Complexity, Information and Noise in Biological Modelling

Abstract: Mathematical modelling is of great importance in the sciences, but the scope and size of our models are limited by practical considerations. Since a fully quantum mechanical simulation of the world is not yet feasible, models of complex systems often focus on a limited subset of the entire dynamics, the rest being treated as nuisance variables or noise. But what is the connection between noise and complexity? In this talk we will attack this question for biological systems such as gene expression or population dynamics, where we encounter a spectrum of models at different resolutions. The complexity of many of these has long motivated research on the problem of model reduction, or simplification. We show that various known techniques for reducing stochastic models can be reinterpreted as an information-theoretic procedure that optimally encodes the original dynamics in a reduced model. This observation allows us to rephrase model reduction as a variational problem that can be tackled using standard techniques in stochastic optimisation, potentially paving the way for automated approaches in the future.