Luca Brusa | Searcharxiv

arXiv2025

Dealing with separation problem in hidden Markov models with covariates based on a penalized maximum likelihood approach

A penalized maximum likelihood estimation approach is proposed for discrete-time hidden Markov models where covariates affect the observed responses and serial dependence is considered. The proposed penalized maximum likelihood method addresses the issue of latent state separation that typically occurs when this model is applied to binary and categorical response variables with a limited number of categories, resulting in extremely large estimates of the support points of the latent variable assumed with a discrete, left unspecified distribution. We also propose a cross-validation approach for jointly selecting the number of hidden states and the roughness of the penalty term. The proposal is illustrated through a simulation study comparing parameter estimation accuracy and computational efficiency across different estimation procedures. We also demonstrate the potential of this class of models through the analysis of longitudinal data collected during spinal anesthesia to monitor the occurrence of hypotension in patients, and we compare the results with those obtained from other standard models.

stat.ME↗

arXiv2024

Model-based clustering in simple hypergraphs through a stochastic blockmodel

We propose a model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co-authorship datasets. Our model generalizes the stochastic blockmodel for graphs and assumes the existence of latent node groups and hyperedges are conditionally independent given these groups. We first establish the generic identifiability of the model parameters. We then develop a variational approximation Expectation-Maximization algorithm for parameter inference and node clustering, and derive a statistical criterion for model selection. To illustrate the performance of our R package HyperSBM, we compare it with other node clustering methods using synthetic data generated from the model, as well as from a line clustering experiment and a co-authorship dataset.

stat.ME↗