Temporal-Conditioned Normalizing Flows for Multivariate Time Series Anomaly Detection

2026-03-10

AI Summary

This work addresses the challenge of anomaly detection in multivariate time series, where complex temporal dependencies and inherent uncertainty hinder reliable identification of rare events. To this end, we propose temporal conditional Normalizing Flows (tcNF), a novel autoregressive probabilistic model that, for the first time, integrates a temporal conditioning mechanism into normalizing flows. By dynamically modeling the joint probability distribution conditioned on historical observations, tcNF effectively captures both the evolving temporal patterns and associated uncertainties, enabling precise detection of low-probability anomalies. Extensive experiments demonstrate that tcNF significantly outperforms current state-of-the-art methods across multiple benchmark datasets, achieving high accuracy and strong robustness. The source code has been made publicly available to support reproducible research.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Data transparency and provenance

Abstract

This paper introduces temporal-conditioned normalizing flows (tcNF), a novel framework that addresses anomaly detection in time series data with accurate modeling of temporal dependencies and uncertainty. By conditioning normalizing flows on previous observations, tcNF effectively captures complex temporal dynamics and generates accurate probability distributions of expected behavior. This autoregressive approach enables robust anomaly detection by identifying low-probability events within the learned distribution. We evaluate tcNF on diverse datasets, demonstrating good accuracy and robustness compared to existing methods. A comprehensive analysis of strengths and limitations and open-source code is provided to facilitate reproducibility and future research.

Problem

• anomaly detection
• multivariate time series
• temporal dependencies
• uncertainty modeling
• normalizing flows

Innovation

• temporal-conditioned normalizing flows
• anomaly detection
• multivariate time series
• autoregressive modeling
• uncertainty quantification