SOLBP: Second-Order Loopy Belief Propagation for Inference in Uncertain Bayesian Networks
This work addresses inference under epistemic uncertainty for researchers and practitioners in probabilistic graphical models, but it is incremental as it builds on existing second-order methods for polytrees.
The paper tackles the problem of inference in second-order uncertain Bayesian networks, where conditional probabilities are distributions, by extending Loopy Belief Propagation to this setting, resulting in SOLBP, which is more computationally efficient and scalable than existing methods like sum-product networks.
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.