Implementing Stochastic Bayesian Inference : Design of the Stochastic Number Generators

Bayes' rule can be computed stochastically using a simple Muller C-element, providing an efficient means of implementing Bayesian inference for autonomous robots. This provides such machines with the ability to make decisions when there is uncertainty in the data or models, enabling adaptation to unknown or dynamic environments. Because of the inherent memory effect in the C-element, the accuracy of this approach is sensitive to autocorrelation in the input signals. Previous work has shown that a simple rotating buffer is effective in mitigating the autocorrelation effects. However, prior studies have not addressed the practical aspects of designing the stochastic number generators (SNGs) required for creating the probabilistically-encoded values at the inputs. In this work, two approaches are evaluated: the use of linear feedback shift registers (LFSRs) and the use of low discrepancy sequence (LDS) generators. In the case of the LFSRs, this paper shows that there is no significant degradation in performance when several SNGs are shared with one LFSR provided a sufficient amount of circular shifting is used between each SNG. Results show an LDS generator is beneficial for lowering the amount of autocorrelation that is input into the C-element, resulting in improved performance.