A Differential Approach for Staged Trees

Abstract

Symbolic inference algorithms in Bayesian networks have now been applied in a variety of domains. These often require the computation of the derivatives of polynomials representing probabilities in such graphical models. In this paper we formalise a symbolic approach for staged trees, a model class making it possible to visualise asymmetric model constraints. We are able to show that the probability parametrisation associated to trees has several advantages over the one associated to Bayesian networks. We then continue to compute certain derivatives of staged trees’ polynomials and show their probabilistic interpretation. We are able to determine that these polynomials can be straightforwardly deduced by compiling a tree into an arithmetic circuit.