Spatio-temporal mixture process estimation to detect population dynamical changes

Solange Pruilh (1, 2, 3) , Anne-Sophie Jannot (4, 2, 3) , Stéphanie Allassonnière (1, 2, 3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CRC (UMR_S_1138 / U1138) - Centre de Recherche des Cordeliers
3 HeKA - Health data- and model- driven Knowledge Acquisition
4 HEGP - Hôpital Européen Georges Pompidou [APHP]

Population monitoring is a challenge in many areas such as public health or ecology. We propose a method to model and monitor population distributions over space and time, in order to build an alert system for spatio-temporal data evolution. Assuming that mixture models can correctly model populations, we propose new versions of the Expectation-Maximization algorithm to better estimate both the number of clusters together with their parameters. We then combine these algorithms with a temporal statistical model, allowing to detect dynamical changes in population distributions, and name it a spatio-temporal mixture process (STMP). We test STMP on synthetic data, and consider several different behaviors of the distributions, to adjust this process. Finally, we validate STMP on a real data set of positive diagnosed patients to corona virus disease 2019. We show that our pipeline correctly models evolving real data and detects epidemic changes.

Mots clés: Gaussian Mixture Model; EM algorithms; Spatio-temporal data

Domaines: Statistiques [math.ST]; Machine Learning [stat.ML]; Méthodologie [stat.ME]; Applications [stat.AP]; Démographie; Santé publique et épidémiologie

Solange Pruilh, Anne-Sophie Jannot, Stéphanie Allassonnière. Spatio-temporal mixture process estimation to detect population dynamical changes. Artificial Intelligence in Medicine, 2022, 126, pp.102258. ⟨10.1016/j.artmed.2022.102258⟩. ⟨hal-02933217v3⟩