Inference of Hyperparameters in Agent-based Dynamics

Dynamic processes on graphs are fundamental to modeling a wide range of real-world phenomena, including the spread of epidemics, information diffusion in social networks and neural cascades. In such cases, the parameters governing these processes are often unknown, and for an accurate description of the processes they must be deduced from observations that are often incomplete or even erroneous. This thesis addresses the challenge of inferring the governing parameters of discrete-time Markov processes on graphs using observations of the time series. A primary focus is placed on the notoriously difficult task of inferring the network topology itself from partial observations. In the past, inference methods have been proposed for non-recurrent models, i.e. those in which the system cannot return to a previous state, which are simpler to address due to the small number of possible single-node trajectories. When considering recurrent models, this number grows exponentially with the time horizon, making their treatment substantially harder. This thesis introduces an innovative inference technique tailored for recurrent models, with a specific emphasis on epidemic spreading models. Central to this approach are two key methodologies: Belief Propagation (BP), an algorithm that approximates the posterior probability distributions of the trajectories conditioned to the observations, and the Tensor Train approximation, which enables efficient representation and manipulation of multi-variable functions, essential for network inference. The method was tested on the Susceptible-Infectious-Susceptible (SIS) model, showing successful reconstruction of the underlying network from limited data. Consequently, this thesis opens up new avenues for applications in diverse fields such as epidemiology, social dynamics, and computational neuroscience. The results represent a substantial advancement in the field of network inference for dynamic stochastic processes, offering a robust toolset for understanding complex systems governed by recurrent interactions.