Marginal likelihood based model comparison in Fuzzy Bayesian Learning
This work provides a model comparison method for fuzzy Bayesian systems, but it is incremental as it extends prior work on the same paradigm.
The paper tackles the problem of selecting the most appropriate fuzzy rule base among competing alternatives in Fuzzy Bayesian Learning by calculating the marginal likelihood, showing its validity through synthetic examples and a real-world financial case study.
In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian approach. The present paper extends this work for selecting the most appropriate rule base among a set of competing alternatives, which best explains the data, by calculating the model evidence or marginal likelihood. We explain why this is an attractive alternative over simply minimizing a mean squared error metric of prediction and show the validity of the proposition using synthetic examples and a real world case study in the financial services sector.