On the Model Shrinkage Effect of Gamma Process Edge Partition Models Iku Ohama
The edge partition model (EPM) is a fundamental Bayesian nonparametric model for extracting an overlapping structure from binary matrix. The EPM adopts a gamma process (ΓP) prior to automatically shrink the number of active atoms. However, we empirically found that the model shrinkage of the EPM does not typically work appropriately and leads to an overfitted solution. An analysis of the expectation of the EPM's intensity function suggested that the gamma priors for the EPM hyperparameters disturb the model shrinkage effect of the internal ΓP. In order to ensure that the model shrinkage effect of the EPM works in an appropriate manner, we proposed two novel generative constructions of the EPM: CEPM incorporating constrained gamma priors, and DEPM incorporating Dirichlet priors instead of the gamma priors. Furthermore, all DEPM's model parameters including the infinite atoms of the ΓP prior could be marginalized out, and thus it was possible to derive a truly infinite DEPM (IDEPM) that can be efficiently inferred using a collapsed Gibbs sampler. We experimentally confirmed that the model shrinkage of the proposed models works well and that the IDEPM indicated state-of-the-art performance in generalization ability, link prediction accuracy, mixing efficiency, and convergence speed.
This paper presents several variants of GP-EPM to solve the shrinkage problem of GP-EPM for modelling relational data. The proposed models are demonstrated to have better link prediction performance than GP-EPM by estimating the number of latent communities better. 
Note I always point out this problem to my students as:  the model is
"non-identifiable".   Don't get me wrong, the whole body of work,
EPM, etc., is fabulous, but identifiability was always an important lesson in class.
The paper is well-written and easy to follow. The proposed models are well-motivated empirically with synthetic examples and then with theoretical analysis. To me, the main contribution of the paper is it points out that the obvious unidentifiability issue in GP-EPM can, interestingly, be a problem in some real cases. The proposed CEPM is just a naive model, while DEPM is a simple but intuitive solution and DEPM to IDEPM is like mapping the Dirichlet distribution to Dirichlet process. The solutions are not novel but straightforward to the problem. Finally the experimental results support the main claims, which makes it an interesting paper.
Note, in 4.3 (line 187), you say "one remarkable property".  This *should* be well known in the non-parametric community.  The result is perhaps the simplest case of the main theorem in "Poisson Latent Feature Calculus for Generalized Indian Buffet Processes", Lancelot James, 2014.  The terms in $K_+$ in (5) are the marginal for the gamma process.  The theorem can be pretty much written down without derivation using standard results.
This is a good paper cleaning up the obvious flaws in EPM and its implementation. It covers good though routine theory, and experimental work.  Section 4.3 should be rewritten.
However, I belief the important issue of identifiability should be better discussed and more experiments done.  For instance, a reviewer points out that the problem is partially overcome more recently using stronger priors.  Clearly, identifiability is something we require to make theory easier and priors more interpretable.  It is not strictly necessary, though it is routinely expected in the statistics community.
Anyway, would be good to see more discussion of the issues and further experimental investigation.