Nonnegative Bayesian nonparametric factor models with completely random measures

We present a Bayesian nonparametric Poisson factorization model for modeling dense network data with an unknown and potentially growing number of overlapping communities. The construction is based on completely random measures and allows the number of communities to either increase with the number o...

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Bibliographic Details
Published in:Statistics and computing 2021-09, Vol.31 (5), Article 63
Main Authors: Ayed, Fadhel, Caron, François
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Bayesian analysis
Markov chains
Mathematics and Statistics
Nonparametric statistics
Polynomials
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:We present a Bayesian nonparametric Poisson factorization model for modeling dense network data with an unknown and potentially growing number of overlapping communities. The construction is based on completely random measures and allows the number of communities to either increase with the number of nodes at a specified logarithmic or polynomial rate, or be bounded. We develop asymptotics for the number and size of the communities of the network and derive a Markov chain Monte Carlo algorithm for targeting the exact posterior distribution for this model. The usefulness of the approach is illustrated on various real networks.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-021-10037-3