Two-Sample Tests for Large Random Graphs Using Network Statistics

Debarghya Ghoshdastidar, Maurilio Gutzeit, Alexandra Carpentier, Ulrike von Luxburg
Proceedings of the 2017 Conference on Learning Theory, PMLR 65:954-977, 2017.

Abstract

We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the friendship networks on Facebook and LinkedIn. The practical approach to such problems is to compare the networks based on certain network statistics. In this paper, we present a general principle for two-sample hypothesis testing in such scenarios without making any assumption about the network generation process. The main contribution of the paper is a general formulation of the problem based on concentration of network statistics, and consequently, a consistent two-sample test that arises as the natural solution for this problem. We also show that the proposed test is minimax optimal for certain network statistics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v65-ghoshdastidar17a, title = {Two-Sample Tests for Large Random Graphs Using Network Statistics}, author = {Ghoshdastidar, Debarghya and Gutzeit, Maurilio and Carpentier, Alexandra and von Luxburg, Ulrike}, booktitle = {Proceedings of the 2017 Conference on Learning Theory}, pages = {954--977}, year = {2017}, editor = {Kale, Satyen and Shamir, Ohad}, volume = {65}, series = {Proceedings of Machine Learning Research}, month = {07--10 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v65/ghoshdastidar17a/ghoshdastidar17a.pdf}, url = {https://proceedings.mlr.press/v65/ghoshdastidar17a.html}, abstract = {We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the friendship networks on Facebook and LinkedIn. The practical approach to such problems is to compare the networks based on certain network statistics. In this paper, we present a general principle for two-sample hypothesis testing in such scenarios without making any assumption about the network generation process. The main contribution of the paper is a general formulation of the problem based on concentration of network statistics, and consequently, a consistent two-sample test that arises as the natural solution for this problem. We also show that the proposed test is minimax optimal for certain network statistics. } }
Endnote
%0 Conference Paper %T Two-Sample Tests for Large Random Graphs Using Network Statistics %A Debarghya Ghoshdastidar %A Maurilio Gutzeit %A Alexandra Carpentier %A Ulrike von Luxburg %B Proceedings of the 2017 Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2017 %E Satyen Kale %E Ohad Shamir %F pmlr-v65-ghoshdastidar17a %I PMLR %P 954--977 %U https://proceedings.mlr.press/v65/ghoshdastidar17a.html %V 65 %X We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the friendship networks on Facebook and LinkedIn. The practical approach to such problems is to compare the networks based on certain network statistics. In this paper, we present a general principle for two-sample hypothesis testing in such scenarios without making any assumption about the network generation process. The main contribution of the paper is a general formulation of the problem based on concentration of network statistics, and consequently, a consistent two-sample test that arises as the natural solution for this problem. We also show that the proposed test is minimax optimal for certain network statistics.
APA
Ghoshdastidar, D., Gutzeit, M., Carpentier, A. & von Luxburg, U.. (2017). Two-Sample Tests for Large Random Graphs Using Network Statistics. Proceedings of the 2017 Conference on Learning Theory, in Proceedings of Machine Learning Research 65:954-977 Available from https://proceedings.mlr.press/v65/ghoshdastidar17a.html.

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