A Consistent Histogram Estimator for Exchangeable Graph Models

Stanley Chan, Edoardo Airoldi
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(1):208-216, 2014.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-chan14, title = {A Consistent Histogram Estimator for Exchangeable Graph Models}, author = {Chan, Stanley and Airoldi, Edoardo}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {208--216}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {1}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/chan14.pdf}, url = {https://proceedings.mlr.press/v32/chan14.html}, 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.} }
Endnote
%0 Conference Paper %T A Consistent Histogram Estimator for Exchangeable Graph Models %A Stanley Chan %A Edoardo Airoldi %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-chan14 %I PMLR %P 208--216 %U https://proceedings.mlr.press/v32/chan14.html %V 32 %N 1 %X 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.
RIS
TY - CPAPER TI - A Consistent Histogram Estimator for Exchangeable Graph Models AU - Stanley Chan AU - Edoardo Airoldi BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/01/27 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-chan14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 1 SP - 208 EP - 216 L1 - http://proceedings.mlr.press/v32/chan14.pdf UR - https://proceedings.mlr.press/v32/chan14.html AB - 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. ER -
APA
Chan, S. & Airoldi, E.. (2014). A Consistent Histogram Estimator for Exchangeable Graph Models. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(1):208-216 Available from https://proceedings.mlr.press/v32/chan14.html.

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