A0907
Title: Hidden Markov linear quantile graphical model
Authors: Beatrice Foroni - University of Pisa, Dip. Economia e Management (Italy) [presenting]
Luca Merlo - Link Campus University (Italy)
Nicola Salvati - University of Pisa (Italy)
Lea Petrella - Sapienza University of Rome (Italy)
Abstract: Graphical models are crucial for understanding interdependencies among multiple variables in fields such as genome biology, finance, and environmental studies. These data often evolve over time and are influenced by hidden variables, necessitating models that capture these temporal dynamics. Hidden Markov models (HMMs) are particularly suited for this purpose. Previous work has explored the estimation of graphical models within HMMs using multivariate Gaussian emission distributions. However, the assumption of Gaussianity is often unrealistic for many practical applications. To address the need for modeling time-varying conditional dependencies without the Gaussian assumption, a sparse hidden Markov linear quantile graphical model (HMLQGM) is proposed. This approach leverages the conditional quantile to infer conditional independence structures. Parameter estimation is achieved through an expectation-maximization (EM) algorithm combined with a LASSO penalty, which facilitates the identification of the most relevant connections in the graph structure. Simulation studies demonstrate that HMLQGM effectively recovers dependency structures across various scenarios, highlighting its potential for broad applicability in analyzing complex, temporally evolving data.
