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

David Baumgartner, Eliezer de Souza da Silva, Iñigo Urteaga
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:448-468, 2026.

Abstract

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed 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 reformulated as 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-baumgartner26a, title = {Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows}, author = {Baumgartner, David and da Silva, Eliezer de Souza and Urteaga, I\~{n}igo}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {448--468}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/baumgartner26a/baumgartner26a.pdf}, url = {https://proceedings.mlr.press/v337/baumgartner26a.html}, abstract = {Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed 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 reformulated as 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.} }
Endnote
%0 Conference Paper %T Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows %A David Baumgartner %A Eliezer de Souza da Silva %A Iñigo Urteaga %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-baumgartner26a %I PMLR %P 448--468 %U https://proceedings.mlr.press/v337/baumgartner26a.html %V 337 %X Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed 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 reformulated as 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.
APA
Baumgartner, D., da Silva, E.d.S. & Urteaga, I.. (2026). Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:448-468 Available from https://proceedings.mlr.press/v337/baumgartner26a.html.

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