Cox process representation and inference for stochastic reaction-diffusion processes
This solves a long-standing problem in computational modeling for disciplines like biology and social sciences, though it is incremental as it builds on existing Cox process methods.
The authors tackled the inverse problem of learning stochastic reaction-diffusion processes from data by connecting them to spatio-temporal Cox processes, resulting in an efficient algorithm that shows excellent accuracy on numeric and real data examples from systems biology and epidemiology.
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.