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Undirected latent variable models represent an important class of graphical models that have been successfully developed to deal with various tasks. One common challenge in learning such models is to determine the number of hidden units that are unknown a priori. Although Bayesian nonparametrics have provided promising results in bypassing the model selection problem in learning directed Bayesian Networks, very little effort has been made toward applying Bayesian nonparametrics to learn undirected latent variable models. In this paper, we present the infinite exponential family Harmonium (iEFH), a bipartite undirected latent variable model that automatically determines the number of latent units from an unbounded pool. We also present two important extensions of iEFH to 1) multiview iEFH for dealing with heterogeneous data, and 2) infinite maximum-margin Harmonium (iMMH) for incorporating supervising side information to learn predictive latent features. We develop variational inference algorithms to learn model parameters. Our methods are computationally competitive because of the avoidance of selecting the number of latent units. Our extensive experiments on real image datasets and text datasets appear to demonstrate the benefits of iEFH and iMMH inherited from Bayesian nonparametrics and max-margin learning. Such results were not available until now and contribute to expanding the scope of Bayesian nonparametrics to learn the structures of undirected latent variable models. [ABSTRACT FROM AUTHOR]