Joaquin Quiñonero Candela, Ole Winther
In this paper, we consider Tipping’s relevance vector machine (RVM)  and formalize an incremental training strategy as a variant of the expectation-maximization (EM) algorithm that we call Subspace EM (SSEM). Working with a subset of active basis functions, the sparsity of the RVM solution will ensure that the number of basis functions and thereby the computational complexity is kept low. We also introduce a mean ﬁeld approach to the intractable classiﬁcation model that is ex- pected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case. We test the algorithms on two large data sets with O(103 (cid:0) 104) examples. The re- sults indicate that Bayesian learning of large data sets, e.g. the MNIST database is realistic.