Bayesian learning of structured dynamical systems

Abstract: In this thesis, we propose some Bayesian approaches to the identificationof structured dynamical systems. In particular, we consider block-orientedmodels in which a complex system is built starting from simple linear andnonlinear building blocks. Each building block has a Gaussian-process modelthat can be used to include prior information into the learning problem.The learning is then guided by Bayes’ theorem. In particular, we use anempirical Bayes approach to perform the identification of models with hyper-parameters. As the models considered in this thesis are, in general, intractable,we propose several approximation methods based on variational Bayes andMarkov-chain Monte Carlo sampling. To estimate the hyperpameters, wepropose iterative algorithms based on variational expectation maximizationand stochastic-approximation expectation maximization.The main contribution of the thesis is developed in Part II. Here, we firststudy uncertain-input systems and Wiener systems as the typical Gaussian-process models of two-block cascades. In addition, we propose a robust ap-proach for uncertain-input systems with outliers in the measurements. Then,we proceed considering more complex structures such as acyclic networksof linear dynamical systems, feedback interconnections of linear systems,and three-block nonlinear structures such as the Wiener-Hammerstein andHammerstein-Wiener cascades. Finally, we consider some problems relatedto quantized measurements: we propose an approximate estimator and weprovide a rigorous analysis of the statistical properties of quantization noise.All the models and methods are discussed in detail and accompanied byalgorithms and implementation details. The proposed techniques are shownin several simulation examples.