Bayesian Networks from a Reaction Theory Perspective

Abstract:Bayesian networks are foundational objects in machine learning, playing a central role as theoretical tools to understand and organize what we know about machine learning, including hierarchical Bayesian inference, belief propagation, variational inference, causality, deep learning, etc. Reaction network theory is a well-developed and deep mathematical discipline with a history dating back to the 1860s.

We show that every Bayesian networks can be described by a corresponding reaction network. This allows us to interpret biochemical reaction networks in living cells as performing inference and learning; to bring the tools of reaction network theory to the analysis of convergence problems in belief propagation; to compare reaction network dynamics with approximate inference algorithms in machine learning; and to design reaction networks that are capable of perform machine learning in a solution.