Dynamic Expectation-Maximization algorithms for Mixed-type Data

Solange Pruilh (1, 2) , Stéphanie Allassonnière (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 HeKA - Health data- and model- driven Knowledge Acquisition

Modelling mixed-type data is still complex because of the heterogeneity of the data encountered. With clustering as the objective, many methods are already doing well, but the inference of models and a posteriori exploitation is made difficult if not impossible. In this article we propose methodological developments of mixture models designed for mixed-type data. Component distributions of the continuous attributes can be either Gaussian, Student or Shifted Asymmetric Laplace. Categorical or discrete attributes, assumed independent conditionally on the class membership, can be distributed according to Bernoulli, Multinomial or Poisson distributions. The joint estimation of the number of classes and the parameters is carried out by EM-like algorithms that we have adapted to perform correctly. We show that our different dynamic algorithms allow us to reach the real number of classes and to correctly estimate the parameters of the discrete and continuous laws. We also highlight the benefits of introducing regularization to improve performance in situations where the sample size is insufficient for the complexity of the model. Our various models are then tested on real datasets from the literature, assessing that the objective of jointly estimating the number of components and the model parameters has been achieved.

Mots clés: Mixed-type data; Mixture models; EM Algorithms

Domaines: Statistiques [math.ST]; Applications [stat.AP]

Solange Pruilh, Stéphanie Allassonnière. Dynamic Expectation-Maximization algorithms for Mixed-type Data. 2024. ⟨hal-04510689⟩