However, we now trust that the reviewers are satisfied with the rigour and the correctness of the methodology and the proofs. Therefore, we can drop the proofs of lemmas 4.1 and 4.2 and make the proof of theorem 4.3 more concise so as to have space to expand the introduction to highlight the above points (explained in detail in section 3 below) and add a few words about the replica technique, and include a concluding section.

We study an explicit parametric model of documents, queries, and rel- evancy assessment for Information Retrieval (IR). Mean-field methods are applied to analyze the model and derive efficient practical algorithms to estimate the parameters in the problem. The hyperparameters are es- timated by a fast approximate leave-one-out cross-validation procedure based on the cavity method. The algorithm is further evaluated on several benchmark databases by comparing with standard algorithms in IR.

In this paper, we consider Tipping's relevance vector machine (RVM) [1] 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 expected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case.

In this paper, we consider Tipping's relevance vector machine (RVM) [1] 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 expected to give a very good approximation to exact Bayesian inference and contains the Laplace approximation as a special case.

In this paper, we consider Tipping's relevance vector machine (RVM)