Analysis of Sparse Bayesian Learning
Anita Faul, Michael E. Tipping · The MIT Press eBooks · 2002
The recent introduction of the `relevance vector machine' has eectively demonstrated how sparsity may be obtained in generalised linear models within a Bayesian framework. Using a particular form of Gaussian parameter prior, `learning' is the maximisation, with respect to hyperparameters, of the marginal likelihood of the data. This paper studies the properties of that objective function, and demonstrates that conditioned on an individual hyperparameter, the marginal likelihood has a unique maximum which is computable in closed form. It is further shown that if a derived `sparsity criterion' is satis ed, this maximum is exactly equivalent to `pruning' the corresponding parameter from the model.