gemseo / mlearning / regression

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moe module

Mixture of experts for regression.

The mixture of experts (MoE) model expresses an output variable as the weighted sum of the outputs of local regression models, whose weights depend on the input data.

During the learning stage, the input space is divided into \(K\) clusters by a clustering model, then a classification model is built to map the input space to the cluster space, and finally a regression model \(f_k\) is built for the \(k\)-th cluster.

The classification may be either hard, in which case only one of the weights is equal to one, and the rest equal to zero:

\[y = \sum_{k=1}^K I_{C_k}(x) f_k(x),\]

or soft, in which case the weights express the probabilities of belonging to each cluster:

\[y = \sum_{k=1}^K \mathbb{P}(x \in C_k) f_k(x),\]

where \(x\) is the input data, \(y\) is the output data, \(K\) is the number of clusters, \((C_k)_{k=1,\cdots,K}\) are the input spaces associated to the clusters, \(I_{C_k}(x)\) is the indicator of class \(k\), \(\mathbb{P}(x \in C_k)\) is the probability that \(x\) belongs to cluster \(k\) and \(f_k(x)\) is the local regression model on cluster \(k\).

class gemseo.mlearning.regression.moe.MOERegressor(data, transformer=mappingproxy({}), input_names=None, output_names=None, hard=True)[source]

Bases: MLRegressionAlgo

Mixture of experts regression.

Parameters:

  • data (IODataset) – The learning dataset.

  • transformer (TransformerType) –

    The strategies to transform the variables. The values are instances of Transformer while the keys are the names of either the variables or the groups of variables, e.g. "inputs" or "outputs" in the case of the regression algorithms. If a group is specified, the Transformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

    By default it is set to {}.

  • input_names (Iterable[str] | None) – The names of the input variables. If None, consider all the input variables of the learning dataset.

  • output_names (Iterable[str] | None) – The names of the output variables. If None, consider all the output variables of the learning dataset.

  • hard (bool) –

    Whether clustering/classification should be hard or soft.

    By default it is set to True.

Raises:

ValueError – When both the variable and the group it belongs to have a transformer.

DataFormatters

alias of MOEDataFormatters

add_classifier_candidate(name, calib_space=None, calib_algo=None, **option_lists)[source]

Add a candidate for classification.

Parameters:

  • name (str) – The name of a classification algorithm.

  • calib_space (DesignSpace | None) – The space defining the calibration variables.

  • calib_algo (dict[str, str | int] | None) – The name and options of the DOE or optimization algorithm, e.g. {“algo”: “fullfact”, “n_samples”: 10}). If None, do not perform calibration.

  • **option_lists (list[MLAlgoParameterType] | None) – Parameters for the clustering algorithm candidate. Each parameter has to be enclosed within a list. The list may contain different values to try out for the given parameter, or only one.

Return type:

None

add_clusterer_candidate(name, calib_space=None, calib_algo=None, **option_lists)[source]

Add a candidate for clustering.

Parameters:

  • name (str) – The name of a clustering algorithm.

  • calib_space (DesignSpace | None) – The space defining the calibration variables.

  • calib_algo (dict[str, str | int] | None) – The name and options of the DOE or optimization algorithm, e.g. {“algo”: “fullfact”, “n_samples”: 10}). If None, do not perform calibration.

  • **option_lists (list[MLAlgoParameterType] | None) – Parameters for the clustering algorithm candidate. Each parameter has to be enclosed within a list. The list may contain different values to try out for the given parameter, or only one.

Return type:

None

add_regressor_candidate(name, calib_space=None, calib_algo=None, **option_lists)[source]

Add a candidate for regression.

Parameters:

  • name (str) – The name of a regression algorithm.

  • calib_space (DesignSpace | None) – The space defining the calibration variables.

  • calib_algo (dict[str, str | int] | None) – The name and options of the DOE or optimization algorithm, e.g. {“algo”: “fullfact”, “n_samples”: 10}). If None, do not perform calibration.

  • **option_lists (list[MLAlgoParameterType] | None) – Parameters for the clustering algorithm candidate. Each parameter has to be enclosed within a list. The list may contain different values to try out for the given parameter, or only one.

Return type:

None

learn(samples=None, fit_transformers=True)

Train the machine learning algorithm from the learning dataset.

Parameters:

  • samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.

  • fit_transformers (bool) –

    Whether to fit the variable transformers. Otherwise, use them as they are.

    By default it is set to True.

Return type:

None

load_algo(directory)[source]

Load a machine learning algorithm from a directory.

Parameters:

directory (str | Path) – The path to the directory where the machine learning algorithm is saved.

Return type:

None

predict(input_data)

Predict output data from input data.

The user can specify these 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.])}.

If the numpy arrays are of dimension 2, their i-th rows represent the input data of the i-th sample; while if the numpy arrays are of dimension 1, there is a single sample.

The type of the output data and the dimension of the output arrays will be consistent with the type of the input data and the size of the input arrays.

Parameters:

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

Returns:

The predicted output data.

Return type:

ndarray | Mapping[str, ndarray]

predict_class(input_data)[source]

Predict classes from input data.

The user can specify these 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.

Returns:

The predicted classes.

Return type:

int | ndarray

predict_jacobian(input_data)

Predict the Jacobians of the regression model at input_data.

The user can specify these 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.])}.

If the NumPy arrays are of dimension 2, their i-th rows represent the input data of the i-th sample; while if the NumPy arrays are of dimension 1, there is a single sample.

The type of the output data and the dimension of the output arrays will be consistent with the type of the input data and the size of the input arrays.

Parameters:

input_data (DataType) – The input data.

Returns:

The predicted Jacobian data.

Return type:

NoReturn

predict_local_model(input_data, index)[source]

Predict output data from input data.

The user can specify these 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:
Returns:

The predicted output data.

Return type:

ndarray | Mapping[str, ndarray]

predict_raw(input_data)

Predict output data from input data.

Parameters:

input_data (ndarray) – The input data with shape (n_samples, n_inputs).

Returns:

The predicted output data with shape (n_samples, n_outputs).

Return type:

ndarray

set_classification_measure(measure, **eval_options)[source]

Set the quality measure for the classification algorithms.

Parameters:

  • measure (MLQualityMeasure) – The quality measure.

  • **eval_options (EvalOptionType) – The options for the quality measure.

Return type:

None

set_classifier(classif_algo, **classif_params)[source]

Set the classification algorithm.

Parameters:

  • classif_algo (str) – The name of the classification algorithm.

  • **classif_params (MLAlgoParameterType | None) – The parameters of the classification algorithm.

Return type:

None

set_clusterer(cluster_algo, **cluster_params)[source]

Set the clustering algorithm.

Parameters:

  • cluster_algo (str) – The name of the clustering algorithm.

  • **cluster_params (MLAlgoParameterType | None) – The parameters of the clustering algorithm.

Return type:

None

set_clustering_measure(measure, **eval_options)[source]

Set the quality measure for the clustering algorithms.

Parameters:

  • measure (MLQualityMeasure) – The quality measure.

  • **eval_options (EvalOptionType) – The options for the quality measure.

Return type:

None

set_regression_measure(measure, **eval_options)[source]

Set the quality measure for the regression algorithms.

Parameters:

  • measure (MLQualityMeasure) – The quality measure.

  • **eval_options (EvalOptionType) – The options for the quality measure.

Return type:

None

set_regressor(regress_algo, **regress_params)[source]

Set the regression algorithm.

Parameters:

  • regress_algo (str) – The name of the regression algorithm.

  • **regress_params (MLAlgoParameterType | None) – The parameters of the regression algorithm.

Return type:

None

to_pickle(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters:

  • directory (str | None) – The name of the directory to save the algorithm.

  • path (str | Path) –

    The path to parent directory where to create the directory.

    By default it is set to “.”.

  • save_learning_set (bool) –

    Whether to save the learning set or get rid of it to lighten the saved files.

    By default it is set to False.

Returns:

The path to the directory where the algorithm is saved.

Return type:

str

DEFAULT_TRANSFORMER: DefaultTransformerType = mappingproxy({'inputs': <gemseo.mlearning.transformers.scaler.min_max_scaler.MinMaxScaler object>, 'outputs': <gemseo.mlearning.transformers.scaler.min_max_scaler.MinMaxScaler object>})

The default transformer for the input and output data, if any.

FILENAME: ClassVar[str] = 'ml_algo.pkl'
IDENTITY: Final[DefaultTransformerType] = mappingproxy({})

A transformer leaving the input and output variables as they are.

LABELS: Final[str] = 'labels'
LIBRARY: ClassVar[str] = ''

The name of the library of the wrapped machine learning algorithm.

SHORT_ALGO_NAME: ClassVar[str] = 'MoE'

The short name of the machine learning algorithm, often an acronym.

Typically used for composite names, e.g. f"{algo.SHORT_ALGO_NAME}_{dataset.name}" or f"{algo.SHORT_ALGO_NAME}_{discipline.name}".

algo: Any

The interfaced machine learning algorithm.

classif_algo: str

The name of the classification algorithm.

classif_cands: list[MLAlgoType]

The classification algorithm candidates.

classif_measure: dict[str, str | EvalOptionType]

The quality measure for the classification algorithms.

classif_params: MLAlgoParameterType

The parameters of the classification algorithm.

classifier: MLClassificationAlgo

The classification algorithm.

cluster_algo: str

The name of the clustering algorithm.

cluster_cands: list[MLAlgoType]

The clustering algorithm candidates.

cluster_measure: dict[str, str | EvalOptionType]

The quality measure for the clustering algorithms.

cluster_params: MLAlgoParameterType

The parameters of the clustering algorithm.

clusterer: MLClusteringAlgo

The clustering algorithm.

hard: bool

Whether clustering/classification should be hard or soft.

property input_data: ndarray

The input data matrix.

property input_dimension: int

The input space dimension.

input_names: list[str]

The names of the input variables.

input_space_center: dict[str, ndarray]

The center of the input space.

property is_trained: bool

Return whether the algorithm is trained.

property labels: list[int]

The cluster labels.

property learning_samples_indices: Sequence[int]

The indices of the learning samples used for the training.

learning_set: Dataset

The learning dataset.

property n_clusters: int

The number of clusters.

property output_data: ndarray

The output data matrix.

property output_dimension: int

The output space dimension.

output_names: list[str]

The names of the output variables.

parameters: dict[str, MLAlgoParameterType]

The parameters of the machine learning algorithm.

regress_algo: str

The name of the regression algorithm.

regress_cands: list[MLAlgoType]

The regression algorithm candidates.

regress_measure: dict[str, str | EvalOptionType]

The quality measure for the regression algorithms.

regress_models: list[MLRegressionAlgo]

The regression algorithms.

regress_params: MLAlgoParameterType

The parameters of the regression algorithm.

resampling_results: dict[str, tuple[Resampler, list[MLAlgo], list[ndarray] | ndarray]]

The resampler class names bound to the resampling results.

A resampling result is formatted as (resampler, ml_algos, predictions) where resampler is a Resampler, ml_algos is the list of the associated machine learning algorithms built during the resampling stage and predictions are the predictions obtained with the latter.

resampling_results stores only one resampling result per resampler type (e.g., "CrossValidation", "LeaveOneOut" and "Boostrap").

transformer: dict[str, Transformer]

The strategies to transform the variables, if any.

The values are instances of Transformer while the keys are the names of either the variables or the groups of variables, e.g. “inputs” or “outputs” in the case of the regression algorithms. If a group is specified, the Transformer will be applied to all the variables of this group.

Examples using MOERegressor

Mixture of experts with PCA on Burgers dataset

Mixture of experts with PCA on Burgers dataset

Advanced mixture of experts

Advanced mixture of experts

Mixture of experts

Mixture of experts