Application of the Evidence Procedure to Linear Problems in Signal Processing

The presented work addresses application of the evidence procedure to the field of signal processing where ill-posed estimation problems are frequently encountered. We base our analysis on the Relevance Vector Machines (RVM) technique originally proposed by M. Tipping. It effectively locally maximizes the evidence integral for linear kernel-based models. We extend the RVM technique by considering correlated additive Gaussian observation noise and complex-valued signals. We also show that grouping model parameters w, such that a single hyperparameter α k controls the kth cluster can be very effective in practice. In particular, it allows to cluster parameters w’s according to their potential relevance which in turns leads to highly improved generalization performance of the therewith parametrized models. The developed scheme is then illustratively applied to the problem of nonlinear system identification based on a discrete-time Volterra model. Similar ideas are used to analyze wireless channels from the channel measurement data. Results for synthetic as well as real-world data are presented.