: ndarray.
"""
return self.algo.predict(input_data)
def _predict_jacobian(self, input_data):
"""Predict Jacobian of the regression model for the given input data.
:param ndarray input_data: input_data (2D).
:return: Jacobian matrices (3D, one for each sample).
:rtype: ndarray
"""
n_samples = input_data.shape[0]
return repeat(self.algo.coef_[None], n_samples, axis=0)
@property
def coefficients(self):
""" Return the regression coefficients of the linear fit. """
return self.algo.coef_
@property
def intercept(self):
""" Return the regression intercepts of the linear fit. """
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=True):
"""Return the regression coefficients of the linear fit
as a numpy array or as a dict.
:param bool as_dict: if True, returns coefficients as a dictionary.
Default: True.
"""
coefficients = self.coefficients
if as_dict:
if any(
[
isinstance(transformer, DimensionReduction)
for _, transformer in self.transformer.items()
]
):
raise ValueError(
"Coefficients are only representable in dict "
"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=True):
"""Returns the regression intercept of the linear fit
as a numpy array or as a dict.
:param bool as_dict: if True, returns intercept as a dictionary.
Default: True.
"""
intercept = self.intercept
if as_dict:
if Dataset.OUTPUT_GROUP in self.transformer:
raise ValueError(
"Intercept is only representable in dict "
"form if the transformers do not change the "
"dimensions of the output variables."
)
varsizes = self.learning_set.sizes
intercept = DataConversion.array_to_dict(
intercept, self.output_names, varsizes
)
intercept = {key: list(val) for key, val in intercept.items()}
return intercept
def __convert_array_to_dict(self, data):
"""Convert a data array into a dictionary.
:param ndarray data: data.
"""
varsizes = self.learning_set.sizes
data = [
DataConversion.array_to_dict(row, self.input_names, varsizes)
for row in data
]
data = [{key: list(val) for key, val in element.items()} for element in data]
data = DataConversion.array_to_dict(array(data), self.output_names, varsizes)
data = {key: list(val) for key, val in data.items()}
return data
