gemseo / mlearning / regression

# 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]

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.

DataFormatters
predict_jacobian(input_data)[source]

Predict the Jacobians of the regression model at input_data.

The user can specify these input data either as a NumPy array, e.g. array([1., 2., 3.]) or as a dictionary, e.g. {'a': array([1.]), 'b': array([2., 3.])}.

If the NumPy arrays are of dimension 2, their i-th rows represent the input data of the i-th sample; while if the NumPy arrays are of dimension 1, there is a single sample.

The type of the output data and the dimension of the output arrays will be consistent with the type of the input data and the size of the input arrays.

Parameters:

input_data (DataType) – The input data.

Returns:

The predicted Jacobian data.

Return type:

NoReturn

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: Dataset

The learning dataset.

output_names: list[str]

The names of the output variables.

parameters: dict[str, MLAlgoParameterType]

The parameters of the machine learning algorithm.

resampling_results: dict[str, tuple[Resampler, list[MLAlgo], list[ndarray] | ndarray]]

The resampler class names bound to the resampling results.

A resampling result is formatted as (resampler, ml_algos, predictions) where resampler is a Resampler, ml_algos is the list of the associated machine learning algorithms built during the resampling stage and predictions are the predictions obtained with the latter.

resampling_results stores only one resampling result per resampler type (e.g., "CrossValidation", "LeaveOneOut" and "Boostrap").

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.

## Examples using MLRegressionAlgo¶

Cross-validation

Cross-validation

Leave-one-out

Leave-one-out

MSE for regression models

MSE for regression models

R2 for regression models

R2 for regression models

RMSE for regression models

RMSE for regression models

Scaling

Scaling