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We investigate a generic problem of learning pairwise exponential familygraphical models with pairwise sufficient statistics defined by a globalmapping function, e.g., Mercer kernels. This subclass of pairwise graphicalmodels allow us to flexibly capture complex interactions among variables beyondpairwise product. We propose two $\ell_1$-norm penalized maximum likelihoodestimators to learn the model parameters from i.i.d. samples. The first one isa joint estimator which estimates all the parameters simultaneously. The secondone is a node-wise conditional estimator which estimates the parametersindividually for each node. For both estimators, we show that under properconditions the extra flexibility gained in our model comes at almost no cost ofstatistical and computational efficiency. We demonstrate the advantages of ourmodel over state-of-the-art methods on synthetic and real datasets.

Learning Pairwise Graphical Models with Nonlinear Sufficient Statistics