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We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images that have been pre-segmented into smaller regions. We propose generalizations of the restricted Boltzmann machine (RBM) that are appropriate in this context and explore how to incorporate different assumptions about the relationship between the input sets and the target class within the RBM. In experiments on standard multiple-instance learning datasets, we demonstrate the competitiveness of approaches based on RBMs and apply the proposed variants to the problem of incoming mail classification.