Online probabilistic learning for fuzzy inference system

• We develop a probability-based online learning method for fuzzy inference systems.
• Our online learning is built upon the statistical concept of maximum a posteriori.
• Experiments show that our method can balance between model accuracy and simplicity.
• Empirical results show our model can handle large and nonstationary data stream.

Online learning is a key methodology for expert systems to gracefully cope with dynamic environments. In the context of neuro-fuzzy systems, research efforts have been directed toward developing online learning methods that can update both system structure and parameters on the fly. However, the current online learning approaches often rely on heuristic methods that lack a formal statistical basis and exhibit limited scalability in the face of large data stream. In light of these issues, we develop a new Sequential Probabilistic Learning for Adaptive Fuzzy Inference System (SPLAFIS) that synergizes the Bayesian Adaptive Resonance Theory (BART) and Rule-Wise Decoupled Extended Kalman Filter (RDEKF) to generate the rule base structure and refine its parameters, respectively. The marriage of the BART and RDEKF methods, both of which are built upon the maximum a posteriori (MAP) principle rooted in the Bayes’ rule, offers a comprehensive probabilistic treatment and an efficient way for online structural and parameter learning suitable for large, dynamic data stream. To manage the model complexity without sacrificing its predictive accuracy, SPLAFIS also includes a simple procedure to prune inconsequential rules that have little contribution over time. The predictive accuracy, structural simplicity, and scalability of the proposed model have been exemplified in empirical studies using chaotic time series, stock index, and large nonlinear regression datasets.