Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks

Benjamin Bloem-Reddy, Adam Foster, Emile Mathieu, Yee Whye Teh
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:476-485, 2018.

Abstract

Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with $\eta$ < 2, and admit tractable inference algorithms; we draw on previous results to show that $\eta$ > 2 cannot be generated by the forms of exchangeability used in existing random graph models. Preferential attachment models generate power law exponents greater than two, but have been of limited use as statistical models due to the inherent difficulty of performing inference in non-exchangeable models. Motivated by this gap, we design and implement inference algorithms for a recently proposed class of models that generates $\eta$ of all possible values. We show that although they are not exchangeable, these models have probabilistic structure amenable to inference. Our methods make a large class of previously intractable models useful for statistical inference.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-bloem-reddy18a, title = {Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks}, author = {Bloem-Reddy, Benjamin and Foster, Adam and Mathieu, Emile and Teh, Yee Whye}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {476--485}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/bloem-reddy18a/bloem-reddy18a.pdf}, url = {https://proceedings.mlr.press/r16/bloem-reddy18a.html}, abstract = {Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with $\eta$ < 2, and admit tractable inference algorithms; we draw on previous results to show that $\eta$ > 2 cannot be generated by the forms of exchangeability used in existing random graph models. Preferential attachment models generate power law exponents greater than two, but have been of limited use as statistical models due to the inherent difficulty of performing inference in non-exchangeable models. Motivated by this gap, we design and implement inference algorithms for a recently proposed class of models that generates $\eta$ of all possible values. We show that although they are not exchangeable, these models have probabilistic structure amenable to inference. Our methods make a large class of previously intractable models useful for statistical inference.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks %A Benjamin Bloem-Reddy %A Adam Foster %A Emile Mathieu %A Yee Whye Teh %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-bloem-reddy18a %I PMLR %P 476--485 %U https://proceedings.mlr.press/r16/bloem-reddy18a.html %V R16 %X Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with $\eta$ < 2, and admit tractable inference algorithms; we draw on previous results to show that $\eta$ > 2 cannot be generated by the forms of exchangeability used in existing random graph models. Preferential attachment models generate power law exponents greater than two, but have been of limited use as statistical models due to the inherent difficulty of performing inference in non-exchangeable models. Motivated by this gap, we design and implement inference algorithms for a recently proposed class of models that generates $\eta$ of all possible values. We show that although they are not exchangeable, these models have probabilistic structure amenable to inference. Our methods make a large class of previously intractable models useful for statistical inference. %Z Reissued by PMLR on 04 October 2026.
APA
Bloem-Reddy, B., Foster, A., Mathieu, E. & Teh, Y.W.. (2018). Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:476-485 Available from https://proceedings.mlr.press/r16/bloem-reddy18a.html. Reissued by PMLR on 04 October 2026.

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