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Abstract |
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. |
