Optimal Sequential Tests for Detection of Changes under Finite measure space for Finite Sequences of Networks

TL;DR

This paper develops an optimal sequential change detection method for finite sequences of networks, using a finite measure space and a new performance metric, demonstrating effectiveness on ERGMs and Erdős-Rényi networks.

Contribution

It introduces a novel finite measure space approach and an optimal sequential test for detecting distribution changes in network sequences, addressing computational challenges.

Findings

The proposed test effectively detects changes in network distributions.

Numerical results show good performance on ERGMs and Erdős-Rényi networks.

The method simplifies computation by avoiding normalization coefficients.

Abstract

This paper considers the change-point problem for finite sequences of networks. To avoid the difficulty of computing the normalization coefficient, such as in Exponential random graphical models (ERGMs) and Markov networks, we construct a finite measure space with measure ratio statistics. A new performance measure of detection delay is proposed to detect the changes in distribution of the network. And an optimal sequential test is proposed under the performance measure. The good performance of the optimal sequential test is illustrated numerically on ERGMs and Erdos-R\'{e}nyi network sequences.