Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows

2026-03-12

AI Summary

This work proposes a novel approach to time series anomaly detection that addresses the limitations of traditional observation-likelihood-based methods, which often fail to capture structured temporal dynamics and misclassify anomalies as normal patterns. By introducing inductive biases into the latent space of conditional normalizing flows, the method models time series as discrete-time state-space systems, enforcing latent trajectories to conform to prescribed dynamical laws. Anomalies are then defined as deviations from these expected dynamics. The approach frames anomaly detection as a goodness-of-fit test for dynamic consistency—a formulation introduced here for the first time—and evaluates compliance of latent trajectories accordingly. Experiments on both synthetic and real-world datasets demonstrate its effectiveness in detecting anomalies in frequency, amplitude, and noise characteristics, achieving high detection performance alongside strong interpretability.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal dynamics, and therefore can assign high probability to anomalous or out-of-distribution samples. We address this structural limitation by relocating the notion of anomaly to a prescribed latent space. We introduce explicit inductive biases in conditional normalizing flows, modeling time-series observations within a discrete-time state-space framework that constrains latent representations to evolve according to prescribed temporal dynamics. Under this formulation, expected behavior corresponds to compliance with a specified distribution over latent trajectories, while anomalies are defined as violations of these dynamics. Anomaly detection is consequently reduced to a statistically grounded compliance test, such that observations are mapped to latent space and evaluated via goodness-of-fit tests against the prescribed latent evolution. This yields a principled decision rule that remains effective even in regions of high observation likelihood. Experiments on synthetic and real-world time-series demonstrate reliable detection of anomalies in frequency, amplitude, and observation noise, while providing interpretable diagnostics of model compliance.

Problem

• anomaly detection
• time-series
• normalizing flows
• latent space
• inductive biases

Innovation

• conditional normalizing flows
• inductive biases
• latent space
• state-space model
• anomaly detection