Laboratoire de Physique Théorique de la Matière Condensée

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Louise Budzynski (Sapienza, Roma)

Calendrier
Séminaires
Date
17.09.2024 10:45 - 11:45

Description

Phase transition in Inference in Epidemic Spreading

We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs, in the large-size limit. The typical inference tasks consist in computing observable of the posterior distribution of the epidemic model given observations taken from a ground truth (sometimes called planted) random trajectory. We give theoretical predictions on the posterior probability distribution of the trajectory of each individual, conditioned to observations on the state of individuals at given times, focusing on the Susceptible Infectious (SI) model.
In the Bayes-optimal condition, i.e. when true dynamic parameters are known, we provide predictions for the information theoretic limits of various inference tasks, in form of phase diagrams. We also identify a region, in the Bayes-Optimal setting, exhibiting a Replica Symmetry Breaking phase transition. When true parameters are unknown, we show how a maximum-likelihood procedure is able to recover them with mostly unaffected performance.