Mixture of experts¶
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:
or soft, in which case the weights express the probabilities of belonging to each cluster:
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=None, input_names=None, output_names=None, hard=True)[source]
Mixture of experts regression.
- Parameters
data (Dataset) – The learning dataset.
transformer (Mapping[str, TransformerType] | None) –
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, theTransformer
will be applied to all the variables of this group. If None, do not transform the variables.By default it is set to None.
input_names (Iterable[str] | None) –
The names of the input variables. If
None
, consider all the input variables of the learning dataset.By default it is set to None.
output_names (Iterable[str] | None) –
The names of the output variables. If
None
, consider all the output variables of the learning dataset.By default it is set to None.
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.
- class DataFormatters[source]
Machine learning regression model decorators.
- classmethod format_dict(predict)
Make an array-based function be called with a dictionary of NumPy arrays.
- Parameters
predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
- Returns
A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
- Return type
Callable[[Union[numpy.ndarray, Mapping[str, numpy.ndarray]]], Union[numpy.ndarray, Mapping[str, numpy.ndarray]]]
- classmethod format_dict_jacobian(predict_jac)
Wrap an array-based function to make it callable with a dictionary of NumPy arrays.
- Parameters
predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
- Returns
The wrapped ‘predict_jac’ function, callable with either a NumPy data array or a dictionary of numpy data arrays indexed by variables names. The return value will have the same type as the input data.
- Return type
Callable[[Union[numpy.ndarray, Mapping[str, numpy.ndarray]]], Union[numpy.ndarray, Mapping[str, numpy.ndarray]]]
- classmethod format_input_output(predict)
Make a function robust to type, array shape and data transformation.
- Parameters
predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
- Returns
A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.
- Return type
Callable[[Union[numpy.ndarray, Mapping[str, numpy.ndarray]]], Union[numpy.ndarray, Mapping[str, numpy.ndarray]]]
- classmethod format_predict_class_dict(predict)[source]
Make an array-based function be called with a dictionary of NumPy arrays.
- Parameters
predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.
- Returns
A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.
- Return type
Callable[[Union[numpy.ndarray, Mapping[str, numpy.ndarray]]], Union[numpy.ndarray, Mapping[str, numpy.ndarray]]]
- classmethod format_samples(predict)
Make a 2D NumPy array-based function work with 1D NumPy array.
- Parameters
predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.
- Returns
A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.
- Return type
Callable[[numpy.ndarray], numpy.ndarray]
- classmethod format_transform(transform_inputs=True, transform_outputs=True)
Force a function to transform its input and/or output variables.
- Parameters
- Returns
A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.
- Return type
Callable[[numpy.ndarray], numpy.ndarray]
- classmethod transform_jacobian(predict_jac)
Apply transformation to inputs and inverse transformation to outputs.
- Parameters
predict_jac (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.
- Returns
A function evaluating the function ‘predict_jac’, after transforming its input data and/or before transforming its output data.
- Return type
Callable[[numpy.ndarray], numpy.ndarray]
- 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.
By default it is set to None.
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.
By default it is set to None.
**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.
By default it is set to None.
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.
By default it is set to None.
**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.
By default it is set to None.
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.
By default it is set to None.
**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.
- 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, *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]]
- predict_class(input_data, *args, **kwargs)[source]
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]]
- predict_jacobian(input_data, *args, **kwargs)
Evaluate ‘predict_jac’ with either array or dictionary-based 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_jac’ 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 – The input data.
*args – The positional arguments of the function ‘predict_jac’.
**kwargs – The keyword arguments of the function ‘predict_jac’.
- Returns
The output data with the same type as the input one.
- predict_local_model(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]]
- predict_raw(input_data)
Predict output data from input data.
- Parameters
input_data (numpy.ndarray) – The input data with shape (n_samples, n_inputs).
- Returns
The predicted output data with shape (n_samples, n_outputs).
- Return type
- save(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.
By default it is set to None.
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
- set_classification_measure(measure, **eval_options)[source]
Set the quality measure for the classification algorithms.
- Parameters
measure (gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasure) – The quality measure.
**eval_options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – 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 (gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasure) – The quality measure.
**eval_options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – 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 (gemseo.mlearning.qual_measure.quality_measure.MLQualityMeasure) – The quality measure.
**eval_options (Optional[Union[Sequence[int], bool, int, gemseo.core.dataset.Dataset]]) – 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
- 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_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: numpy.ndarray
The input data matrix.
- property input_dimension: int
The input space dimension.
- property is_trained: bool
Return whether the algorithm is trained.
- property learning_samples_indices: Sequence[int]
The indices of the learning samples used for the training.
- property n_clusters: int
The number of clusters.
- property output_data: numpy.ndarray
The output data matrix.
- property output_dimension: int
The output space dimension.
- regress_algo: str
The name of the regression algorithm.
- regress_cands: list[MLAlgoType]
The regression algorithm candidates.
- regress_models: list[MLRegressionAlgo]
The regression algorithms.
- regress_params: MLAlgoParameterType
The parameters of the regression algorithm.