Statistical Anomaly Detection via Composite Hypothesis Testing for Markov Models

Abstract

Under Markovian assumptions, we leverage a Central Limit Theorem (CLT) for the empirical measure in the test statistic of the composite hypothesis Hoeffding test so as to establish weak convergence results for the test statistic, and, thereby, derive a new estimator for the threshold needed by the test. We first show the advantages of our estimator over an existing estimator by conducting extensive numerical experiments. We find that our estimator controls better for false alarms while maintaining satisfactory detection probabilities. We then apply the Hoeffding test with our threshold estimator to detecting anomalies in two distinct applications domains: one in communication networks and the other in transportation networks. The former application seeks to enhance cyber security and the latter aims at building smarter transportation systems in cities.