Augmented Quantization: a General Approach to Mixture Models

Charlie Sire (1, 2) , Rodolphe Le Riche (3, 4, 5, 6) , Didier Rullière (3, 4, 5) , Jérémy Rohmer (7) , Lucie Pheulpin (8) , Yann Richet (8)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 ASCII - Analyse d’interactions stochastiques intelligentes et coopératives
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
4 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
5 FAYOL-ENSMSE - Département Génie mathématique et industriel
6 CNRS - Centre National de la Recherche Scientifique
7 BRGM - Bureau de Recherches Géologiques et Minières
8 IRSN/PSE-ENV/SCAN/BEHRIG - Bureau d'expertise en hydrogéologie, risques Inondation, météorologiques et géotechniques

The investigation of mixture models is a key to understand and visualize the distribution of multivariate data. Most mixture models approaches are based on likelihoods, and are not adapted to distribution with finite support or without a well-defined density function. This study proposes the Augmented Quantization method, which is a reformulation of the classical quantization problem but which uses the p-Wasserstein distance. This metric can be computed in very general distribution spaces, in particular with varying supports. The clustering interpretation of quantization is revisited in a more general framework. The performance of Augmented Quantization is first demonstrated through analytical toy problems. Subsequently, it is applied to a practical case study involving river flooding, wherein mixtures of Dirac and Uniform distributions are built in the input space, enabling the identification of the most influential variables.

Domaines: Statistiques [stat]

Charlie Sire, Rodolphe Le Riche, Didier Rullière, Jérémy Rohmer, Lucie Pheulpin, et al.. Augmented Quantization: a General Approach to Mixture Models. UQ 2024 - SIAM Conference on Uncertainty Quantification, Society for Industrial and Applied Mathematics, Feb 2024, Trieste, Italy. ⟨hal-04527349⟩