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

TL;DR

This paper proposes a novel anomaly detection method for multivariate time-series that uses inductive biases in the latent space of conditional normalizing flows, improving detection accuracy and interpretability.

Contribution

It introduces a latent space framework with structured temporal dynamics, enabling anomaly detection through goodness-of-fit tests rather than likelihood alone.

Findings

Effective detection of anomalies in frequency, amplitude, and noise.

Provides interpretable diagnostics of model compliance.

Works reliably on synthetic and real-world data.

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.