Conditional normalizing flow for multivariate time series anomaly detection

Abstract

Multivariate time series data is becoming increasingly ubiquitous in various fields such as servers, industrial applications, and healthcare. However, detecting anomalies in such data is challenging due to its complex time-dependent, high-dimensional, and label scarcity. Aiming at this problem, this paper proposes an Attention Factorization Normalizing Flow (AFNF) algorithm for unsupervised multivariate time series anomaly detection. Our hypothesis is that anomalies are in a low-density region of the distribution. To transform the complex density of high-dimensional time series into a simple evaluable conditional density, we propose a time series factorization strategy and parameterize the conditional information generated by factorization in the time and attribute dimensions using an attention mechanism. Moreover, to compensate for the lack of temporal information due to the permutation invariance attention mechanism, a adjacency contrasting approach is proposed to model the local invariance of the time series. To provide long-term location information, a learnable global location encoding is introduced. Conditional normalizing flows are applied to evaluate the conditional probability of the observations. Finally, through extensive experiments on three real data sets, our method yielded the best results and its effectiveness in density estimation and anomaly detection is demonstrated.

Keywords: Anomaly detection; Attention mechanism; Multivariate time series; Normalizing flow.