Jul 12, 2020

Hypothesis testing of random networks is an emerging area of modern research, especially in the high-dimensional regime, where the number of samples is smaller or comparable to the size of the graph. In this paper we consider the goodness-of-fit testing problem for large inhomogeneous random (IER) graphs, where given a (known) reference symmetric matrix Q ∈ [0, 1]^n × n and m independent samples from an IER graph given by an unknown symmetric matrix P ∈ [0, 1]^n × n, the goal is to test the hypothesis P=Q versus ||P-Q|| ≥ε, where ||·|| is some specified norm on symmetric matrices. Building on recent related work on two-sample testing for IER graphs, we derive the optimal minimax sample complexities for the goodness-of-fit problem in various natural norms, such as the Frobenius norm and the operator norm. We also propose practical implementations of natural test statistics, using their asymptotic distributions and through the parametric bootstrap. We compare the performances of the different tests in simulations, and show that the proposed tests outperform the baseline tests across various natural random graphs models.

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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