Variational Bayes identification of acyclic dynamic networks

We study the problem of identifying dynamic networks that do not present loops. We model the impulse responses of the modules in the network as zero-mean independent Gaussian processes. The covariance matrices of the processes can be used to encode prior information, such as stability and smoothness, about the impulse responses of the modules. To estimate the modules, we approximate the joint posterior distribution of the impulse responses using a variational Bayes approach. In particular, using a mean-field approximation, we assume a factorization of the posterior where each factor corresponds to a single module. We estimate the kernel hyperparameters and the measurement noise variances by combining variational Bayes with the expectation-maximization method. We evaluate the performance of the identification procedure in a simulation experiment, where we compare to other kernel-based approaches.