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. 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 classication model that is expected 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 examples. The results indicate that Bayesian learning of large data sets, e.g. the MNIST database is realistic.