Towards an Efficient Simulation-Based Anytime Inference in Subjective Bayesian Networks

Subjective Bayesian networks (SBN) integrate Bayesian Networks (BN) with Subjective Logic, enabling the representation of second-order uncertainty, denoting the uncertainty surrounding the probability distribution of an event. Although prior research predominantly centers on exact inference within the SBN framework, there is a notable dearth of exploration into the realm of approximate inference in SBN. Our work is specifically geared towards addressing this gap, focusing on the application of diverse sampling methodologies (i.e., forward and Gibbs sampling) for approximate inference in SBN. The primary contribution of this work lies not only in the introduction of approximate inference in SBN but also in the formulation of an “anytime” SBN inference algorithm. This implies that a best inference estimate can be obtained at any given moment, given trade-offs in the precision. Moreover, the allocation of computational resources is a customizable and potentially optimizable process. Through a rigorous series of experiments, we empirically demonstrate that the number of iterations to convergence decreases as we provide more samples for both forward and Gibbs sampling. Furthermore, we discover the difference between approximate and exact inference in belief ($\delta_{\text {belief }}$) and uncertainty ($\delta_{\text {uncertainty }}$) mass of subjective opinion becomes more unpredictable as the error gets large in BN probability. Lastly, in our experiments, we demonstrate the number of BN samples has a greater impact on $\delta_{\text {belief }}$ than the number of SBN iterations. These findings indicate that the family of greedy algorithms (based on local graded changes - such as gradients) can be a promising approach for finding optimal allocations of computational resources in this framework. The software assets produced and used in this work will be made available as an open source Python library.