Collective anomaly detection in High-dimensional VAR Models

TL;DR

This paper introduces a new lasso-based method for detecting sparse collective anomalies in high-dimensional VAR models, especially effective for short anomalous intervals, with proven error control and high power.

Contribution

It presents a novel lasso-based test statistic for detecting sparse changes in VAR coefficients, improving detection efficiency for short anomalies.

Findings

Controls Type 1 error effectively

Achieves asymptotic power tending to one

Demonstrated on taxi and EEG data

Abstract

There is increasing interest in detecting collective anomalies: potentially short periods of time where the features of data change before reverting back to normal behaviour. We propose a new method for detecting a collective anomaly in VAR models. Our focus is on situations where the change in the VAR coefficient matrix at an anomaly is sparse, i.e. a small number of entries of the VAR coefficient matrix change. To tackle this problem, we propose a test statistic for a local segment that is built on the lasso estimator of the change in model parameters. This enables us to detect a sparse change more efficiently and our lasso-based approach becomes especially advantageous when the anomalous interval is short. We show that the new procedure controls Type 1 error and has asymptotic power tending to one. The practicality of our approach is demonstrated through simulations and two data examples, involving New York taxi trip data and EEG data.