..
   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: Base | 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"`` and the Pydantic model associated with the algorithm:

   .. code-block:: python

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





.. raw:: html

    <style>
    th {
      cursor: pointer;
    }

    th, td {
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      table = document.getElementById("myTable");
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              break;
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            if (x.innerHTML.toLowerCase() < y.innerHTML.toLowerCase()) {
              shouldSwitch = true;
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            switching = true;
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      }
    }
    </script>



.. _GaussianProcessRegressor_options:

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



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


:code:`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** : *typing.Union[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** : *typing.Union[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[typing.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:`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:`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:`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`


:code:`from gemseo.settings.mlearning import MOE_Settings`

















































.. 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:`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** : *typing.Union[collections.abc.Sequence[typing.Union[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** : *typing.Optional[gemseo.algos.design_space.DesignSpace], 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** : *typing.Optional[bool], 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:`from gemseo.settings.mlearning import PCERegressor_Settings`































































































.. raw:: html

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

    <li>

**probability_space** : *<class 'gemseo.algos.parameter_space.ParameterSpace'>*

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

.. raw:: html

    </li>

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



.. raw:: html

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


    <li>

**cleaning_options** : *typing.Optional[gemseo.mlearning.regression.algos.pce_settings.CleaningOptions], 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 polynomial degree of the PCE.


By default it is set to 2.


.. raw:: html

    </li>

    <li>

**discipline** : *typing.Optional[gemseo.core.discipline.discipline.Discipline], 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>

**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>

**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>

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



.. _PolynomialRegressor_options:

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



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


:code:`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 True.


.. 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:`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[typing.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** : *typing.Optional[float], 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.Function, typing.Annotated[typing.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[typing.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:`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:`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:`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[typing.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:`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[typing.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** : *typing.Optional[float], 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[<Function.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[typing.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>