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On the Model Shrinkage Effect of Gamma Process Edge Partition Models
Iku Ohama · Issei Sato · Takuya Kida · Hiroki Arimura

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #187 #None
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.

Author Information

Iku Ohama (Panasonic Corporation)
Issei Sato (The University of Tokyo/RIKEN)
Takuya Kida (Hokkaido University)
Hiroki Arimura (Hokkaido University)

Hiroki Arimura * received the B.S. degree in 1988 in Physics, the M.S. and the Dr.Sci. degrees in 1990 and 1994, respectively, in Information Systems from Kyushu University. * He was from 1990 to 1994 a research associate, in 1995 a lecturer, in 1996 an associate professor in Kyushu Institute of Technology, and from 1996 to 2004, he was an as sociate professor in Kyushu University. Since 2006, he has been a professor of Hokkaido University. * He also joined National Institute of Informatics (NII) as an adjunct professor in 2008. Since 2016, he has been a director of GSB (Global Station for Big Data and Cybersecurity), GI-CoRE, Hokkaido University. * He has served as a planning group member from 2004 to 2008), as a advisory board member from 2011 to present for JSPS Frontiers of Science (FoS) Symposium including JSPS-NAS JAFoS, JSPS-AvH JGFoS etc. * His research interests include data mining, computational learning theory, information retrieval, artificial intelligence, and algorithm theory. He is a member of ACM, IEICE, IPSJ, and JSAI.

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