Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models
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Abstract (arXiv)
For graph-valued data sampled iid from a distribution μ, the sample moments are computed with respect to a choice of metric. In this work, we equip the set of graphs with the pseudo-metric defined by the ℓ2 norm between the eigenvalues of the respective adjacency matrices. We use this pseudo metric and the respective sample moments of a graph valued data set to infer the parameters of a distribution hatμ and interpret this distribution as an approximation of μ. We verify experimentally that complex distributions μ can be approximated well taking this approach.
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References · 11
- 2017Community Detection and Stochastic Block Modelscited by 317
- 2020A Systematic Survey on Deep Generative Models for Graph Generationcited by 94
- 2016Fr'echet Regression for Random Objects with Euclidean Predictorscited by 57
- 2019Metrics for Graph Comparison: A Practitioner's Guidecited by 37
- 2013Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embeddingcited by 23
- 2019Modeling Network Populations via Graph Distancescited by 13
- 2015A spectral method for community detection in moderately-sparse degree-corrected stochastic block modelscited by 7
- 2018The eigenvalues of stochastic blockmodel graphscited by 7
- 2019Regularized Stochastic Block Model for robust community detection in complex networkscited by 2
- 2021Clustering of heterogeneous populations of networkscited by 2
- 2022Theoretical analysis and computation of the sample Frechet mean for sets of large graphs based on spectral informationcited by 2
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