A0492
Title: Understanding dependencies in compositional data through graphical models
Authors: Agnese Maria Di Brisco - University of Piemonte Orientale (Italy) [presenting]
Roberto Ascari - University of Milano-Bicocca (Italy)
Federica Nicolussi - University of Milan (Italy)
Anna Maria Fiori - University of Milano-Bicocca (Italy)
Abstract: A methodology is introduced for analyzing (in)dependencies in compositional data using graphical models. Compositional data are first mapped to an unconstrained space, where Gaussian graphical models serve as a starting point for representing dependency structures. A novel subclass of these models is defined and proposed, tailored to respect the specific constraints of compositional data through block-diagonal covariance structures. An extension to the non-Gaussian setting is introduced, while preserving the compositional structure of the data. Estimation is based on block-diagonal covariance matrices, with model selection guided by a penalized likelihood criterion and cross-validation. The methodology is validated through applications to both simulated and real-world data, demonstrating its ability to reveal meaningful relationships in compositional contexts.
