Goodness-of-Fit Tests for Inhomogeneous Random Graphs
Jul 12, 2020
Speakers
Bhaswar B. Bhattacharya
Speaker · 0 followers
About
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.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 hypo…
Categories
AI & Data Science
Category · 10.8k presentations
Mathematics
Category · 2.4k presentations
About ICML 2020
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.
Like the format? Trust SlidesLive to capture your next event!
Professional recording and live streaming, delivered globally.
Sharing
Recommended Videos
Presentations on similar topic, category or speaker
Unbiased Risk Estimators Can Mislead: A Case Study of Learning with Complementary Labels
Watch later
Yu-Ting Chou, …
Prediction of Edverse Event on Drug-Drug Combination using Graph Embedding
Watch later
Ankita Saha, …
Bisection-Based Pricing for Repeated Contextual Auctions against Strategic Buyer
Watch later
Deep Active Learning Toward Crisis-related Tweets Classification
Watch later
Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation
Watch later
Recurrent Hierarchical Topic-Guided RNN for Language Generation
Watch later
Dandan Guo, …