gemseo / mlearning / qual_measure

# error_measure module¶

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

Attributes:

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.
BOOTSTRAP = 'bootstrap'
KFOLDS = 'kfolds'
LEARN = 'learn'
LOO = 'loo'
SMALLER_IS_BETTER = True
TEST = 'test'
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')