..
   Copyright 2021 IRT Saint-Exupéry, https://www.irt-saintexupery.com

   This work is licensed under the Creative Commons Attribution-ShareAlike 4.0
   International License. To view a copy of this license, visit
   http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative
   Commons, PO Box 1866, Mountain View, CA 94042, USA.

.. _gen_regression_algos:

Regression algorithms
=====================

.. warning::
   Some capabilities may require the :ref:`installation <installation>` of |g| with :ref:`all its features <dependencies>`
   and some others may depend on :ref:`plugins <plugins>`.

.. warning::
   All the features of the wrapped libraries may not be exposed through |g|.


.. note::
   The algorithm settings can be passed to a function of the form

   .. code-block:: python

      function(..., settings_model: AlgorithmSettings | None = None, **settings: Any)

   either one by one:

   .. code-block:: python

      function(..., setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)

   or using the argument name ``"settings_model"`` and the Pydantic model associated with the algorithm:

   .. code-block:: python

      settings_model = AlgorithmSettings(setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)
      function(..., settings_model=settings_model)








.. _FCERegressor_options:

FCERegressor
------------



Module: :class:`gemseo.mlearning.regression.algos.fce`




.. code-block:: python
   :caption: Pydantic model of the settings for FCERegressor

   from gemseo.settings.mlearning import FCERegressor_Settings








































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**basis** : *<enum 'OrthonormalFunctionBasis'>, optional*

The orthonormal function basis.


By default it is set to Polynomial.


.. raw:: html

    </li>

    <li>

**degree** : *<class 'int'>, optional*

The maximum total degree of the FCE.


By default it is set to 2.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**learn_jacobian_data** : *<class 'bool'>, optional*

Whether to learn the Jacobian data from training dataset.

The training dataset cannot contain both Jacobian data and special Jacobian data.

The options ``learn_jacobian_data`` and ``use_special_jacobian_data``
 are not compatible.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**linear_model_fitter_settings** : *gemseo.mlearning.linear_model_fitting.base_linear_model_fitter_settings.BaseLinearModelFitter_Settings | None, optional*

The settings of the linear solver.
If ``None``, use the default :class:`.OrthogonalMatchingPursuit_Settings`.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**use_special_jacobian_data** : *<class 'bool'>, optional*

Whether to use the special Jacobian data from training dataset.

Special Jacobian data are samples of partial derivatives
with respect to variables that are not inputs of the FCE.

The training dataset cannot contain both Jacobian data and special Jacobian data.

The options ``use_special_jacobian_data`` and ``learn_jacobian_data``
 are not compatible.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _GaussianProcessRegressor_options:

GaussianProcessRegressor
------------------------



Module: :class:`gemseo.mlearning.regression.algos.gpr`




.. code-block:: python
   :caption: Pydantic model of the settings for GaussianProcessRegressor

   from gemseo.settings.mlearning import GaussianProcessRegressor_Settings














































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**alpha** : *float | gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]], optional*

The nugget effect to regularize the model.


By default it is set to 1e-10.


.. raw:: html

    </li>

    <li>

**bounds** : *tuple | tuple[float, float] | collections.abc.Mapping[str, tuple[float, float]], optional*

The lower and upper bounds of the length scales.

Either a unique lower-upper pair common to all the inputs
or lower-upper pairs for some of them.
When ``bounds`` is empty or when an input has no pair,
the lower bound is 0.01 and the upper bound is 100.

This argument is ignored when ``kernel`` is ``None``.


By default it is set to ().


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**kernel** : *typing.Optional[typing.Annotated[sklearn.gaussian_process.kernels.Kernel, WithJsonSchema(json_schema={}, mode=None)]], optional*

The kernel specifying the covariance model.

If ``None``, use a Matérn(2.5).


By default it is set to None.


.. raw:: html

    </li>

    <li>

**n_restarts_optimizer** : *<class 'int'>, optional*

The number of restarts of the optimizer.


By default it is set to 10.


.. raw:: html

    </li>

    <li>

**optimizer** : *typing.Union[str, typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional*

The optimization algorithm to find the parameter length scales.


By default it is set to fmin_l_bfgs_b.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**random_state** : *typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional*

The random state parameter.

If ``None``, use the global random state instance from ``numpy.random``.
Creating the model multiple times will produce different results.
If ``int``, use a new random number generator seeded by this integer.
This will produce the same results.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _GradientBoostingRegressor_options:

GradientBoostingRegressor
-------------------------



Module: :class:`gemseo.mlearning.regression.algos.gradient_boosting`




.. code-block:: python
   :caption: Pydantic model of the settings for GradientBoostingRegressor

   from gemseo.settings.mlearning import GradientBoostingRegressor_Settings
















































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**n_estimators** : *<class 'int'>, optional*

The number of boosting stages to perform.


By default it is set to 100.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _LinearRegressor_options:

LinearRegressor
---------------



Module: :class:`gemseo.mlearning.regression.algos.linreg`




.. code-block:: python
   :caption: Pydantic model of the settings for LinearRegressor

   from gemseo.settings.mlearning import LinearRegressor_Settings


































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**fit_intercept** : *<class 'bool'>, optional*

Whether to fit the intercept.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**l2_penalty_ratio** : *<class 'float'>, optional*

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.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**penalty_level** : *<class 'float'>, optional*

The penalty level greater or equal to 0.

If zero, there is no penalty.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**random_state** : *typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional*

The random state parameter in the case of a penalty.

If ``None``, use the global random state instance from ``numpy.random``.
Creating the model multiple times will produce different results.
If ``int``, use a new random number generator seeded by this integer.
This will produce the same results.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _MLPRegressor_options:

MLPRegressor
------------



Module: :class:`gemseo.mlearning.regression.algos.mlp`




.. code-block:: python
   :caption: Pydantic model of the settings for MLPRegressor

   from gemseo.settings.mlearning import MLPRegressor_Settings






















































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**hidden_layer_sizes** : *tuple[typing.Annotated[int, Gt(gt=0)], ...], optional*

The number of neurons per hidden layer.


By default it is set to (100,).


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**random_state** : *typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional*

The random state parameter.

If ``None``, use the global random state instance from ``numpy.random``.
Creating the model multiple times will produce different results.
If ``int``, use a new random number generator seeded by this integer.
This will produce the same results.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _MOERegressor_options:

MOERegressor
------------



Module: :class:`gemseo.mlearning.regression.algos.moe`


















































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**hard** : *<class 'bool'>, optional*

Whether to use a hard classification.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _OTGaussianProcessRegressor_options:

OTGaussianProcessRegressor
--------------------------



Module: :class:`gemseo.mlearning.regression.algos.ot_gpr`




.. code-block:: python
   :caption: Pydantic model of the settings for OTGaussianProcessRegressor

   from gemseo.settings.mlearning import OTGaussianProcessRegressor_Settings


























































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**covariance_model** : *collections.abc.Sequence[openturns.statistics.CovarianceModelImplementation | type[openturns.statistics.CovarianceModelImplementation] | gemseo.mlearning.regression.algos.ot_gpr_settings.CovarianceModel] | openturns.statistics.CovarianceModelImplementation | type[openturns.statistics.CovarianceModelImplementation] | gemseo.mlearning.regression.algos.ot_gpr_settings.CovarianceModel, optional*

The covariance model of the Gaussian process.

Either an OpenTURNS covariance model class,
an OpenTURNS covariance model class instance,
a name of covariance model,
or a list of OpenTURNS covariance model classes,
OpenTURNS class instances and covariance model names,
whose size is equal to the output dimension.


By default it is set to Matern52.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**multi_start_algo_name** : *<enum 'DOEAlgorithmName'>, optional*

The name of the DOE algorithm.

This DOE is used for the multi-start optimization
of the covariance model parameters.


By default it is set to OT_OPT_LHS.


.. raw:: html

    </li>

    <li>

**multi_start_algo_settings** : *collections.abc.Mapping[str, typing.Any], optional*

The settings of the DOE algorithm.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**multi_start_n_samples** : *<class 'int'>, optional*

The number of starting points of the multi-start optimizer.

This optimizer is used for the covariance model parameters.


By default it is set to 10.


.. raw:: html

    </li>

    <li>

**optimization_space** : *gemseo.algos.design_space.DesignSpace | None, optional*

The covariance model parameter space.

The size of a variable must take into account the size of the output space.
If ``None``,
the algorithm will use a design space with bounds defined by OpenTURNS.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**optimizer** : *<class 'openturns.optim.OptimizationAlgorithmImplementation'>, optional*

The solver used to optimize the covariance model parameters.


By default it is set to class=TNC class=OptimizationAlgorithmImplementation problem=class=OptimizationProblem implementation=class=OptimizationProblemImplementation objective=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[] evaluationImplementation=class=NoEvaluation name=Unnamed gradientImplementation=class=NoGradient name=Unnamed hessianImplementation=class=NoHessian name=Unnamed equality constraint=none inequality constraint=none bounds=none minimization=true dimension=0 startingPoint=class=Point name=Unnamed dimension=0 values=[] maximumIterationNumber=100 maximumCallsNumber=1000 maximumAbsoluteError=1e-05 maximumRelativeError=1e-05 maximumResidualError=1e-05 maximumConstraintError=1e-05 scale=class=Point name=Unnamed dimension=0 values=[] offset=class=Point name=Unnamed dimension=0 values=[] maxCGit=50 eta=0.25 stepmx=10 accuracy=0.0001 fmin=1 rescale=1.3.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**trend** : *<enum 'Trend'>, optional*

The name of the trend.


By default it is set to constant.


.. raw:: html

    </li>

    <li>

**use_hmat** : *bool | None, optional*

Whether to use the HMAT or LAPACK as linear algebra method.

If ``None``,
use HMAT when the learning size is greater than
:attr:`~.OTGaussianProcessRegressor.MAX_SIZE_FOR_LAPACK`.


By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PCERegressor_options:

PCERegressor
------------



Module: :class:`gemseo.mlearning.regression.algos.pce`




.. code-block:: python
   :caption: Pydantic model of the settings for PCERegressor

   from gemseo.settings.mlearning import PCERegressor_Settings












































































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**cleaning_options** : *gemseo.mlearning.regression.algos.pce_settings.CleaningOptions | None, optional*

The options of the `CleaningStrategy`_.

        If ``None``, use :attr:`.DEFAULT_CLEANING_OPTIONS`.
        


By default it is set to None.


.. raw:: html

    </li>

    <li>

**degree** : *<class 'int'>, optional*

The maximum total degree of the FCE.


By default it is set to 2.


.. raw:: html

    </li>

    <li>

**discipline** : *gemseo.core.discipline.discipline.Discipline | None, optional*

The discipline to be sampled.

Used only when ``use_quadrature`` is ``True`` and ``data`` is ``None``.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**hyperbolic_parameter** : *<class 'float'>, optional*

The :math:`q`-quasi norm parameter of the `hyperbolic and
anisotropic enumerate function`_, defined over the interval:math:`]0,1]`.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**learn_jacobian_data** : *<class 'bool'>, optional*

Whether to learn the Jacobian data from training dataset.

The training dataset cannot contain both Jacobian data and special Jacobian data.

The options ``learn_jacobian_data`` and ``use_special_jacobian_data``
 are not compatible.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**n_quadrature_points** : *<class 'int'>, optional*

The total number of quadrature points.

These points are used
to compute the marginal number of points by input dimension
when ``discipline`` is not ``None``.
If ``0``, use :math:`(1+P)^d` points,
where :math:`d` is the dimension of the input space
and :math:`P` is the polynomial degree of the PCE.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**probability_space** : *gemseo.algos.parameter_space.ParameterSpace | None, optional*

The random input variables using :class:`.OTDistribution`.

If ``None``,
:class:`.PCERegressor` uses ``data.misc["input_space"]``
where ``data`` is the :class:`.IODataset` passed at instantiation.



By default it is set to None.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**use_cleaning** : *<class 'bool'>, optional*

Whether to use the `CleaningStrategy`_ algorithm.

Otherwise,
use a fixed truncation strategy (`FixedStrategy`_).


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_lars** : *<class 'bool'>, optional*

Whether to use the `LARS`_ algorithm.

This argument is ignored when ``use_quadrature`` is ``True``.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_quadrature** : *<class 'bool'>, optional*

Whether to estimate the coefficients of the PCE by quadrature.

If so,
use the quadrature points stored in ``data`` or sample ``discipline``.
Otherwise,
estimate the coefficients by least-squares regression.


By default it is set to False.


.. raw:: html

    </li>

    <li>

**use_special_jacobian_data** : *<class 'bool'>, optional*

Whether to use the special Jacobian data from training dataset.

Special Jacobian data are samples of partial derivatives
with respect to variables that are not inputs of the FCE.

The training dataset cannot contain both Jacobian data and special Jacobian data.

The options ``use_special_jacobian_data`` and ``learn_jacobian_data``
 are not compatible.


By default it is set to False.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _PolynomialRegressor_options:

PolynomialRegressor
-------------------



Module: :class:`gemseo.mlearning.regression.algos.polyreg`




.. code-block:: python
   :caption: Pydantic model of the settings for PolynomialRegressor

   from gemseo.settings.mlearning import PolynomialRegressor_Settings








































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**degree** : *<class 'int'>, optional*

The polynomial degree.


By default it is set to 2.


.. raw:: html

    </li>

    <li>

**fit_intercept** : *<class 'bool'>, optional*

Whether to fit the intercept.


By default it is set to True.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**l2_penalty_ratio** : *<class 'float'>, optional*

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.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**penalty_level** : *<class 'float'>, optional*

The penalty level greater or equal to 0.

If zero, there is no penalty.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**random_state** : *typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional*

The random state parameter in the case of a penalty.

If ``None``, use the global random state instance from ``numpy.random``.
Creating the model multiple times will produce different results.
If ``int``, use a new random number generator seeded by this integer.
This will produce the same results.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _RBFRegressor_options:

RBFRegressor
------------



Module: :class:`gemseo.mlearning.regression.algos.rbf`




.. code-block:: python
   :caption: Pydantic model of the settings for RBFRegressor

   from gemseo.settings.mlearning import RBFRegressor_Settings








































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**der_function** : *typing.Optional[typing.Annotated[collections.abc.Callable[[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], WithJsonSchema(json_schema={}, mode=None)]], optional*

The derivative of the radial basis function.

Only to be provided if ``function`` is a callable
and if the use of the model with its derivative is required.
If ``None`` and if ``function`` is a callable,
an error will be raised.
If ``None`` and if ``function`` is a string,
the class will look for its internal implementation
and will raise an error if it is missing.
The ``der_function`` shall take three arguments
(``input_data``, ``norm_input_data``, ``eps``).
For an RBF of the form function(:math:`r`),
der_function(:math:`x`, :math:`|x|`, :math:`\epsilon`) shall
return :math:`\epsilon^{-1} x/|x| f'(|x|/\epsilon)`.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**epsilon** : *float | None, optional*

An adjustable constant for Gaussian or multiquadric functions.

If ``None``, use the average distance between input data.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**function** : *typing.Union[gemseo.mlearning.regression.algos.rbf_settings.RBF, typing.Annotated[collections.abc.Callable[[float, float], float], WithJsonSchema(json_schema={}, mode=None)]], optional*

The radial basis function.

This function takes a radius :math:`r` as input,
representing a distance between two points.
If it is a string,
then it must be one of the following:

- ``"multiquadric"`` for :math:`\sqrt{(r/\epsilon)^2 + 1}`,
- ``"inverse"`` for :math:`1/\sqrt{(r/\epsilon)^2 + 1}`,
- ``"gaussian"`` for :math:`\exp(-(r/\epsilon)^2)`,
- ``"linear"`` for :math:`r`,
- ``"cubic"`` for :math:`r^3`,
- ``"quintic"`` for :math:`r^5`,
- ``"thin_plate"`` for :math:`r^2\log(r)`.

If it is a callable,
then it must take the two arguments ``self`` and ``r`` as inputs,
e.g. ``lambda self, r: sqrt((r/self.epsilon)**2 + 1)``
for the multiquadric function.
The epsilon parameter will be available as ``self.epsilon``.
Other keyword arguments passed in will be available as well.


By default it is set to multiquadric.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**norm** : *typing.Union[str, typing.Annotated[collections.abc.Callable[[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], float], WithJsonSchema(json_schema={}, mode=None)]], optional*

The distance metric.

Either a distance function name `known by SciPy
<https://docs.scipy.org/doc/scipy/reference/generated/
scipy.spatial.distance.cdist.html>`_
or a function that computes the distance between two points.


By default it is set to euclidean.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**smooth** : *<class 'float'>, optional*

The degree of smoothness.

``0`` involves an interpolation of the learning points.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _RandomForestRegressor_options:

RandomForestRegressor
---------------------



Module: :class:`gemseo.mlearning.regression.algos.random_forest`




.. code-block:: python
   :caption: Pydantic model of the settings for RandomForestRegressor

   from gemseo.settings.mlearning import RandomForestRegressor_Settings






















































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**n_estimators** : *<class 'int'>, optional*

The number of trees in the forest.


By default it is set to 100.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**random_state** : *typing.Optional[typing.Annotated[int, Ge(ge=0)]], optional*

The random state parameter.

If ``None``, use the global random state instance from ``numpy.random``.
Creating the model multiple times will produce different results.
If ``int``, use a new random number generator seeded by this integer.
This will produce the same results.


By default it is set to 0.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _RegressorChain_options:

RegressorChain
--------------



Module: :class:`gemseo.mlearning.regression.algos.regressor_chain`




.. code-block:: python
   :caption: Pydantic model of the settings for RegressorChain

   from gemseo.settings.mlearning import RegressorChain_Settings










































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SVMRegressor_options:

SVMRegressor
------------



Module: :class:`gemseo.mlearning.regression.algos.svm`




.. code-block:: python
   :caption: Pydantic model of the settings for SVMRegressor

   from gemseo.settings.mlearning import SVMRegressor_Settings
















































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**kernel** : *typing.Union[str, typing.Annotated[collections.abc.Callable, WithJsonSchema(json_schema={}, mode=None)]], optional*

The name of the kernel or a callable for the SVM.

Examples of names: "linear", "poly", "rbf", "sigmoid", "precomputed".


By default it is set to rbf.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _TPSRegressor_options:

TPSRegressor
------------



Module: :class:`gemseo.mlearning.regression.algos.thin_plate_spline`




.. code-block:: python
   :caption: Pydantic model of the settings for TPSRegressor

   from gemseo.settings.mlearning import TPSRegressor_Settings








































































.. raw:: html

    <dl class="field-list simple">
    <dt class="field-odd">Optional settings</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**der_function** : *typing.Optional[typing.Annotated[collections.abc.Callable[[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], WithJsonSchema(json_schema={}, mode=None)]], optional*

The derivative of the radial basis function.

Only to be provided if ``function`` is a callable
and if the use of the model with its derivative is required.
If ``None`` and if ``function`` is a callable,
an error will be raised.
If ``None`` and if ``function`` is a string,
the class will look for its internal implementation
and will raise an error if it is missing.
The ``der_function`` shall take three arguments
(``input_data``, ``norm_input_data``, ``eps``).
For an RBF of the form function(:math:`r`),
der_function(:math:`x`, :math:`|x|`, :math:`\epsilon`) shall
return :math:`\epsilon^{-1} x/|x| f'(|x|/\epsilon)`.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**epsilon** : *float | None, optional*

An adjustable constant for Gaussian or multiquadric functions.

If ``None``, use the average distance between input data.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**function** : *typing.Literal[<RBF.THIN_PLATE: 'thin_plate'>], optional*

The thin plate radial basis function for :math:`r^2\log(r)`.


By default it is set to thin_plate.


.. raw:: html

    </li>

    <li>

**input_names** : *collections.abc.Sequence[str], optional*

The names of the input variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**norm** : *typing.Union[str, typing.Annotated[collections.abc.Callable[[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], float], WithJsonSchema(json_schema={}, mode=None)]], optional*

The distance metric.

Either a distance function name `known by SciPy
<https://docs.scipy.org/doc/scipy/reference/generated/
scipy.spatial.distance.cdist.html>`_
or a function that computes the distance between two points.


By default it is set to euclidean.


.. raw:: html

    </li>

    <li>

**output_names** : *collections.abc.Sequence[str], optional*

The names of the output variables


By default it is set to ().


.. raw:: html

    </li>

    <li>

**parameters** : *collections.abc.Mapping[str, typing.Any], optional*

Other parameters.


By default it is set to {}.


.. raw:: html

    </li>

    <li>

**smooth** : *<class 'float'>, optional*

The degree of smoothness.

``0`` involves an interpolation of the learning points.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**transformer** : *collections.abc.Mapping[str, typing.Any], optional*

The strategies to transform the variables.

The values are instances of :class:`.BaseTransformer`
while the keys are the names of
either the variables
or the groups of variables,
e.g. ``"inputs"`` or ``"outputs"``
in the case of the regression algorithms.
If a group is specified,
the :class:`.BaseTransformer` will be applied
to all the variables of this group.
If :attr:`.IDENTITY`, do not transform the variables.


By default it is set to {}.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>