regression module¶

This module contains the baseclass for regression algorithms.

The regression module implements regression algorithms, where the goal is to find relationships between continuous input and output variables. After being fitted to a learning set, the regression algorithms can predict output values of new input data.

A regression algorithm consists of identifying a function \(f: \mathbb{R}^{n_{\textrm{inputs}}} \to \mathbb{R}^{n_{\textrm{outputs}}}\). Given an input point \(x \in \mathbb{R}^{n_{\textrm{inputs}}}\), the predict method of the regression algorithm will return the output point \(y = f(x) \in \mathbb{R}^{n_{\textrm{outputs}}}\). See supervised for more information.

Wherever possible, the regression algorithms should also be able to compute the Jacobian matrix of the function it has learned to represent. Thus, given an input point \(x \in \mathbb{R}^{n_{\textrm{inputs}}}\), the Jacobian prediction method of the regression algorithm should return the matrix

\[\begin{split}J_f(x) = \frac{\partial f}{\partial x} = \begin{pmatrix} \frac{\partial f_1}{\partial x_1} & \cdots & \frac{\partial f_1} {\partial x_{n_{\textrm{inputs}}}}\\ \vdots & \ddots & \vdots\\ \frac{\partial f_{n_{\textrm{outputs}}}}{\partial x_1} & \cdots & \frac{\partial f_{n_{\textrm{outputs}}}} {\partial x_{n_{\textrm{inputs}}}} \end{pmatrix} \in \mathbb{R}^{n_{\textrm{outputs}}\times n_{\textrm{inputs}}}.\end{split}\]

This concept is implemented through the MLRegressionAlgo class which inherits from the MLSupervisedAlgo class.

class gemseo.mlearning.regression.regression.MLRegressionAlgo(data, transformer=mappingproxy({}), input_names=None, output_names=None, **parameters)[source]

Bases: MLSupervisedAlgo

Machine Learning Regression Model Algorithm.

Inheriting classes shall implement the MLSupervisedAlgo._fit() and MLSupervisedAlgo._predict() methods, and MLRegressionAlgo._predict_jacobian() method if possible.

Parameters:

data (IODataset) – The learning dataset.
transformer (TransformerType) –
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 IDENTITY, do not transform the variables.

By default it is set to {}.
input_names (Iterable[str] | None) – The names of the input variables. If None, consider all the input variables of the learning dataset.
output_names (Iterable[str] | None) – The names of the output variables. If None, consider all the output variables of the learning dataset.
**parameters (MLAlgoParameterType) – The parameters of the machine learning algorithm.

Raises:

ValueError – When both the variable and the group it belongs to have a transformer.

class DataFormatters[source]

Bases: DataFormatters

Machine learning regression model decorators.

classmethod format_dict_jacobian(predict_jac)[source]

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

Parameters:: predict_jac (Callable[[ndarray], 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[[ndarray | Mapping[str, ndarray]], ndarray | Mapping[str, ndarray]]

classmethod transform_jacobian(predict_jac)[source]

Apply transformation to inputs and inverse transformation to outputs.

Parameters:: predict_jac (Callable[[ndarray], 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[[ndarray], ndarray]

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

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)[source]

Predict output data from input data.

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

DEFAULT_TRANSFORMER: DefaultTransformerType = mappingproxy({'inputs': <gemseo.mlearning.transformers.scaler.min_max_scaler.MinMaxScaler object>, 'outputs': <gemseo.mlearning.transformers.scaler.min_max_scaler.MinMaxScaler object>}): The default transformer for the input and output data, if any.

algo: Any: The interfaced machine learning algorithm.

input_names: list[str]: The names of the input variables.

input_space_center: dict[str, ndarray]: The center of the input space.

learning_set: IODataset: The learning dataset.

output_names: list[str]: The names of the output variables.

parameters: dict[str, MLAlgoParameterType]: The parameters of the machine learning algorithm.

transformer: dict[str, Transformer]

The strategies to transform the variables, if any.

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.