A Consistent Histogram Estimator for Exchangeable Graph Models
Abstract
Exchangeable graph models (ExGM) subsume a number of popular network models. The mathematical object that characterizes an ExGM is termed a graphon. Finding scalable estimators of graphons, provably consistent, remains an open issue. In this paper, we propose a histogram estimator of a graphon that is provably consistent and numerically efficient. The proposed estimator is based on a sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree of a graph, then smooths the sorted graph using total variation minimization. The consistency of the SAS algorithm is proved by leveraging sparsity concepts from compressed sensing.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- 10.48550/arXiv.1402.1888
- arXiv:
- arXiv:1402.1888
- Bibcode:
- 2014arXiv1402.1888C
- Keywords:
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- Statistics - Methodology
- E-Print:
- 28 pages, 5 figures