A Noise-Robust Fast Sparse Bayesian Learning Model

This paper utilizes the hierarchical model structure from the Bayesian Lasso in the Sparse Bayesian Learning process to develop a new type of probabilistic supervised learning approach. This approach has several performance advantages, such as being fast, sparse and especially robust to the variance in random noise. The hierarchical model structure in this Bayesian framework is designed in such a way that the priors do not only penalize the unnecessary complexity of the model but also depend on the variance of the random noise in the data. The hyperparameters in the model are estimated by the Fast Marginal Likelihood Maximization algorithm and can achieve low computational cost and faster learning process. We compare our methodology with two other popular Sparse Bayesian Learning models: The Relevance Vector Machine and a sparse Bayesian model that has been used for signal reconstruction in compressive sensing. We show that our method will generally provide more sparse solutions and be more flexible and stable when data is polluted by high variance noise.