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Belief Propagation in Fuzzy Bayesian Networks

Fuzzy Bayesian networks (FBN) are a graphical machine learning model representation with variables which are simultaneously fuzzy and uncertain[2]. Bayesian networks (BN) are commonly used in machine learning. This is due to their statistical rationality, capacity for rigorous causal inference, and robustness in the face of noisy, partially missing and realistic data. They are also more easily human-interpretable than other machine learning representations such as neural networks, and experts can specify prior knowledge in a principled manner to guide the machine learning search. A wide range of search algorithms have been developed for structural and parameter inference, including structural EM [3] and MCMC. Classically, Bayesian networks use continuous (Gaussian) or multinomial variables. Similarly, a fuzzy model has a wide range of advantages. Fuzzy models are also robust in the face of noise-corrupted data. The use of linguistic terms aids human comprehension of the learnt model, and they are particularly useful when the data is insufficient to formulate a precise model. The need to specify membership functions also forces the designer to consider the semantic interpretation of the model parameterisation and construction more explicitly. For these reasons, FBN (which combine these advantages) may be useful. Theoretical analysis in current research[1] indicates that fuzzy variables can be more expressive than multinomial or continuous variables. FBN may also be used as part of an integrated sequence of machine learning techniques that include reversible dimensionality reduction techniques such as fuzzy cover clustering algorithms. This may allow larger problems to be addressed with FBN than with classic BN.