Online sequential ensembling of predictive fuzzy systems

Evolving fuzzy systems (EFS) have enjoyed a wide attraction in the community to handle learning from data streams in an incremental, single-pass and transparent manner. The main concentration so far lied in the development of approaches for single EFS models, basically used for prediction purposes. Forgetting mechanisms have been used to increase their flexibility, especially for the purpose to adapt quickly to changing situations such as drifting data distributions. These require forgetting factors steering the degree of timely out-weighing older learned concepts, whose adequate setting in advance or in adaptive fashion is not an easy and not a fully resolved task. In this paper, we propose a new concept of learning fuzzy systems from data streams, which we call online sequential ensembling of fuzzy systems (OS-FS). It is able to model the recent dependencies in streams on a chunk-wise basis: for each new incoming chunk, a new fuzzy model is trained from scratch and added to the ensemble (of fuzzy systems trained before). This induces (i) maximal flexibility in terms of being able to apply variable chunk sizes according to the actual system delay in receiving target values and (ii) fast reaction possibilities in the case of arising drifts. The latter are realized with specific prediction techniques on new data chunks based on the sequential ensemble members trained so far over time. We propose four different prediction variants including various weighting concepts in order to put higher weights on the members with higher inference certainty during the amalgamation of predictions of single members to a final prediction. In this sense, older members, which keep in mind knowledge about past states, may get dynamically reactivated in the case of cyclic drifts, which induce dynamic changes in the process behavior which are re-occurring from time to time later. Furthermore, we integrate a concept for properly resolving possible contradictions among members with similar inference certainties. The reaction onto drifts is thus autonomously handled on demand and on the fly during the prediction stage (and not during model adaptation/evolution stage as conventionally done in single EFS models), which yields enormous flexibility. Finally, in order to cope with large-scale and (theoretically) infinite data streams within a reasonable amount of prediction time, we demonstrate two concepts for pruning past ensemble members, one based on atypical high error trends of single members and one based on the non-diversity of ensemble members. The results based on two data streams showed significantly improved performance compared to single EFS models in terms of a better convergence of the accumulated chunk-wise ahead prediction error trends, especially in the case of regular and cyclic drifts. Moreover, the more advanced prediction schemes could significantly outperform standard averaging over all members’ outputs. Furthermore, resolving contradictory outputs among members helped to improve the performance of the sequential ensemble further. Results on a wider range of data streams from different application scenarios showed (i) improved error trend lines over single EFS models, as well as over related AI methods OS-ELM and MLPs neural networks retrained on data chunks, and (ii) slightly worse trend lines than on-line bagged EFS (as specific EFS ensembles), but with around 100 times faster processing times (achieving low processing times way below requiring milli-seconds for single samples updates).