TwoSample Tests for Large Random Graphs Using Network Statistics
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Proceedings of the 2017 Conference on Learning Theory, PMLR 65:954977, 2017.
Abstract
We consider a twosample 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 twosample 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 twosample test that arises as the natural solution for this problem. We also show that the proposed test is minimax optimal for certain network statistics.
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