This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classi cation tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the`relevance vector machine' (RVM), a model of identical functional form to the popular and state-of-the-art`support vector machine' (SVM). We demonstrate that by exploiting a probabilistic Bayesian learning framework, we can derive accurate prediction models which typically utilise dramatically fewer basis functions than a comparable SVM while o¬ering a number of additional advantages. These include the bene ts of probabilistic predictions, automatic estimation of`nuisance' parameters, and the facility to utilise arbitrary basis functions (e.g. non-`Mercer' kernels). We detail the Bayesian framework and associated learning algorithm for the RVM, and give some illustrative examples of its application along with some comparative benchmarks. We o¬er some explanation for the exceptional degree of sparsity obtained, and discuss and demonstrate some of the advantageous features, and potential extensions, of Bayesian relevance learning.
It then uses a Relevance Vector Machine (RVM) REF to estimate the entries of the sparse vector.
Sparse Bayesian Learning and the Relevance Vector Machine
J. Mach. Learn. Res.
J. Mach. Learn. Res.
Computer Science