Regression algorithms¶

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Note

All the features of the wrapped libraries may not be exposed through GEMSEO.

GaussianProcessRegressor¶

Module: gemseo.mlearning.regression.algos.gpr

Required parameters

data : IODataset

The learning dataset.

Optional parameters

alpha : float | RealArray, optional

The nugget effect to regularize the model.

By default it is set to 1e-10.
bounds : __Bounds | Mapping[str, __Bounds], optional

The lower and upper bounds of the parameter length scales when kernel is None. 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.

By default it is set to ().
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
kernel : Kernel | None, optional

The kernel specifying the covariance model. If None, use a Matérn(2.5).

By default it is set to None.
n_restarts_optimizer : int, optional

The number of restarts of the optimizer.

By default it is set to 10.
optimizer : str | Callable, optional

The optimization algorithm to find the parameter length scales.

By default it is set to fmin_l_bfgs_b.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
random_state : int | None, optional

The random state passed to the random number generator. Use an integer for reproducible results.

By default it is set to 0.
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.

GradientBoostingRegressor¶

Module: gemseo.mlearning.regression.algos.gradient_boosting

Required parameters

data : IODataset

The learning dataset.

Optional parameters

input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
n_estimators : int, optional

The number of boosting stages to perform.

By default it is set to 100.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
**parameters : Any

The parameters of the machine learning algorithm.

LinearRegressor¶

Module: gemseo.mlearning.regression.algos.linreg

Required parameters

data : IODataset

The learning dataset.

Optional parameters

fit_intercept : bool, optional

Whether to fit the intercept.

By default it is set to True.
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
l2_penalty_ratio : 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.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
penalty_level : float, optional

The penalty level greater or equal to 0. If 0, there is no penalty.

By default it is set to 0.0.
random_state : int | None, optional

The random state passed to the random number generator when there is a penalty. Use an integer for reproducible results.

By default it is set to 0.
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
**parameters : float | str | bool | None

The parameters of the machine learning algorithm.

MLPRegressor¶

Module: gemseo.mlearning.regression.algos.mlp

Required parameters

data : IODataset

The learning dataset.

Optional parameters

hidden_layer_sizes : tuple[int], optional

The number of neurons per hidden layer.

By default it is set to (100,).
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
**parameters : Any

The parameters of the machine learning algorithm.

MOERegressor¶

Module: gemseo.mlearning.regression.algos.moe

Required parameters

data : IODataset

The learning dataset.

Optional parameters

hard : bool, optional

Whether clustering/classification should be hard or soft.

By default it is set to True.
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.

OTGaussianProcessRegressor¶

Module: gemseo.mlearning.regression.algos.ot_gpr

Required parameters

data : IODataset

The learning dataset.

Optional parameters

covariance_model : Iterable[CovarianceModelType] | CovarianceModelType, 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.
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
multi_start_algo_name : DOEAlgorithmName, optional

The name of the DOE algorithm for multi-start optimization of the covariance model parameters.

By default it is set to OT_OPT_LHS.
multi_start_algo_options : StrKeyMapping, optional

The options of the DOE algorithm for multi-start optimization of the covariance model parameters.

By default it is set to {}.
multi_start_n_samples : int, optional

The number of starting points for multi-start optimization of the covariance model parameters; if 0, do not use multi-start optimization.

By default it is set to 10.
optimization_space : DesignSpace | None, optional

The covariance model parameter space; the size of a variable must take into account the size of the output space.

By default it is set to None.
optimizer : 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.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
trend : Trend, optional

The name of the trend.

By default it is set to constant.
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 [MAX_SIZE_FOR_LAPACK][gemseo_mlearning.regression.ot_gpr.OTGaussianProcessRegressor.MAX_SIZE_FOR_LAPACK].

By default it is set to None.

PCERegressor¶

Module: gemseo.mlearning.regression.algos.pce

Required parameters

data : IODataset | None

The learning dataset required in the case of the least-squares regression or when discipline is None in the case of quadrature.
probability_space : ParameterSpace

The set of random input variables defined by OTDistribution instances.

Optional parameters

cleaning_options : CleaningOptions | None, optional

The options of the `CleaningStrategy`_. If None, use DEFAULT_CLEANING_OPTIONS.

By default it is set to None.
degree : int, optional

The polynomial degree of the PCE.

By default it is set to 2.
discipline : MDODiscipline | None, optional

The discipline to be sampled if use_quadrature is True and data is None.

By default it is set to None.
hyperbolic_parameter : float, optional

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

By default it is set to 1.0.
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
n_quadrature_points : int, optional

The total number of quadrature points used by the quadrature strategy to compute the marginal number of points by input dimension when discipline is not None. If 0, use \((1+P)^d\) points, where \(d\) is the dimension of the input space and \(P\) is the polynomial degree of the PCE.

By default it is set to 0.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
use_cleaning : bool, optional

Whether to use the `CleaningStrategy`_ algorithm. Otherwise, use a fixed truncation strategy (`FixedStrategy`_).

By default it is set to False.
use_lars : bool, optional

Whether to use the `LARS`_ algorithm in the case of the least-squares regression.

By default it is set to False.
use_quadrature : bool, optional

Whether to estimate the coefficients of the PCE by a quadrature rule; 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.

PolynomialRegressor¶

Module: gemseo.mlearning.regression.algos.polyreg

Required parameters

data : IODataset

The learning dataset.
degree : int

The polynomial degree.

Optional parameters

fit_intercept : bool, optional

Whether to fit the intercept.

By default it is set to True.
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
l2_penalty_ratio : float, optional

The 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.

By default it is set to 1.0.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
penalty_level : float, optional

The penalty level greater or equal to 0. If 0, there is no penalty.

By default it is set to 0.0.
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
**parameters : float | str | bool | None

The parameters of the machine learning algorithm.

RBFRegressor¶

Module: gemseo.mlearning.regression.algos.rbf

Required parameters

data : IODataset

The learning dataset.

Optional parameters

der_function : Callable[[RealArray], RealArray] | 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(\(r\)), der_function(\(x\), \(|x|\), \(\epsilon\)) shall return \(\epsilon^{-1} x/|x| f'(|x|/\epsilon)\).

By default it is set to None.
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.
function : Function | Callable[[float, float], float], optional

The radial basis function taking a radius \(r\) as input, representing a distance between two points. If it is a string, then it must be one of the following:
- "multiquadric" for \(\sqrt{(r/\epsilon)^2 + 1}\),
- "inverse" for \(1/\sqrt{(r/\epsilon)^2 + 1}\),
- "gaussian" for \(\exp(-(r/\epsilon)^2)\),
- "linear" for \(r\),
- "cubic" for \(r^3\),
- "quintic" for \(r^5\),
- "thin_plate" for \(r^2\log(r)\).
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.
input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
norm : str | Callable[[RealArray, RealArray], float], optional

The distance metric to be used, either a distance function name known by SciPy or a function that computes the distance between two points.

By default it is set to euclidean.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
smooth : float, optional

The degree of smoothness, 0 involving an interpolation of the learning points.

By default it is set to 0.0.
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.

RandomForestRegressor¶

Module: gemseo.mlearning.regression.algos.random_forest

Required parameters

data : IODataset

The learning dataset.

Optional parameters

input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
n_estimators : int, optional

The number of trees in the forest.

By default it is set to 100.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
random_state : int | None, optional

The random state passed to the random number generator. Use an integer for reproducible results.

By default it is set to 0.
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.

RegressorChain¶

Module: gemseo.mlearning.regression.algos.regressor_chain

Required parameters

data : IODataset

The learning dataset.

Optional parameters

input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
**parameters : Any

The parameters of the machine learning algorithm.

SVMRegressor¶

Module: gemseo.mlearning.regression.algos.svm

Required parameters

data : IODataset

The learning dataset.

Optional parameters

input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
kernel : str, optional

The kernel type to be used.

By default it is set to rbf.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.
**parameters : Any

The parameters of the machine learning algorithm.

TPSRegressor¶

Module: gemseo.mlearning.regression.algos.thin_plate_spline

Required parameters

data : IODataset

The learning dataset.

Optional parameters

input_names : Iterable[str], optional

The names of the input variables. If empty, consider all the input variables of the learning dataset.

By default it is set to ().
norm : str | Callable[[NumberArray, NumberArray], float], optional

The distance metric to be used, either a distance function name known by SciPy or a function that computes the distance between two points.

By default it is set to euclidean.
output_names : Iterable[str], optional

The names of the output variables. If empty, consider all the output variables of the learning dataset.

By default it is set to ().
smooth : float, optional

The degree of smoothness, 0 involving an interpolation of the learning points.

By default it is set to 0.0.
transformer : TransformerType, optional

The strategies to transform the variables. The values are instances of 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 BaseTransformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.