Inference in spreading processes with neural-network priors.

Area of Science:

• Complex Systems
• Statistical Inference
• Machine Learning

Background:

• Stochastic processes on graphs model epidemics, but often assume random initial states.
• Real-world systems have node covariates influencing initial states, a factor often ignored in inference.

Purpose of the Study:

• To model the initial state of stochastic processes on graphs as a neural network function of node covariates.
• To develop a Bayesian inference framework that leverages both process dynamics and covariate information.
• To analyze the impact of neural network priors on state and trajectory recovery.

Main Methods:

• A hybrid belief propagation and approximate message passing (BP-AMP) algorithm was derived.
• The algorithm integrates spreading dynamics with information from node covariates.
• Performance was compared against methods using only spreading or only covariate information.

Main Results:

• The proposed model enhances the recovery of initial states and spreading trajectories by incorporating covariate information.
• First-order phase transitions were observed in some regimes, particularly with Rademacher distributed neural network weights.
• A statistical-to-computational gap emerged where perfect recovery is theoretically possible but computationally unachievable.

Conclusions:

• Integrating neural network priors based on node covariates improves inference for stochastic processes on graphs.
• Phase transitions and the resulting statistical-to-computational gap present challenges for accurate state estimation.
• The BP-AMP algorithm offers a robust approach to handling complex inference problems with integrated covariate information.