Paper ID: 2208.07368

SOLBP: Second-Order Loopy Belief Propagation for Inference in Uncertain Bayesian Networks

Conrad D. Hougen, Lance M. Kaplan, Magdalena Ivanovska, Federico Cerutti, Kumar Vijay Mishra, Alfred O. Hero

In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to propagate both means and variances through sum-product networks derived from Bayesian networks, thereby characterizing epistemic uncertainty, or the uncertainty in the model itself. Alternatively, second-order belief propagation has been demonstrated for polytrees but not for general directed acyclic graph structures. In this work, we extend Loopy Belief Propagation to the setting of second-order Bayesian networks, giving rise to Second-Order Loopy Belief Propagation (SOLBP). For second-order Bayesian networks, SOLBP generates inferences consistent with those generated by sum-product networks, while being more computationally efficient and scalable.

Submitted: Aug 16, 2022