gemseo / mlearning / quality_measures

r2_measure module¶

The R2 to measure the quality of a regression algorithm.

The r2_measure module implements the concept of R2 measures for machine learning algorithms.

This concept is implemented through the R2Measure class and overloads the MLErrorMeasure._compute_measure() method.

The R2 is defined by

\[\begin{split}R_2(\\hat{y}) = 1 - \\frac{\\sum_i (\\hat{y}_i - y_i)^2} {\\sum_i (y_i-\\bar{y})^2},\end{split}\]

where \(\\hat{y}\) are the predictions, \(y\) are the data points and \(\\bar{y}\) is the mean of \(y\).

class gemseo.mlearning.quality_measures.r2_measure.R2Measure(algo, fit_transformers=True)[source]

Bases: MLErrorMeasure

The R2 measure for machine learning.

Parameters:

algo (MLRegressionAlgo) – A machine learning algorithm for regression.
fit_transformers (bool) –
Whether to re-fit the transformers when using resampling techniques. If False, use the transformers of the algorithm fitted from the whole learning dataset.

By default it is set to True.

compute_bootstrap_measure(n_replicates=100, samples=None, multioutput=True, seed=None, as_dict=False, store_resampling_result=False)[source]

Evaluate the quality measure using the bootstrap technique.

Parameters:

n_replicates (int) –
The number of bootstrap replicates.

By default it is set to 100.
samples (list[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator will be used.
as_dict (bool) –
Whether the full quality measure is returned as a mapping from algo.output names to quality measures. Otherwise, the full quality measure as an array stacking these quality measures according to the order of algo.output_names.

By default it is set to False.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of bootstrap replicates.

By default it is set to False.

Returns:

The value of the quality measure.

Return type:

NoReturn

compute_cross_validation_measure(n_folds=5, samples=None, multioutput=True, randomize=True, seed=None, as_dict=False, store_resampling_result=False)[source]

Evaluate the quality measure using the k-folds technique.

Parameters:

n_folds (int) –
The number of folds.

By default it is set to 5.
samples (list[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
randomize (bool) –
Whether to shuffle the samples before dividing them in folds.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator is used.
as_dict (bool) –
Whether the full quality measure is returned as a mapping from algo.output names to quality measures. Otherwise, the full quality measure as an array stacking these quality measures according to the order of algo.output_names.

By default it is set to False.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of folds.

By default it is set to False.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True, seed=None, as_dict=False, store_resampling_result=False)

Evaluate the quality measure using the bootstrap technique.

Parameters:

n_replicates (int) –
The number of bootstrap replicates.

By default it is set to 100.
samples (list[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator will be used.
as_dict (bool) –
Whether the full quality measure is returned as a mapping from algo.output names to quality measures. Otherwise, the full quality measure as an array stacking these quality measures according to the order of algo.output_names.

By default it is set to False.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of bootstrap replicates.

By default it is set to False.

Returns:

The value of the quality measure.

Return type:

NoReturn

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=True, seed=None, as_dict=False, store_resampling_result=False)

Evaluate the quality measure using the k-folds technique.

Parameters:

n_folds (int) –
The number of folds.

By default it is set to 5.
samples (list[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
randomize (bool) –
Whether to shuffle the samples before dividing them in folds.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator is used.
as_dict (bool) –
Whether the full quality measure is returned as a mapping from algo.output names to quality measures. Otherwise, the full quality measure as an array stacking these quality measures according to the order of algo.output_names.

By default it is set to False.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of folds.

By default it is set to False.

Returns:

The value of the quality measure.

Return type:

MeasureType

SMALLER_IS_BETTER: ClassVar[bool] = False: Whether to minimize or maximize the measure.

algo: MLSupervisedAlgo: The machine learning algorithm whose quality we want to measure.

Examples using R2Measure¶

Error from surrogate discipline

R2 for regression models

Scaling