On the Model Shrinkage Effect of Gamma Process Edge Partition Models

09/26/2017
by   Iku Ohama, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 8

research
11/06/2019

Regularization of Bayesian shrinkage priors and inference via geometrically / uniformly ergodic Gibbs sampler

Use of continuous shrinkage priors — with a "spike" near zero and heavy-...
research
01/25/2015

Infinite Edge Partition Models for Overlapping Community Detection and Link Prediction

A hierarchical gamma process infinite edge partition model is proposed t...
research
06/04/2023

Bayesian nonparametric modeling of latent partitions via Stirling-gamma priors

Dirichlet process mixtures are particularly sensitive to the value of th...
research
01/11/2014

Multiscale Shrinkage and Lévy Processes

A new shrinkage-based construction is developed for a compressible vecto...
research
02/12/2019

Bayesian cumulative shrinkage for infinite factorizations

There are a variety of Bayesian models relying on representations in whi...
research
08/26/2021

Selection of inverse gamma and half-t priors for hierarchical models: sensitivity and recommendations

While the importance of prior selection is well understood, establishing...
research
11/19/2012

Bayesian nonparametric models for ranked data

We develop a Bayesian nonparametric extension of the popular Plackett-Lu...

Please sign up or login with your details

Forgot password? Click here to reset