Solving inference problems of Bayesian networks by probabilistic computing

Recently, probabilistic computing approach has shown its broad application in problems ranging from combinatorial optimizations and machine learning to quantum simulation where a randomly fluctuating bit called p-bit constitutes a basic building block. This new type of computing scheme tackles domain-specific and computationally hard problems that can be efficiently solved using probabilistic algorithms compared to classical deterministic counterparts. Here, we apply the probabilistic computing scheme to various inference problems of Bayesian networks with non-linear synaptic connections without auxiliary p-bits. The results are supported by nanomagnet-based SPICE (Simulation Program with Integrated Circuit Emphasis) results, behavioral model, and hardware implementations using a field-programmable gate array. Two types of Monte Carlo sampling methods are tested, namely rejection and importance samplings, where clamping of p-bits is applicable as in Boltzmann networks in the latter. Partial parallelism that can be used for the sequential update of each p-bit in Bayesian networks is presented. Finally, the model is directly applied to temporal Bayesian networks with relevant inference problems. We believe that the proposed approaches provide valuable tools and practical methods for various inference problems in Bayesian networks.