linreg module¶
Linear regression model.
The linear regression model expresses the output variables as a weighted sum of the input ones:
where the coefficients \((w_1, w_2, ..., w_d)\) and the intercept
\(w_0\) are estimated by least square regression. They are easily
accessible via the arguments coefficients
and intercept
.
The penalty level \(\alpha\) is a non-negative parameter intended to prevent overfitting, while the penalty ratio \(\lambda\in [0, 1]\) expresses the ratio between \(\ell_2\)- and \(\ell_1\)-regularization. When \(\lambda=1\), there is no \(\ell_1\)-regularization, and a Ridge regression is performed. When \(\lambda=0\), there is no \(\ell_2\)-regularization, and a Lasso regression is performed. For \(\lambda\) between 0 and 1, an Elastic Net regression is performed.
One may also choose not to penalize the regression at all, by setting \(\alpha=0\). In this case, a simple least squares regression is performed.
Dependence¶
The linear model relies on the LinearRegression
,
Ridge
, Lasso
and ElasticNet
classes of the scikit-learn library.
- class gemseo.mlearning.regression.linreg.LinearRegressor(data, transformer=mappingproxy({}), input_names=None, output_names=None, fit_intercept=True, penalty_level=0.0, l2_penalty_ratio=1.0, random_state=0, **parameters)[source]
Bases:
BaseMLRegressionAlgo
Linear regression model.
- Parameters:
data (IODataset) – The learning dataset.
transformer (TransformerType) –
The strategies to transform the variables. The values are instances of
BaseTransformer
while the keys are the names of either the variables or the groups of variables, e.g."inputs"
or"outputs"
in the case of the regression algorithms. If a group is specified, theBaseTransformer
will be applied to all the variables of this group. IfIDENTITY
, 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.fit_intercept (bool) –
Whether to fit the intercept.
By default it is set to True.
penalty_level (float) –
The penalty level greater or equal to 0. If 0, there is no penalty.
By default it is set to 0.0.
l2_penalty_ratio (float) –
The penalty ratio related to the l2 regularization. If 1, use the Ridge penalty. If 0, use the Lasso penalty. Between 0 and 1, use the ElasticNet penalty.
By default it is set to 1.0.
random_state (int | None) –
The random state passed to the random number generator when there is a penalty. Use an integer for reproducible results.
By default it is set to 0.
**parameters (float | int | str | bool | None) – The parameters of the machine learning algorithm.
- Raises:
ValueError – When both the variable and the group it belongs to have a transformer.
- 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.arrayBy default it is set to True.
- 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:
- 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.arrayBy default it is set to True.
- 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:
- LIBRARY: ClassVar[str] = 'scikit-learn'
The name of the library of the wrapped machine learning algorithm.
- SHORT_ALGO_NAME: ClassVar[str] = 'LinReg'
The short name of the machine learning algorithm, often an acronym.
Typically used for composite names, e.g.
f"{algo.SHORT_ALGO_NAME}_{dataset.name}"
orf"{algo.SHORT_ALGO_NAME}_{discipline.name}"
.
- algo: Any
The interfaced machine learning algorithm.
- property coefficients: RealArray
The regression coefficients of the linear model.
- property intercept: RealArray
The regression intercepts of the linear model.
- learning_set: Dataset
The learning dataset.
- resampling_results: dict[str, tuple[BaseResampler, list[BaseMLAlgo], list[ndarray] | ndarray]]
The resampler class names bound to the resampling results.
A resampling result is formatted as
(resampler, ml_algos, predictions)
whereresampler
is aBaseResampler
,ml_algos
is the list of the associated machine learning algorithms built during the resampling stage andpredictions
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, BaseTransformer]
The strategies to transform the variables, if any.
The values are instances of
BaseTransformer
while the keys are the names of either the variables or the groups of variables, e.g. “inputs” or “outputs” in the case of the regression algorithms. If a group is specified, theBaseTransformer
will be applied to all the variables of this group.