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The edge partition model (EPM) is a fundamental Bayesian nonparametric modelfor extracting an overlapping structure from binary matrix. The EPM adopts agamma process ($\Gamma$P) prior to automatically shrink the number of activeatoms. However, we empirically found that the model shrinkage of the EPM doesnot typically work appropriately and leads to an overfitted solution. Ananalysis of the expectation of the EPM's intensity function suggested that thegamma priors for the EPM hyperparameters disturb the model shrinkage effect ofthe internal $\Gamma$P. In order to ensure that the model shrinkage effect ofthe EPM works in an appropriate manner, we proposed two novel generativeconstructions of the EPM: CEPM incorporating constrained gamma priors, and DEPMincorporating Dirichlet priors instead of the gamma priors. Furthermore, allDEPM's model parameters including the infinite atoms of the $\Gamma$P priorcould be marginalized out, and thus it was possible to derive a truly infiniteDEPM (IDEPM) that can be efficiently inferred using a collapsed Gibbs sampler.We experimentally confirmed that the model shrinkage of the proposed modelsworks well and that the IDEPM indicated state-of-the-art performance ingeneralization ability, link prediction accuracy, mixing efficiency, andconvergence speed.

On the Model Shrinkage Effect of Gamma Process Edge Partition Models