A Differential Approach to Inference in Bayesian Networks

Understand

We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation.

• According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial derivatives of this polynomial with respect to each variable.
• We show that once such derivatives are made available, one can compute in constant-time answers to a large class of probabilistic queries, which are central to classical inference, parameter estimation, model validation and sensitivity analysis.
• We present a number of complexity results relating to the compilation of such polynomials and to the computation of their partial derivatives.