gemseo / mlearning / quality_measures

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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.

class EvaluationFunctionName(value)

Bases: StrEnum

The name of the function associated with an evaluation method.

BOOTSTRAP = 'evaluate_bootstrap'
KFOLDS = 'evaluate_kfolds'
LEARN = 'evaluate_learn'
LOO = 'evaluate_loo'
TEST = 'evaluate_test'
class EvaluationMethod(value)

Bases: StrEnum

The evaluation method.

BOOTSTRAP = 'BOOTSTRAP'

The name of the method to evaluate the measure by bootstrap.

KFOLDS = 'KFOLDS'

The name of the method to evaluate the measure by cross-validation.

LEARN = 'LEARN'

The name of the method to evaluate the measure on the learning dataset.

LOO = 'LOO'

The name of the method to evaluate the measure by leave-one-out.

TEST = 'TEST'

The name of the method to evaluate the measure on a test dataset.

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

compute_learning_measure(samples=None, multioutput=True, as_dict=False)

Evaluate the quality measure from the learning dataset.

Parameters:

  • samples (Sequence[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.

  • 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.

Returns:

The value of the quality measure.

Return type:

MeasureType

compute_leave_one_out_measure(samples=None, multioutput=True, as_dict=False, store_resampling_result=False)

Evaluate the quality measure using the leave-one-out technique.

Parameters:

  • samples (Sequence[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.

  • 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 learning samples.

    By default it is set to False.

Returns:

The value of the quality measure.

Return type:

MeasureType

compute_test_measure(test_data, samples=None, multioutput=True, as_dict=False)

Evaluate the quality measure using a test dataset.

Parameters:

  • test_data (IODataset) – The test dataset.

  • samples (Sequence[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.

  • 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.

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

evaluate_learn(samples=None, multioutput=True, as_dict=False)

Evaluate the quality measure from the learning dataset.

Parameters:

  • samples (Sequence[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.

  • 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.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_loo(samples=None, multioutput=True, as_dict=False, store_resampling_result=False)

Evaluate the quality measure using the leave-one-out technique.

Parameters:

  • samples (Sequence[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.

  • 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 learning samples.

    By default it is set to False.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_test(test_data, samples=None, multioutput=True, as_dict=False)

Evaluate the quality measure using a test dataset.

Parameters:

  • test_data (IODataset) – The test dataset.

  • samples (Sequence[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.

  • 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.

Returns:

The value of the quality measure.

Return type:

MeasureType

classmethod is_better(val1, val2)

Compare the quality between two values.

This method returns True if the first one is better than the second one.

For most measures, a smaller value is “better” than a larger one (MSE etc.). But for some, like an R2-measure, higher values are better than smaller ones. This comparison method correctly handles this, regardless of the type of measure.

Parameters:

  • val1 (float) – The value of the first quality measure.

  • val2 (float) – The value of the second quality measure.

Returns:

Whether val1 is of better quality than val2.

Return type:

bool

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

Error from surrogate discipline

R2 for regression models

R2 for regression models

Scaling

Scaling