Variational learning of autoregressive Mixtures of Experts for fully Bayesian hybrid system identification

This paper presents a new learning method for Mixture of Expert ARX (MEARX) models and its application to identification of PieceWise ARX (PWARX) hybrid systems models. While accurate deterministically-switched PWARX models are obtainable from probabilistically-switched MEARX models, important issues such as model structure selection (i.e. estimation of the number of modes and ARX lag orders) and estimation with sparse/noisy data remain open. This paper addresses these issues through a new variational Bayesian MEARX learning approximation. This not only permits computationally efficient estimates for MEARX/PWARX regressor weights and mode boundary parameters, but also allows for theoretically sound Bayesian model structure selection. Numerical hybrid system ID examples from the literature demonstrate the proposed approach.