gemseo_mlearning / adaptive / distributions

regressor_distribution module

Universal distribution for regression models.

A RegressorDistribution samples a MLSupervisedAlgo, by learning new versions of the latter from subsets of the original learning dataset.

These new MLAlgo instances are based on sampling methods, such as bootstrap, cross-validation or leave-one-out.

Sampling a MLAlgo can be particularly useful to:

• study the robustness of a MLAlgo w.r.t. learning dataset elements,

• estimate infill criteria for adaptive learning purposes,

• etc.

class gemseo_mlearning.adaptive.distributions.regressor_distribution.RegressorDistribution(algo, bootstrap=True, loo=False, size=None)

Bases: gemseo_mlearning.adaptive.distribution.MLRegressorDistribution

Distribution related to a regression algorithm.

# noqa: D205 D212 D415

Parameters

• algo (MLRegressionAlgo) – A regression model.

• bootstrap (bool) –

  The resampling method. If True, use bootstrap resampling. Otherwise, use cross-validation resampling.

  By default it is set to True.

• loo (bool) –

  The leave-One-Out sub-method, when bootstrap is False. If False, use parameterized cross-validation, Otherwise use leave-one-out.

  By default it is set to False.

• size (int | None) –

  The size of the resampling set, i.e. the number of times the machine learning algorithm is rebuilt. If None, use the default size for bootstrap (MLAlgoSampler.N_BOOTSTRAP) and cross-validation (MLAlgoSampler.N_FOLDS).

  By default it is set to None.

Return type

None

change_learning_set(learning_set)

Re-train the machine learning algorithm relying on the initial learning set.

Parameters

learning_set (gemseo.core.dataset.Dataset) – The new learning set.

Return type

None

compute_confidence_interval(input_data, level=0.95)

Predict the lower bounds and upper bounds from input data.

The user can specify the input data either as a NumPy array, e.g. array([1., 2., 3.]) or as a dictionary, e.g. {'a': array([1.]), 'b': array([2., 3.])}.

The output data type will be consistent with the input data type.

Parameters

• input_data (DataType) – The input data.

• level (float) –

  A quantile level.

  By default it is set to 0.95.

Returns

The lower and upper bound values.

Return type

tuple[dict[str, ndarray], dict[str, ndarray], tuple[ndarray, ndarray]] | None

compute_expected_improvement(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

• input_data (Union[numpy.ndarray, Mapping[str, numpy.ndarray]]) – The input data.

• *args – The positional arguments of the function ‘predict’.

• **kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Mapping[str, numpy.ndarray]]

compute_mean(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

• input_data (Union[numpy.ndarray, Mapping[str, numpy.ndarray]]) – The input data.

• *args – The positional arguments of the function ‘predict’.

• **kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Mapping[str, numpy.ndarray]]

compute_standard_deviation(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

• input_data (Union[numpy.ndarray, Mapping[str, numpy.ndarray]]) – The input data.

• *args – The positional arguments of the function ‘predict’.

• **kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Mapping[str, numpy.ndarray]]

compute_variance(input_data, *args, **kwargs)

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters

• input_data (Union[numpy.ndarray, Mapping[str, numpy.ndarray]]) – The input data.

• *args – The positional arguments of the function ‘predict’.

• **kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Mapping[str, numpy.ndarray]]

learn(samples=None)

Train the machine learning algorithm from the learning dataset.

Parameters

samples (list[int] | None) –

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

By default it is set to None.

Return type

None

predict(input_data)

Predict the output of the original machine learning algorithm.

The user can specify the input data either as a NumPy array, e.g. array([1., 2., 3.]) or as a dictionary, e.g. {'a': array([1.]), 'b': array([2., 3.])}.

The output data type will be consistent with the input data type.

Parameters

input_data (Union[numpy.ndarray, Mapping[str, numpy.ndarray]]) – The input data.

Returns

The predicted output data.

Return type

Union[numpy.ndarray, Mapping[str, numpy.ndarray]]

predict_members(input_data)

Predict the output value with the different machine learning algorithms.

After prediction, the method stacks the results.

Parameters

input_data (Union[numpy.ndarray, Mapping[str, numpy.ndarray]]) – The input data, specified as either as a numpy.array or as dictionary of numpy.array indexed by inputs names. The numpy.array can be either a (d,) array representing a sample in dimension d, or a (M, d) array representing M samples in dimension d.

Returns

The output data (dimension p) of N machine learning algorithms.

If input_data.shape == (d,), then output_data.shape == (N, p). If input_data.shape == (M,d), then output_data;shape == (N,M,p).

Return type

Union[numpy.ndarray, Mapping[str, numpy.ndarray]]

BOOTSTRAP: Final[str] = 'b'

CROSS_VALIDATION: Final[str] = 'cv'

LOO: Final[str] = 'loo'

N_BOOTSTRAP: ClassVar[int] = 100

N_FOLDS: ClassVar[int] = 5

algo: gemseo.mlearning.regression.regression.MLRegressionAlgo

The regression model.

property input_names: list[str]

The names of the original machine learning algorithm inputs.

property learning_set: gemseo.core.dataset.Dataset

The learning dataset used by the original machine learning algorithm.

method: str

The resampling method.

property output_dimension: int

The dimension of the machine learning output space.

property output_names: list[str]

The names of the original machine learning algorithm outputs.

size: int

The size of the resampling set.

weights: list[Callable[[numpy.ndarray], float]]

The weight functions related to the sub-algorithms.

A weight function computes a weight from an input data array.

gemseo_mlearning.adaptive.distributions.regressor_distribution.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 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 it 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. Default is True, meaning that a value of a can be selected multiple times.

• 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

See also

randint, shuffle, permutation

Generator.choice

which should be used in new code

Notes

Setting user-specified probabilities through p uses a more general but less efficient sampler than the default. The general sampler produces a different sample than the optimized sampler even if each element of p is 1 / len(a).

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')