Mixture of experts¶
Mixture of Experts¶
The mixture of experts (MoE) regression model expresses the output as a weighted sum of local surrogate models, where the weights are indicating the class of the input.
Inputs are grouped into clusters by a classification model that is trained on a training set where the output labels are determined through a clustering algorithm. The outputs may be preprocessed trough a sensor or a dimension reduction algorithm.
The classification may either be hard, in which 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 class:
where \(x\) is the input, \(y\) is the output, \(K\) is the number of classes, \((C_k)_{k=1,\cdots,K}\) are the input spaces associated to the classes, \(i_{C_k}(x)\) is the indicator of class \(k\), \(\mathbb{P}(x\in C_k)\) is the probability of class \(k\) given \(x\) and \(f_k(x)\) is the local surrogate model on class \(k\).
This concept is implemented through the MixtureOfExperts
class which
inherits from the MLRegressionAlgo
class.
Constructor¶

class
gemseo.mlearning.regression.moe.
MixtureOfExperts
(data, transformer=None, input_names=None, output_names=None, hard=True)[source] Mixture of experts regression.
Constructor.
 Parameters
data (Dataset) – learning dataset.
transformer (dict(str)) – transformation strategy for data groups. If None, do not transform data. Default: None.
input_names (list(str)) – names of the input variables.
output_names (list(str)) – names of the output variables.
hard (bool) – Indicator for hard or soft clustering/classification. Hard clustering/classification if True. Default: True.