In this paper, we propose a statistical model for relevance-dependent biclustering to analyze relational data. The proposed model factorizes relational data into bicluster structure with two features: (1) each object in a cluster has a relevance value, which indicates how strongly the object relates to the cluster and (2) all clusters are related to at least one dense block. These features simplify the task of understanding the meaning of each cluster because only a few highly relevant objects need to be inspected. We introduced the Relevance-Dependent Bernoulli Distribution (R-BD) as a prior for relevance-dependent binary matrices and proposed the novel Relevance-Dependent Infinite Biclustering (R-IB) model, which automatically estimates the number of clusters. Posterior inference can be performed efficiently using a collapsed Gibbs sampler because the parameters of the R-IB model can be fully marginalized out. Experimental results show that the R-IB extracts more essential bicluster structure with better computational efficiency than conventional models. We further observed that the biclustering results obtained by R-IB facilitate interpretation of the meaning of each cluster.

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 ($\Gamma$P) 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 $\Gamma$P. 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 $\Gamma$P 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.

Latent variable models for relational data enable us to extract a co-cluster structure underlying observed relational data. The Infinite Relational Model (IRM) is a well-known relational model for discovering co-cluster structures with an unknown number of clusters. The IRM and several related models commonly assume that link probability between two objects depends only on their cluster assignment. However, relational models based on this assumption often lead us to extract many non-informative and unexpected clusters. This is because the cluster structures underlying real-world relationships are often blurred by biases that are inherent to individual objects. To overcome this problem, we propose a multilayered framework that extracts a clear co-cluster structure in the presence of objects' biases. Then, we propose a new model which is a special instance of the proposed framework that incorporates the IRM. Furthermore, we reveal that some relational models can be regarded as special cases of the proposed model. We present an efficient Gibbs sampler for posterior inference. Experiments conducted using real-world datasets confirm that the proposed model successfully extracts clear and interpretable cluster structures from blurred relational data.