# Measure the quality of a machine learning algorithm¶

Here is the baseclass to measure the quality of machine learning algorithms.

The concept of quality measure is implemented with the MLQualityMeasure class.

Classes:

 An abstract quality measure for machine learning algorithms. MLQualityMeasureFactory(*args, **kwargs) A factory of MLQualityMeasure.

Functions:

 Modify a sequence in-place by shuffling its contents.
class gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasure(algo)[source]

An abstract quality measure for machine learning algorithms.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLAlgo) – A machine learning algorithm.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)[source]

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)[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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

NoReturn

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

NoReturn

evaluate_learn(samples=None, multioutput=True)[source]

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

NoReturn

evaluate_loo(samples=None, multioutput=True)[source]

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_test(test_data, samples=None, multioutput=True)[source]

Evaluate the quality measure using a test dataset.

Parameters
• dataset – The test dataset.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

NoReturn

classmethod is_better(val1, val2)[source]

Compare the quality between two values.

This methods 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

class gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasureFactory(*args, **kwargs)[source]

A factory of MLQualityMeasure.

Parameters
• base_class – The base class to be considered.

• module_names – The fully qualified modules names to be searched.

Attributes:

 classes Return the available classes.

Methods:

 create(class_name, **options) Return an instance of a class. get_class(name) Return a class from its name. Return the constructor kwargs default values of a class. get_default_sub_options_values(name, **options) Return the default values of the sub options of a class. Return the constructor documentation of a class. get_options_grammar(name[, write_schema, ...]) Return the options JSON grammar for a class. get_sub_options_grammar(name, **options) Return the JSONGrammar of the sub options of a class. is_available(name) Return whether a class can be instantiated. Search for the classes that can be instantiated.
property classes

Return the available classes.

Returns

The sorted names of the available classes.

create(class_name, **options)

Return an instance of a class.

Parameters
• class_name (str) – The name of the class.

• **options (Any) – The arguments to be passed to the class constructor.

Returns

The instance of the class.

Raises

TypeError – If the class cannot be instantiated.

Return type

Any

get_class(name)

Return a class from its name.

Parameters

name (str) – The name of the class.

Returns

The class.

Raises

ImportError – If the class is not available.

Return type

Type[Any]

get_default_options_values(name)

Return the constructor kwargs default values of a class.

Parameters

name (str) – The name of the class.

Returns

The mapping from the argument names to their default values.

Return type

Dict[str, Union[str, int, float, bool]]

get_default_sub_options_values(name, **options)

Return the default values of the sub options of a class.

Parameters
• name (str) – The name of the class.

• **options (str) – The options to be passed to the class required to deduce the sub options.

Returns

The JSON grammar.

Return type

gemseo.core.grammars.json_grammar.JSONGrammar

get_options_doc(name)

Return the constructor documentation of a class.

Parameters

name (str) – The name of the class.

Returns

The mapping from the argument names to their documentation.

Return type

Dict[str, str]

get_options_grammar(name, write_schema=False, schema_file=None)

Return the options JSON grammar for a class.

Attempt to generate a JSONGrammar from the arguments of the __init__ method of the class.

Parameters
• name (str) – The name of the class.

• write_schema (bool) –

If True, write the JSON schema to a file.

By default it is set to False.

• schema_file (Optional[str]) –

The path to the JSON schema file. If None, the file is saved in the current directory in a file named after the name of the class.

By default it is set to None.

Returns

The JSON grammar.

Return type

gemseo.core.grammars.json_grammar.JSONGrammar

get_sub_options_grammar(name, **options)

Return the JSONGrammar of the sub options of a class.

Parameters
• name (str) – The name of the class.

• **options (str) – The options to be passed to the class required to deduce the sub options.

Returns

The JSON grammar.

Return type

gemseo.core.grammars.json_grammar.JSONGrammar

is_available(name)

Return whether a class can be instantiated.

Parameters

name (str) – The name of the class.

Returns

Whether the class can be instantiated.

Return type

bool

update()

Search for the classes that can be instantiated.

The search is done in the following order:
1. The fully qualified module names

2. The plugin packages

3. The packages from the environment variables

Return type

None

gemseo.mlearning.qual_measure.quality_measure.shuffle(x)

Modify a sequence in-place by shuffling its contents.

This function only shuffles the array along the first axis of a multi-dimensional array. The order of sub-arrays is changed but their contents remains the same.

Note

New code should use the shuffle method of a default_rng() instance instead; please see the random-quick-start.

Parameters

x (ndarray or MutableSequence) – The array, list or mutable sequence to be shuffled.

Returns

Return type

None

Generator.shuffle

which should be used for new code.

Examples

>>> arr = np.arange(10)
>>> np.random.shuffle(arr)
>>> arr
[1 7 5 2 9 4 3 6 0 8] # random


Multi-dimensional arrays are only shuffled along the first axis:

>>> arr = np.arange(9).reshape((3, 3))
>>> np.random.shuffle(arr)
>>> arr
array([[3, 4, 5], # random
[6, 7, 8],
[0, 1, 2]])


Here is the baseclass to measure the error of machine learning algorithms.

The concept of error measure is implemented with the MLErrorMeasure class and proposes different evaluation methods.

Classes:

 MLErrorMeasure(algo) An abstract error measure for machine learning.

Functions:

 choice(a[, size, replace, p]) Generates a random sample from a given 1-D array
class gemseo.mlearning.qual_measure.error_measure.MLErrorMeasure(algo)[source]

An abstract error measure for machine learning.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLSupervisedAlgo) – A machine learning algorithm for supervised learning.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)[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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_learn(samples=None, multioutput=True)[source]

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_loo(samples=None, multioutput=True)

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_test(test_data, samples=None, multioutput=True)[source]

Evaluate the quality measure using a test dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

classmethod is_better(val1, val2)

Compare the quality between two values.

This methods 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

gemseo.mlearning.qual_measure.error_measure.choice(a, size=None, replace=True, p=None)

Generates a random sample from a given 1-D array

New in version 1.7.0.

Note

New code should use the choice method of a default_rng() instance instead; please see the random-quick-start.

Parameters
• a (1-D array-like or int) – If an ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if a were np.arange(a)

• size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned.

• replace (boolean, optional) – Whether the sample is with or without replacement

• p (1-D array-like, optional) – The probabilities associated with each entry in a. If not given the sample assumes a uniform distribution over all entries in a.

Returns

samples – The generated random samples

Return type

single item or ndarray

Raises

ValueError – If a is an int and less than zero, if a or p are not 1-dimensional, if a is an array-like of size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size

randint, shuffle, permutation

Generator.choice

which should be used in new code

Notes

Sampling random rows from a 2-D array is not possible with this function, but is possible with Generator.choice through its axis keyword.

Examples

Generate a uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3)
array([0, 3, 4]) # random
>>> #This is equivalent to np.random.randint(0,5,3)


Generate a non-uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])
array([3, 3, 0]) # random


Generate a uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False)
array([3,1,0]) # random
>>> #This is equivalent to np.random.permutation(np.arange(5))[:3]


Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])
array([2, 3, 0]) # random


Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:

>>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']
>>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])
array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random
dtype='<U11')


Here is the baseclass to measure the quality of machine learning algorithms.

The concept of clustering quality measure is implemented with the MLClusteringMeasure class and proposes different evaluation methods.

Classes:

 An abstract clustering measure for clustering algorithms. An abstract clustering measure for predictive clustering algorithms.

Functions:

 choice(a[, size, replace, p]) Generates a random sample from a given 1-D array
class gemseo.mlearning.qual_measure.cluster_measure.MLClusteringMeasure(algo)[source]

An abstract clustering measure for clustering algorithms.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLClusteringAlgo) – A machine learning algorithm for clustering.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)

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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

NoReturn

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

NoReturn

evaluate_learn(samples=None, multioutput=True)[source]

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_loo(samples=None, multioutput=True)

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

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

Evaluate the quality measure using a test dataset.

Parameters
• dataset – The test dataset.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

NoReturn

classmethod is_better(val1, val2)

Compare the quality between two values.

This methods 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

class gemseo.mlearning.qual_measure.cluster_measure.MLPredictiveClusteringMeasure(algo)[source]

An abstract clustering measure for predictive clustering algorithms.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLPredictiveClusteringAlgo) – A machine learning algorithm for predictive clustering.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)[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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_learn(samples=None, multioutput=True)

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_loo(samples=None, multioutput=True)

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_test(test_data, samples=None, multioutput=True)[source]

Evaluate the quality measure using a test dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

classmethod is_better(val1, val2)

Compare the quality between two values.

This methods 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

gemseo.mlearning.qual_measure.cluster_measure.choice(a, size=None, replace=True, p=None)

Generates a random sample from a given 1-D array

New in version 1.7.0.

Note

New code should use the choice method of a default_rng() instance instead; please see the random-quick-start.

Parameters
• a (1-D array-like or int) – If an ndarray, a random sample is generated from its elements. If an int, the random sample is generated as if a were np.arange(a)

• size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned.

• replace (boolean, optional) – Whether the sample is with or without replacement

• p (1-D array-like, optional) – The probabilities associated with each entry in a. If not given the sample assumes a uniform distribution over all entries in a.

Returns

samples – The generated random samples

Return type

single item or ndarray

Raises

ValueError – If a is an int and less than zero, if a or p are not 1-dimensional, if a is an array-like of size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size

randint, shuffle, permutation

Generator.choice

which should be used in new code

Notes

Sampling random rows from a 2-D array is not possible with this function, but is possible with Generator.choice through its axis keyword.

Examples

Generate a uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3)
array([0, 3, 4]) # random
>>> #This is equivalent to np.random.randint(0,5,3)


Generate a non-uniform random sample from np.arange(5) of size 3:

>>> np.random.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0])
array([3, 3, 0]) # random


Generate a uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False)
array([3,1,0]) # random
>>> #This is equivalent to np.random.permutation(np.arange(5))[:3]


Generate a non-uniform random sample from np.arange(5) of size 3 without replacement:

>>> np.random.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0])
array([2, 3, 0]) # random


Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance:

>>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher']
>>> np.random.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3])
array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random
dtype='<U11')


The mean squared error to measure the quality of a regression algorithm.

The mse_measure module implements the concept of mean squared error measures for machine learning algorithms.

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

The mean squared error (MSE) is defined by

$\operatorname{MSE}(\hat{y})=\frac{1}{n}\sum_{i=1}^n(\hat{y}_i-y_i)^2,$

where $$\hat{y}$$ are the predictions and $$y$$ are the data points.

Classes:

 MSEMeasure(algo) The Mean Squared Error measure for machine learning.
class gemseo.mlearning.qual_measure.mse_measure.MSEMeasure(algo)[source]

The Mean Squared Error measure for machine learning.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLRegressionAlgo) – A machine learning algorithm for regression.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)

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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_learn(samples=None, multioutput=True)

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_loo(samples=None, multioutput=True)

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

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

Evaluate the quality measure using a test dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

classmethod is_better(val1, val2)

Compare the quality between two values.

This methods 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

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

$R_2(\hat{y}) = 1 - \frac{\sum_i (\hat{y}_i - y_i)^2} {\sum_i (y_i-\bar{y})^2},$

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

Classes:

 R2Measure(algo) The R2 measure for machine learning.
class gemseo.mlearning.qual_measure.r2_measure.R2Measure(algo)[source]

The R2 measure for machine learning.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLRegressionAlgo) – A machine learning algorithm for regression.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)[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 (Optional[List[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

NoReturn

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[List[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_learn(samples=None, multioutput=True)

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_loo(samples=None, multioutput=True)

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

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

Evaluate the quality measure using a test dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

classmethod is_better(val1, val2)

Compare the quality between two values.

This methods 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

The F1 to measure the quality of a classification algorithm.

The F1 is defined by

$F_1 = 2\frac{\mathit{precision}\mathit{recall}} {\mathit{precision}+\mathit{recall}}$

where $$\mathit{precision}$$ is the number of correctly predicted positives divided by the total number of predicted positives and $$\mathit{recall}$$ is the number of correctly predicted positives divided by the total number of true positives.

Classes:

 F1Measure(algo) The F1 measure for machine learning.
class gemseo.mlearning.qual_measure.f1_measure.F1Measure(algo)[source]

The F1 measure for machine learning.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLClassificationAlgo) – A machine learning algorithm for classification.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)

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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_learn(samples=None, multioutput=True)

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_loo(samples=None, multioutput=True)

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

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

Evaluate the quality measure using a test dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

classmethod is_better(val1, val2)

Compare the quality between two values.

This methods 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

The silhouette coefficient to measure the quality of a clustering algorithm.

The silhouette module implements the concept of silhouette coefficient measure for machine learning algorithms.

This concept is implemented through the SilhouetteMeasure class and overloads the MLClusteringMeasure._compute_measure() method.

The silhouette coefficient is defined for each point as the difference between the average distance from the point to each of the other points in its cluster and the average distance from the point to each of the points in the nearest cluster different from its own.

More formally, the silhouette coefficient $$s_i$$ of a point $$x_i$$ is given by

$\begin{split}a_i = \\frac{1}{|C_{k_i}| - 1} \\sum_{j\\in C_{k_i}\setminus\{i\} } \\|x_i-x_j\\|\\\\ b_i = \\underset{\\ell=1,\\cdots,K\\atop{\\ell\\neq k_i}}{\\min}\\ \\frac{1}{|C_\\ell|} \\sum_{j\\in C_\\ell} \\|x_i-x_j\\|\\\\ s_i = \\frac{b_i-a_i}{\\max(b_i,a_i)}\end{split}$

where $$k_i$$ is the index of the cluster to which $$x_i$$ belongs, $$K$$ is the number of clusters, $$C_k$$ is the set of indices of points belonging to the cluster $$k$$ ($$k=1,\\cdots,K$$), and $$|C_k| = \\sum_{j\\in C_k} 1$$ is the number of points in the cluster $$k$$, $$k=1,\\cdots,K$$.

Classes:

 The silhouette coefficient measure for machine learning.
class gemseo.mlearning.qual_measure.silhouette.SilhouetteMeasure(algo)[source]

The silhouette coefficient measure for machine learning.

algo

The machine learning algorithm.

Type

MLAlgo

Parameters

algo (MLPredictiveClusteringAlgo) – A machine learning algorithm for clustering.

Return type

None

Methods:

 evaluate([method, samples]) Evaluate the quality measure. evaluate_bootstrap([n_replicates, samples, ...]) Evaluate the quality measure using the bootstrap technique. evaluate_kfolds([n_folds, samples, ...]) Evaluate the quality measure using the k-folds technique. evaluate_learn([samples, multioutput]) Evaluate the quality measure using the learning dataset. evaluate_loo([samples, multioutput]) Evaluate the quality measure using the leave-one-out technique. evaluate_test(test_data[, samples, multioutput]) Evaluate the quality measure using a test dataset. is_better(val1, val2) Compare the quality between two values.
evaluate(method='learn', samples=None, **options)

Evaluate the quality measure.

Parameters
• method (str) –

The name of the method to evaluate the quality measure.

By default it is set to learn.

• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• **options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – The options of the estimation method (e.g. ‘test_data’ for

• method

• one ('n_replicates' for the bootstrap) –

• ...)

Returns

The value of the quality measure.

Raises

ValueError – If the name of the method is unknown.

Return type

Union[float, numpy.ndarray]

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True)[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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=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 (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

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 False.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_learn(samples=None, multioutput=True)

Evaluate the quality measure using the learning dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

Whether to return the quality measure for each output component. If not, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_loo(samples=None, multioutput=True)

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

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

evaluate_test(test_data, samples=None, multioutput=True)[source]

Evaluate the quality measure using a test dataset.

Parameters
• samples (Optional[Sequence[int]]) –

The indices of the learning samples. If None, use the whole learning dataset.

By default it is set to None.

• multioutput (bool) –

If True, return the quality measure for each output component. Otherwise, average these measures.

By default it is set to True.

• test_data (gemseo.core.dataset.Dataset) –

Returns

The value of the quality measure.

Return type

Union[float, numpy.ndarray]

classmethod is_better(val1, val2)

Compare the quality between two values.

This methods 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