Regression models options¶

GaussianProcessRegression¶

class gemseo.mlearning.regression.gpr.GaussianProcessRegression(data, transformer=None, input_names=None, output_names=None, kernel=None, alpha=1e-10, optimizer='fmin_l_bfgs_b', n_restarts_optimizer=10, random_state=None)[source]

Gaussian process regression.

Parameters

kernel (Optional[openturns.CovarianceModel]) – The kernel function. If None, use a Matern(2.5).
alpha (Union[float,ndarray]) – The nugget effect to regularize the model.
optimizer (Union[str,Callable]) – The optimization algorithm to find the hyperparameters.
n_restarts_optimizer (int) – The number of restarts of the optimizer.
random_state (Optional[int]) – The seed used to initialize the centers. If None, the random number generator is the RandomState instance used by numpy.random.
data (Dataset) –
transformer (Optional[TransformerType]) –
input_names (Optional[Iterable[str]]) –
output_names (Optional[Iterable[str]]) –

Return type

None

Classes:

DataFormatters()

Machine learning regression model decorators.

Attributes:

`input_data`	The input data matrix.
`input_shape`	The dimension of the input variables before applying the transformers.
`is_trained`	Return whether the algorithm is trained.
`output_data`	The output data matrix.
`output_shape`	The dimension of the output variables before applying the transformers.

Methods:

`learn`([samples])	Train the machine learning algorithm from the learning dataset.
`load_algo`(directory)	Load a machine learning algorithm from a directory.
`predict`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_jacobian`(input_data, args, *kwargs)	Evaluate ‘predict_jac’ with either array or dictionary-based data.
`predict_raw`(input_data)	Predict output data from input data.
`predict_std`(input_data)	Predict the standard deviation from input data.
`save`([directory, path, save_learning_set])	Save the machine learning algorithm.

class DataFormatters

Machine learning regression model decorators.

Methods:

`format_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_dict_jacobian`(predict_jac)	Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
`format_input_output`(predict)	Make a function robust to type, array shape and data transformation.
`format_samples`(predict)	Make a 2D NumPy array-based function work with 1D NumPy array.
`format_transform`([transform_inputs, …])	Force a function to transform its input and/or output variables.
`transform_jacobian`(predict_jac)	Apply transformation to inputs and inverse transformation to outputs.

classmethod format_dict(predict)

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_dict_jacobian(predict_jac)

Wrap an array-based function to make it callable with a dictionary of NumPy arrays.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)

Make a function robust to type, array shape and data transformation.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
Returns: A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)

Force a function to transform its input and/or output variables.

Parameters

transform_inputs (bool) – If True, apply the transformers to the input variables.
transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod transform_jacobian(predict_jac)

Apply transformation to inputs and inverse transformation to outputs.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

property input_data: The input data matrix.

property input_shape: The dimension of the input variables before applying the transformers.

property is_trained: Return whether the algorithm is trained.

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters: samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.
Raises: NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.
Return type: None

load_algo(directory)

Load a machine learning algorithm from a directory.

Parameters: directory (str) – The path to the directory where the machine learning algorithm is saved.
Return type: None

property output_data: The output data matrix.

property output_shape: The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_jacobian(input_data, *args, **kwargs)

Evaluate ‘predict_jac’ with either array or dictionary-based data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict_jac’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.

Returns

The output data with the same type as the input one.

predict_raw(input_data)

Predict output data from input data.

Parameters: input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
Returns: The predicted output data with shape (n_samples, n_outputs).
Return type: numpy.ndarray

predict_std(input_data)[source]

Predict the standard deviation from input data.

Parameters: input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data with shape (n_samples, n_inputs).
Returns: The output data with shape (n_samples, n_outputs).
Return type: output_data

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters

directory (Optional[str]) – The name of the directory to save the algorithm.
path (str) – The path to parent directory where to create the directory.
save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str

LinearRegression¶

class gemseo.mlearning.regression.linreg.LinearRegression(data, transformer=None, input_names=None, output_names=None, fit_intercept=True, penalty_level=0.0, l2_penalty_ratio=1.0, **parameters)[source]

Linear regression.

Attributes

learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.

Parameters

data (Dataset) –
transformer (Optional[TransformerType]) –
input_names (Optional[Iterable[str]]) –
output_names (Optional[Iterable[str]]) –
fit_intercept (bool) –
penalty_level (float) –
l2_penalty_ratio (float) –
parameters (Optional[Union[float,int,str,bool]]) –

Return type

None

Parameters: input_names: The names of the input variables.

If None, consider all input variables mentioned in the learning dataset.

output_names: The names of the output variables.: If None, consider all input variables mentioned in the learning dataset.

fit_intercept: If True, fit intercept. penalty_level: The penalty level greater or equal to 0.

If 0, there is no penalty.

l2_penalty_ratio: The penalty ratio related to the l2 regularization.: If 1, use the Ridge penalty. If 0, use the Lasso penalty. Between 0 and 1, use the ElasticNet penalty.

**parameters: The parameters of the machine learning algorithm.

Classes:

DataFormatters()

Machine learning regression model decorators.

Attributes:

`coefficients`	The regression coefficients of the linear model.
`input_data`	The input data matrix.
`input_shape`	The dimension of the input variables before applying the transformers.
`intercept`	The regression intercepts of the linear model.
`is_trained`	Return whether the algorithm is trained.
`output_data`	The output data matrix.
`output_shape`	The dimension of the output variables before applying the transformers.

Methods:

`get_coefficients`([as_dict])	Return the regression coefficients of the linear model.
`get_intercept`([as_dict])	Return the regression intercepts of the linear model.
`learn`([samples])	Train the machine learning algorithm from the learning dataset.
`load_algo`(directory)	Load a machine learning algorithm from a directory.
`predict`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_jacobian`(input_data, args, *kwargs)	Evaluate ‘predict_jac’ with either array or dictionary-based data.
`predict_raw`(input_data)	Predict output data from input data.
`save`([directory, path, save_learning_set])	Save the machine learning algorithm.

class DataFormatters

Machine learning regression model decorators.

Methods:

`format_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_dict_jacobian`(predict_jac)	Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
`format_input_output`(predict)	Make a function robust to type, array shape and data transformation.
`format_samples`(predict)	Make a 2D NumPy array-based function work with 1D NumPy array.
`format_transform`([transform_inputs, …])	Force a function to transform its input and/or output variables.
`transform_jacobian`(predict_jac)	Apply transformation to inputs and inverse transformation to outputs.

classmethod format_dict(predict)

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_dict_jacobian(predict_jac)

Wrap an array-based function to make it callable with a dictionary of NumPy arrays.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)

Make a function robust to type, array shape and data transformation.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
Returns: A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)

Force a function to transform its input and/or output variables.

Parameters

transform_inputs (bool) – If True, apply the transformers to the input variables.
transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod transform_jacobian(predict_jac)

Apply transformation to inputs and inverse transformation to outputs.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

property coefficients: The regression coefficients of the linear model.

get_coefficients(as_dict=True)[source]

Return the regression coefficients of the linear model.

Parameters: as_dict (bool) – If True, return the coefficients as a dictionary. Otherwise, return the coefficients as a numpy.array
Returns: The regression coefficients of the linear model.
Raises: ValueError – If the coefficients are required as a dictionary even though the transformers change the variables dimensions.
Return type: Union[numpy.ndarray, Dict[str, numpy.ndarray]]

get_intercept(as_dict=True)[source]

Return the regression intercepts of the linear model.

Parameters: as_dict (bool) – If True, return the intercepts as a dictionary. Otherwise, return the intercepts as a numpy.array
Returns: The regression intercepts of the linear model.
Raises: ValueError – If the coefficients are required as a dictionary even though the transformers change the variables dimensions.
Return type: Union[numpy.ndarray, Dict[str, numpy.ndarray]]

property input_data: The input data matrix.

property input_shape: The dimension of the input variables before applying the transformers.

property intercept: The regression intercepts of the linear model.

property is_trained: Return whether the algorithm is trained.

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters: samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.
Raises: NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.
Return type: None

load_algo(directory)

Load a machine learning algorithm from a directory.

Parameters: directory (str) – The path to the directory where the machine learning algorithm is saved.
Return type: None

property output_data: The output data matrix.

property output_shape: The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_jacobian(input_data, *args, **kwargs)

Evaluate ‘predict_jac’ with either array or dictionary-based data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict_jac’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.

Returns

The output data with the same type as the input one.

predict_raw(input_data)

Predict output data from input data.

Parameters: input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
Returns: The predicted output data with shape (n_samples, n_outputs).
Return type: numpy.ndarray

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters

directory (Optional[str]) – The name of the directory to save the algorithm.
path (str) – The path to parent directory where to create the directory.
save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str

MixtureOfExperts¶

class gemseo.mlearning.regression.moe.MixtureOfExperts(data, transformer=None, input_names=None, output_names=None, hard=True)[source]

Mixture of experts regression.

Attributes

learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
hard (bool) – Whether clustering/classification should be hard or soft.
cluster_algo (str) – The name of the clustering algorithm.
classif_algo (str) – The name of the classification algorithm.
regress_algo (str) – The name of the regression algorithm.
cluster_params (Optional[MLAlgoParameterType]) – The parameters of the clustering algorithm.
classif_params (Optional[MLAlgoParameterType]) – The parameters of the classification algorithm.
regress_params (Optional[MLAlgoParameterType]) – The parameters of the regression algorithm.
cluster_measure (Dict[str,Union[str,EvalOptionType]]) – The quality measure for the clustering algorithms.
classif_measure (Dict[str,Union[str,EvalOptionType]]) – The quality measure for the classification algorithms.
regress_measure (Dict[str,Union[str,EvalOptionType]]) – The quality measure for the regression algorithms.
cluster_cands (List[MLAlgoType]) – The clustering algorithm candidates.
classif_cands (List[MLAlgoType]) – The classification algorithm candidates.
regress_cands (List[MLAlgoType]) – The regression algorithm candidates.
clusterer (MLClusteringAlgo) – The clustering algorithm.
classifier (MLClassificationAlgo) – The classification algorithm.
regress_models (List(MLRegressionAlgo)) – The regression algorithms.

Parameters

hard (bool) – Whether clustering/classification should be hard or soft.
data (Dataset) –
transformer (Optional[TransformerType]) –
input_names (Optional[Iterable[str]]) –
output_names (Optional[Iterable[str]]) –

Return type

None

Classes:

DataFormatters()

Machine learning regression model decorators.

Methods:

`add_classifier_candidate`(name[, …])	Add a candidate for classification.
`add_clusterer_candidate`(name[, calib_space, …])	Add a candidate for clustering.
`add_regressor_candidate`(name[, calib_space, …])	Add a candidate for regression.
`learn`([samples])	Train the machine learning algorithm from the learning dataset.
`load_algo`(directory)	Load a machine learning algorithm from a directory.
`predict`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_class`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_jacobian`(input_data, args, *kwargs)	Evaluate ‘predict_jac’ with either array or dictionary-based data.
`predict_local_model`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_raw`(input_data)	Predict output data from input data.
`save`([directory, path, save_learning_set])	Save the machine learning algorithm.
`set_classification_measure`(measure, …)	Set the quality measure for the classification algorithms.
`set_classifier`(classif_algo, **classif_params)	Set the classification algorithm.
`set_clusterer`(cluster_algo, **cluster_params)	Set the clustering algorithm.
`set_clustering_measure`(measure, **eval_options)	Set the quality measure for the clustering algorithms.
`set_regression_measure`(measure, **eval_options)	Set the quality measure for the regression algorithms.
`set_regressor`(regress_algo, **regress_params)	Set the regression algorithm.

Attributes:

`input_data`	The input data matrix.
`input_shape`	The dimension of the input variables before applying the transformers.
`is_trained`	Return whether the algorithm is trained.
`labels`	The cluster labels.
`n_clusters`	The number of clusters.
`output_data`	The output data matrix.
`output_shape`	The dimension of the output variables before applying the transformers.

class DataFormatters[source]

Machine learning regression model decorators.

Methods:

`format_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_dict_jacobian`(predict_jac)	Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
`format_input_output`(predict)	Make a function robust to type, array shape and data transformation.
`format_predict_class_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_samples`(predict)	Make a 2D NumPy array-based function work with 1D NumPy array.
`format_transform`([transform_inputs, …])	Force a function to transform its input and/or output variables.
`transform_jacobian`(predict_jac)	Apply transformation to inputs and inverse transformation to outputs.

classmethod format_dict(predict)

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_dict_jacobian(predict_jac)

Wrap an array-based function to make it callable with a dictionary of NumPy arrays.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)

Make a function robust to type, array shape and data transformation.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_predict_class_dict(predict)[source]

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
Returns: A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)

Force a function to transform its input and/or output variables.

Parameters

transform_inputs (bool) – If True, apply the transformers to the input variables.
transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod transform_jacobian(predict_jac)

Apply transformation to inputs and inverse transformation to outputs.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

add_classifier_candidate(name, calib_space=None, calib_algo=None, **option_lists)[source]

Add a candidate for classification.

Parameters

name (str) – The name of a classification algorithm.
calib_space (Optional[gemseo.algos.design_space.DesignSpace]) – The space defining the calibration variables.
calib_algo (Optional[Dict[str, Union[int, str]]]) – The name and options of the DOE or optimization algorithm, e.g. {“algo”: “fullfact”, “n_samples”: 10}). If None, do not perform calibration.
option_lists (***) – Parameters for the clustering algorithm candidate. Each parameter has to be enclosed within a list. The list may contain different values to try out for the given parameter, or only one.

Return type

None

add_clusterer_candidate(name, calib_space=None, calib_algo=None, **option_lists)[source]

Add a candidate for clustering.

Parameters

name (str) – The name of a clustering algorithm.
calib_space (Optional[gemseo.algos.design_space.DesignSpace]) – The space defining the calibration variables.
calib_algo (Optional[Dict[str, Union[int, str]]]) – The name and options of the DOE or optimization algorithm, e.g. {“algo”: “fullfact”, “n_samples”: 10}). If None, do not perform calibration.
option_lists (***) – Parameters for the clustering algorithm candidate. Each parameter has to be enclosed within a list. The list may contain different values to try out for the given parameter, or only one.

Return type

None

add_regressor_candidate(name, calib_space=None, calib_algo=None, **option_lists)[source]

Add a candidate for regression.

Parameters

name (str) – The name of a regression algorithm.
calib_space (Optional[gemseo.algos.design_space.DesignSpace]) – The space defining the calibration variables.
calib_algo (Optional[Dict[str, Union[int, str]]]) – The name and options of the DOE or optimization algorithm, e.g. {“algo”: “fullfact”, “n_samples”: 10}). If None, do not perform calibration.
option_lists (***) – Parameters for the clustering algorithm candidate. Each parameter has to be enclosed within a list. The list may contain different values to try out for the given parameter, or only one.

Return type

None

property input_data: The input data matrix.

property input_shape: The dimension of the input variables before applying the transformers.

property is_trained: Return whether the algorithm is trained.

property labels: The cluster labels.

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters: samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.
Raises: NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.
Return type: None

load_algo(directory)[source]

Load a machine learning algorithm from a directory.

Parameters: directory (str) – The path to the directory where the machine learning algorithm is saved.
Return type: None

property n_clusters: The number of clusters.

property output_data: The output data matrix.

property output_shape: The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_class(input_data, *args, **kwargs)[source]

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_jacobian(input_data, *args, **kwargs)

Evaluate ‘predict_jac’ with either array or dictionary-based data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict_jac’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.

Returns

The output data with the same type as the input one.

predict_local_model(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_raw(input_data)

Predict output data from input data.

Parameters: input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
Returns: The predicted output data with shape (n_samples, n_outputs).
Return type: numpy.ndarray

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters

directory (Optional[str]) – The name of the directory to save the algorithm.
path (str) – The path to parent directory where to create the directory.
save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str

set_classification_measure(measure, **eval_options)[source]

Set the quality measure for the classification algorithms.

Parameters

measure (gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasure) – The quality measure.
**eval_options – The options for the quality measure.
eval_options (Optional[Union[List[int], bool, int, gemseo.core.dataset.Dataset]]) –

Return type

None

set_classifier(classif_algo, **classif_params)[source]

Set the classification algorithm.

Parameters

classif_algo (str) – The name of the classification algorithm.
**classif_params – The parameters of the classification algorithm.
classif_params (Optional[Any]) –

Return type

None

set_clusterer(cluster_algo, **cluster_params)[source]

Set the clustering algorithm.

Parameters

cluster_algo (str) – The name of the clustering algorithm.
**cluster_params – The parameters of the clustering algorithm.
cluster_params (Optional[Any]) –

Return type

None

set_clustering_measure(measure, **eval_options)[source]

Set the quality measure for the clustering algorithms.

Parameters

measure (gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasure) – The quality measure.
**eval_options – The options for the quality measure.
eval_options (Optional[Union[List[int], bool, int, gemseo.core.dataset.Dataset]]) –

Return type

None

set_regression_measure(measure, **eval_options)[source]

Set the quality measure for the regression algorithms.

Parameters

measure (gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasure) – The quality measure.
**eval_options – The options for the quality measure.
eval_options (Optional[Union[List[int], bool, int, gemseo.core.dataset.Dataset]]) –

Return type

None

set_regressor(regress_algo, **regress_params)[source]

Set the regression algorithm.

Parameters

regress_algo (str) – The name of the regression algorithm.
**regress_params – The parameters of the regression algorithm.
regress_params (Optional[Any]) –

Return type

None

PCERegression¶

class gemseo.mlearning.regression.pce.PCERegression(data, probability_space, discipline=None, transformer=None, input_names=None, output_names=None, strategy='LS', degree=2, n_quad=None, stieltjes=True, sparse_param=None)[source]

Polynomial chaos expansion.

Parameters

probability_space (ParameterSpace) – The probability space defining the probability distributions of the model inputs.
discipline (Optional[MDODiscipline]) – The discipline to evaluate with the quadrature strategy if the learning set does not have output data. If None, use the output data from the learning set.
strategy (str) – The strategy to compute the parameters of the PCE, either ‘LS’ for least-square, ‘Quad’ for quadrature or ‘SparseLS’ for sparse least-square.
degree (int) – The polynomial degree of the PCE.
n_quad (Optional[int]) – The total number of quadrature points used by the quadrature strategy to compute the marginal number of points by input dimension. If None, this degree will be set equal to the polynomial degree of the PCE plus one.
stieltjes (bool) – Use the Stieltjes method.
sparse_param (Optional[Mapping[str,Union[int,float]]]) –
The parameters for the Sparse Cleaning Truncation Strategy and/or hyperbolic truncation of the initial basis:
- max_considered_terms (int) – The maximum considered terms (default: 120),
- most_significant (int) – The most Significant number to retain (default: 30),
- significance_factor (float) – Significance Factor (default: 1e-3),
- hyper_factor (float) – The factor for the hyperbolic truncation strategy (default: 1.0).
If None, use default values.
data (Dataset) –
transformer (Optional[TransformerType]) –
input_names (Optional[Iterable[str]]) –
output_names (Optional[Iterable[str]]) –

Raises

ValueError – Either if the variables of the probability space and the input variables of the dataset are different, if transformers are specified for the inputs, or if the strategy to compute the parameters of the PCE is unknown.

Return type

None

Classes:

DataFormatters()

Machine learning regression model decorators.

Attributes:

`first_sobol_indices`	The first Sobol’ indices.
`input_data`	The input data matrix.
`input_shape`	The dimension of the input variables before applying the transformers.
`is_trained`	Return whether the algorithm is trained.
`output_data`	The output data matrix.
`output_shape`	The dimension of the output variables before applying the transformers.
`total_sobol_indices`	The total Sobol’ indices.

Methods:

`learn`([samples])	Train the machine learning algorithm from the learning dataset.
`load_algo`(directory)	Load a machine learning algorithm from a directory.
`predict`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_jacobian`(input_data, args, *kwargs)	Evaluate ‘predict_jac’ with either array or dictionary-based data.
`predict_raw`(input_data)	Predict output data from input data.
`save`([directory, path, save_learning_set])	Save the machine learning algorithm.

class DataFormatters

Machine learning regression model decorators.

Methods:

`format_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_dict_jacobian`(predict_jac)	Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
`format_input_output`(predict)	Make a function robust to type, array shape and data transformation.
`format_samples`(predict)	Make a 2D NumPy array-based function work with 1D NumPy array.
`format_transform`([transform_inputs, …])	Force a function to transform its input and/or output variables.
`transform_jacobian`(predict_jac)	Apply transformation to inputs and inverse transformation to outputs.

classmethod format_dict(predict)

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_dict_jacobian(predict_jac)

Wrap an array-based function to make it callable with a dictionary of NumPy arrays.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)

Make a function robust to type, array shape and data transformation.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
Returns: A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)

Force a function to transform its input and/or output variables.

Parameters

transform_inputs (bool) – If True, apply the transformers to the input variables.
transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod transform_jacobian(predict_jac)

Apply transformation to inputs and inverse transformation to outputs.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

property first_sobol_indices: The first Sobol’ indices.

property input_data: The input data matrix.

property input_shape: The dimension of the input variables before applying the transformers.

property is_trained: Return whether the algorithm is trained.

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters: samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.
Raises: NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.
Return type: None

load_algo(directory)

Load a machine learning algorithm from a directory.

Parameters: directory (str) – The path to the directory where the machine learning algorithm is saved.
Return type: None

property output_data: The output data matrix.

property output_shape: The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_jacobian(input_data, *args, **kwargs)

Evaluate ‘predict_jac’ with either array or dictionary-based data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict_jac’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.

Returns

The output data with the same type as the input one.

predict_raw(input_data)

Predict output data from input data.

Parameters: input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
Returns: The predicted output data with shape (n_samples, n_outputs).
Return type: numpy.ndarray

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters

directory (Optional[str]) – The name of the directory to save the algorithm.
path (str) – The path to parent directory where to create the directory.
save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str

property total_sobol_indices: The total Sobol’ indices.

PolynomialRegression¶

class gemseo.mlearning.regression.polyreg.PolynomialRegression(data, degree, transformer=None, input_names=None, output_names=None, fit_intercept=True, penalty_level=0.0, l2_penalty_ratio=1.0, **parameters)[source]

Polynomial regression.

Attributes

learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.

Parameters

data (Dataset) –
degree (int) –
transformer (Optional[TransformerType]) –
input_names (Optional[Iterable[str]]) –
output_names (Optional[Iterable[str]]) –
fit_intercept (bool) –
penalty_level (float) –
l2_penalty_ratio (float) –
parameters (Optional[Union[float,int,str,bool]]) –

Return type

None

Parameters: input_names: The names of the input variables.

If None, consider all input variables mentioned in the learning dataset.

output_names: The names of the output variables.: If None, consider all input variables mentioned in the learning dataset.

fit_intercept: If True, fit intercept. penalty_level: The penalty level greater or equal to 0.

If 0, there is no penalty.

l2_penalty_ratio: The penalty ratio related to the l2 regularization.

If 1, use the Ridge penalty. If 0, use the Lasso penalty. Between 0 and 1, use the ElasticNet penalty.

**parameters: The parameters of the machine learning algorithm.

degree: The polynomial degree. fit_intercept: If True, fit intercept. penalty_level: The penalty level greater or equal to 0.

If 0, there is no penalty.

l2_penalty_ratio: The penalty ratio: related to the l2 regularization. If 1, the penalty is the Ridge penalty. If 0, this is the Lasso penalty. Between 0 and 1, the penalty is the ElasticNet penalty.

Raises

ValueError – If the degree is lower than one.

Parameters

data (Dataset) –
degree (int) –
transformer (Optional[TransformerType]) –
input_names (Optional[Iterable[str]]) –
output_names (Optional[Iterable[str]]) –
fit_intercept (bool) –
penalty_level (float) –
l2_penalty_ratio (float) –
parameters (Optional[Union[float,int,str,bool]]) –

Return type

None

Classes:

DataFormatters()

Machine learning regression model decorators.

Attributes:

`coefficients`	The regression coefficients of the linear model.
`input_data`	The input data matrix.
`input_shape`	The dimension of the input variables before applying the transformers.
`intercept`	The regression intercepts of the linear model.
`is_trained`	Return whether the algorithm is trained.
`output_data`	The output data matrix.
`output_shape`	The dimension of the output variables before applying the transformers.

Methods:

`get_coefficients`([as_dict])	Return the regression coefficients of the linear model.
`get_intercept`([as_dict])	Return the regression intercepts of the linear model.
`learn`([samples])	Train the machine learning algorithm from the learning dataset.
`load_algo`(directory)	Load a machine learning algorithm from a directory.
`predict`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_jacobian`(input_data, args, *kwargs)	Evaluate ‘predict_jac’ with either array or dictionary-based data.
`predict_raw`(input_data)	Predict output data from input data.
`save`([directory, path, save_learning_set])	Save the machine learning algorithm.

class DataFormatters

Machine learning regression model decorators.

Methods:

`format_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_dict_jacobian`(predict_jac)	Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
`format_input_output`(predict)	Make a function robust to type, array shape and data transformation.
`format_samples`(predict)	Make a 2D NumPy array-based function work with 1D NumPy array.
`format_transform`([transform_inputs, …])	Force a function to transform its input and/or output variables.
`transform_jacobian`(predict_jac)	Apply transformation to inputs and inverse transformation to outputs.

classmethod format_dict(predict)

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_dict_jacobian(predict_jac)

Wrap an array-based function to make it callable with a dictionary of NumPy arrays.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)

Make a function robust to type, array shape and data transformation.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
Returns: A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)

Force a function to transform its input and/or output variables.

Parameters

transform_inputs (bool) – If True, apply the transformers to the input variables.
transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod transform_jacobian(predict_jac)

Apply transformation to inputs and inverse transformation to outputs.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

property coefficients: The regression coefficients of the linear model.

get_coefficients(as_dict=False)[source]

Return the regression coefficients of the linear model.

Parameters

as_dict (bool) – If True, return the coefficients as a dictionary. Otherwise, return the coefficients as a numpy.array
as_dict – If True, return the coefficients as a dictionary of Numpy arrays indexed by the names of the coefficients. Otherwise, return the coefficients as a Numpy array. For now the only valid value is False.

Returns

The regression coefficients of the linear model. The regression coefficients of the linear model.

Raises

ValueError – If the coefficients are required as a dictionary even though the transformers change the variables dimensions.
NotImplementedError – If the coefficients are required as a dictionary.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

get_intercept(as_dict=True)

Return the regression intercepts of the linear model.

Parameters: as_dict (bool) – If True, return the intercepts as a dictionary. Otherwise, return the intercepts as a numpy.array
Returns: The regression intercepts of the linear model.
Raises: ValueError – If the coefficients are required as a dictionary even though the transformers change the variables dimensions.
Return type: Union[numpy.ndarray, Dict[str, numpy.ndarray]]

property input_data: The input data matrix.

property input_shape: The dimension of the input variables before applying the transformers.

property intercept: The regression intercepts of the linear model.

property is_trained: Return whether the algorithm is trained.

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters: samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.
Raises: NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.
Return type: None

load_algo(directory)[source]

Load a machine learning algorithm from a directory.

Parameters: directory (str) – The path to the directory where the machine learning algorithm is saved.
Return type: None

property output_data: The output data matrix.

property output_shape: The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_jacobian(input_data, *args, **kwargs)

Evaluate ‘predict_jac’ with either array or dictionary-based data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict_jac’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.

Returns

The output data with the same type as the input one.

predict_raw(input_data)

Predict output data from input data.

Parameters: input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
Returns: The predicted output data with shape (n_samples, n_outputs).
Return type: numpy.ndarray

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters

directory (Optional[str]) – The name of the directory to save the algorithm.
path (str) – The path to parent directory where to create the directory.
save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str

RBFRegression¶

class gemseo.mlearning.regression.rbf.RBFRegression(data, transformer=None, input_names=None, output_names=None, function='multiquadric', der_function=None, epsilon=None, **parameters)[source]

Regression based on radial basis functions.

Attributes

learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
der_function (Callable[[ndarray],ndarray]) – The derivative of the radial basis function.
y_average (ndarray) – The mean of the learning output data.

Parameters

function (str) – The radial basis function.
der_function (Optional[Callable[[ndarray],ndarray]]) – 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 a RBF of the form function(\(r\)), der_function(\(x\), \(|x|\), \(\epsilon\)) shall return \(\epsilon^{-1} x/|x| f'(|x|/\epsilon)\).
epsilon (Optional[float]) – An adjustable constant for Gaussian or multiquadrics functions. If None, use the average distance between input data.
data (Dataset) –
transformer (Optional[TransformerType]) –
input_names (Optional[Iterable[str]]) –
output_names (Optional[Iterable[str]]) –
parameters (Optional[MLAlgoParameterType]) –

Return type

None

Classes:

`DataFormatters`()	Machine learning regression model decorators.
`RBFDerivatives`()	Derivatives of functions used in `RBFRegression`.

Attributes:

`function`	The name of the kernel function.
`input_data`	The input data matrix.
`input_shape`	The dimension of the input variables before applying the transformers.
`is_trained`	Return whether the algorithm is trained.
`output_data`	The output data matrix.
`output_shape`	The dimension of the output variables before applying the transformers.

Methods:

`learn`([samples])	Train the machine learning algorithm from the learning dataset.
`load_algo`(directory)	Load a machine learning algorithm from a directory.
`predict`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_jacobian`(input_data, args, *kwargs)	Evaluate ‘predict_jac’ with either array or dictionary-based data.
`predict_raw`(input_data)	Predict output data from input data.
`save`([directory, path, save_learning_set])	Save the machine learning algorithm.

class DataFormatters

Machine learning regression model decorators.

Methods:

`format_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_dict_jacobian`(predict_jac)	Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
`format_input_output`(predict)	Make a function robust to type, array shape and data transformation.
`format_samples`(predict)	Make a 2D NumPy array-based function work with 1D NumPy array.
`format_transform`([transform_inputs, …])	Force a function to transform its input and/or output variables.
`transform_jacobian`(predict_jac)	Apply transformation to inputs and inverse transformation to outputs.

classmethod format_dict(predict)

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_dict_jacobian(predict_jac)

Wrap an array-based function to make it callable with a dictionary of NumPy arrays.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)

Make a function robust to type, array shape and data transformation.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
Returns: A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)

Force a function to transform its input and/or output variables.

Parameters

transform_inputs (bool) – If True, apply the transformers to the input variables.
transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod transform_jacobian(predict_jac)

Apply transformation to inputs and inverse transformation to outputs.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

class RBFDerivatives[source]

Derivatives of functions used in RBFRegression.

For a RBF of the form \(f(r)\), \(r\) scalar, the derivative functions are defined by \(d(f(r))/dx\), with \(r=|x|/\epsilon\). The functions are thus defined by \(df/dx = \epsilon^{-1} x/|x| f'(|x|/\epsilon)\). This convention is chosen to avoid division by \(|x|\) when the terms may be cancelled out, as \(f'(r)\) often has a term in \(r\).

Attributes:

TOL

Methods:

`der_cubic`(input_data, norm_input_data, eps)	Compute derivative w.r.t.
`der_gaussian`(input_data, norm_input_data, eps)	Compute derivative w.r.t.
`der_inverse_multiquadric`(input_data, …)	Compute derivative w.r.t.
`der_linear`(input_data, norm_input_data, eps)	Compute derivative w.r.t.
`der_multiquadric`(input_data, …)	Compute derivative of \(f(r) = \sqrt{r^2 + 1}\) wrt \(x\).
`der_quintic`(input_data, norm_input_data, eps)	Compute derivative w.r.t.
`der_thin_plate`(input_data, norm_input_data, eps)	Compute derivative w.r.t.

TOL = 2.220446049250313e-16

classmethod der_cubic(input_data, norm_input_data, eps)[source]

Compute derivative w.r.t. \(x\) of the function \(f(r) = r^3\).

Parameters

input_data (numpy.ndarray) – The 1D input data.
norm_input_data (float) – The norm of the input variable.
eps (float) – The correlation length.

Returns

The derivative of the function.

Return type

numpy.ndarray

classmethod der_gaussian(input_data, norm_input_data, eps)[source]

Compute derivative w.r.t. \(x\) of the function \(f(r) = \exp(-r^2)\).

Parameters

input_data (numpy.ndarray) – The 1D input data.
norm_input_data (float) – The norm of the input variable.
eps (float) – The correlation length.

Returns

The derivative of the function.

Return type

numpy.ndarray

classmethod der_inverse_multiquadric(input_data, norm_input_data, eps)[source]

Compute derivative w.r.t. \(x\) of the function \(f(r) = 1/\sqrt{r^2 + 1}\).

Parameters

input_data (numpy.ndarray) – The 1D input data.
norm_input_data (float) – The norm of the input variable.
eps (float) – The correlation length.

Returns

The derivative of the function.

Return type

numpy.ndarray

classmethod der_linear(input_data, norm_input_data, eps)[source]

Compute derivative w.r.t. \(x\) of the function \(f(r) = r\). If \(x=0\), return 0 (determined up to a tolerance).

Parameters

input_data (numpy.ndarray) – The 1D input data.
norm_input_data (float) – The norm of the input variable.
eps (float) – The correlation length.

Returns

The derivative of the function.

Return type

numpy.ndarray

classmethod der_multiquadric(input_data, norm_input_data, eps)[source]

Compute derivative of \(f(r) = \sqrt{r^2 + 1}\) wrt \(x\).

Parameters

input_data (numpy.ndarray) – The 1D input data.
norm_input_data (float) – The norm of the input variable.
eps (float) – The correlation length.

Returns

The derivative of the function.

Return type

numpy.ndarray

classmethod der_quintic(input_data, norm_input_data, eps)[source]

Compute derivative w.r.t. \(x\) of the function \(f(r) = r^5\).

Parameters

input_data (numpy.ndarray) – The 1D input data.
norm_input_data (float) – The norm of the input variable.
eps (float) – The correlation length.

Returns

The derivative of the function.

Return type

numpy.ndarray

classmethod der_thin_plate(input_data, norm_input_data, eps)[source]

Compute derivative w.r.t. \(x\) of the function \(f(r) = r^2 \log(r)\). If \(x=0\), return 0 (determined up to a tolerance).

Parameters

input_data (numpy.ndarray) – The 1D input data.
norm_input_data (float) – The norm of the input variable.
eps (float) – The correlation length.

Returns

The derivative of the function.

Return type

numpy.ndarray

property function

The name of the kernel function.

The name is possibly different from self.parameters[‘function’], as it is mapped (scipy). Examples:

‘inverse’ -> ‘inverse_multiquadric’ ‘InverSE MULtiQuadRIC’ -> ‘inverse_multiquadric’

property input_data: The input data matrix.

property input_shape: The dimension of the input variables before applying the transformers.

property is_trained: Return whether the algorithm is trained.

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters: samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.
Raises: NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.
Return type: None

load_algo(directory)[source]

Load a machine learning algorithm from a directory.

Parameters: directory (str) – The path to the directory where the machine learning algorithm is saved.
Return type: None

property output_data: The output data matrix.

property output_shape: The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_jacobian(input_data, *args, **kwargs)

Evaluate ‘predict_jac’ with either array or dictionary-based data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict_jac’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.

Returns

The output data with the same type as the input one.

predict_raw(input_data)

Predict output data from input data.

Parameters: input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
Returns: The predicted output data with shape (n_samples, n_outputs).
Return type: numpy.ndarray

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters

directory (Optional[str]) – The name of the directory to save the algorithm.
path (str) – The path to parent directory where to create the directory.
save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str

RandomForestRegressor¶

class gemseo.mlearning.regression.random_forest.RandomForestRegressor(data, transformer=None, input_names=None, output_names=None, n_estimators=100, **parameters)[source]

Random forest regression.

Attributes

learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
learning_set (Dataset) – The learning dataset.
parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.
transformer (Dict[str,Transformer]) – The strategies to transform the variables. The values are instances of Transformer 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 Transformer will be applied to all the variables of this group. If None, do not transform the variables.
algo (Any) – The interfaced machine learning algorithm.
input_names (List[str]) – The names of the input variables.
output_names (List[str]) – The names of the output variables.
input_space_center (Dict[str,ndarray]) – The center of the input space.

Parameters

n_estimators (int, optional) – The number of trees in the forest.

Classes:

DataFormatters()

Machine learning regression model decorators.

Attributes:

`input_data`	The input data matrix.
`input_shape`	The dimension of the input variables before applying the transformers.
`is_trained`	Return whether the algorithm is trained.
`output_data`	The output data matrix.
`output_shape`	The dimension of the output variables before applying the transformers.

Methods:

`learn`([samples])	Train the machine learning algorithm from the learning dataset.
`load_algo`(directory)	Load a machine learning algorithm from a directory.
`predict`(input_data, args, *kwargs)	Evaluate ‘predict’ with either array or dictionary-based input data.
`predict_jacobian`(input_data, args, *kwargs)	Evaluate ‘predict_jac’ with either array or dictionary-based data.
`predict_raw`(input_data)	Predict output data from input data.
`save`([directory, path, save_learning_set])	Save the machine learning algorithm.

class DataFormatters

Machine learning regression model decorators.

Methods:

`format_dict`(predict)	Make an array-based function be called with a dictionary of NumPy arrays.
`format_dict_jacobian`(predict_jac)	Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
`format_input_output`(predict)	Make a function robust to type, array shape and data transformation.
`format_samples`(predict)	Make a 2D NumPy array-based function work with 1D NumPy array.
`format_transform`([transform_inputs, …])	Force a function to transform its input and/or output variables.
`transform_jacobian`(predict_jac)	Apply transformation to inputs and inverse transformation to outputs.

classmethod format_dict(predict)

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_dict_jacobian(predict_jac)

Wrap an array-based function to make it callable with a dictionary of NumPy arrays.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
Returns: The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)

Make a function robust to type, array shape and data transformation.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
Return type: Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters: predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
Returns: A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)

Force a function to transform its input and/or output variables.

Parameters

transform_inputs (bool) – If True, apply the transformers to the input variables.
transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod transform_jacobian(predict_jac)

Apply transformation to inputs and inverse transformation to outputs.

Parameters: predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
Returns: A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
Return type: Callable[[numpy.ndarray], numpy.ndarray]

property input_data: The input data matrix.

property input_shape: The dimension of the input variables before applying the transformers.

property is_trained: Return whether the algorithm is trained.

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters: samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.
Raises: NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.
Return type: None

load_algo(directory)

Load a machine learning algorithm from a directory.

Parameters: directory (str) – The path to the directory where the machine learning algorithm is saved.
Return type: None

property output_data: The output data matrix.

property output_shape: The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.
*args – The positional arguments of the function ‘predict’.
**kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

predict_jacobian(input_data, *args, **kwargs)

Evaluate ‘predict_jac’ with either array or dictionary-based data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict_jac’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

input_data – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.

Returns

The output data with the same type as the input one.

predict_raw(input_data)

Predict output data from input data.

Parameters: input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
Returns: The predicted output data with shape (n_samples, n_outputs).
Return type: numpy.ndarray

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters

directory (Optional[str]) – The name of the directory to save the algorithm.
path (str) – The path to parent directory where to create the directory.
save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str