# Are we certain it's anomalous?

arXiv: https://arxiv.org/abs/2211.09224 · HTML: https://mlsanity.com/paper/2211.09224/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 68 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## Builds on (most cited first, 29 of 29)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks](https://mlsanity.com/paper/1703.10593/) (2017)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection](https://mlsanity.com/paper/1607.00148/) (2016)
- [Acquisition of Localization Confidence for Accurate Object Detection](https://mlsanity.com/paper/1807.11590/) (2018)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Multivariate Confidence Calibration for Object Detection](https://mlsanity.com/paper/2004.13546/) (2020)
- [Evaluating Real-time Anomaly Detection Algorithms - the Numenta Anomaly Benchmark](https://mlsanity.com/paper/1510.03336/) (2015)
- [An Evaluation of Anomaly Detection and Diagnosis in Multivariate Time Series](https://mlsanity.com/paper/2109.11428/) (2021)
- [Cooperative Training of Descriptor and Generator Networks](https://mlsanity.com/paper/1609.09408/) (2016)
- [TadGAN: Time Series Anomaly Detection Using Generative Adversarial Networks](https://mlsanity.com/paper/2009.07769/) (2020)
- [Differentiating through the Fr'echet Mean](https://mlsanity.com/paper/2003.00335/) (2020)
- [Learning the Predictability of the Future](https://mlsanity.com/paper/2101.01600/) (2021)
- [Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder](https://mlsanity.com/paper/2102.01331/) (2021)
- [Time Series Anomaly Detection for Cyber-Physical Systems via Neural System Identification and Bayesian Filtering](https://mlsanity.com/paper/2106.07992/) (2021)
- [Self Paced Deep Learning for Weakly Supervised Object Detection](https://mlsanity.com/paper/1605.07651/) (2016)
- [Multi-Scale One-Class Recurrent Neural Networks for Discrete Event Sequence Anomaly Detection](https://mlsanity.com/paper/2008.13361/) (2020)
- [Uncertainty-Aware Camera Pose Estimation from Points and Lines](https://mlsanity.com/paper/2107.03890/) (2021)
- [Dense Uncertainty Estimation](https://mlsanity.com/paper/2110.06427/) (2021)
- [Unsupervised Boosting-based Autoencoder Ensembles for Outlier Detection](https://mlsanity.com/paper/1910.09754/) (2019)

## Built on by (most cited first, 13 of 13)

- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Navigating the Metric Maze: A Taxonomy of Evaluation Metrics for Anomaly Detection in Time Series](https://mlsanity.com/paper/2303.01272/) (2023)
- [Hyperbolic Active Learning for Semantic Segmentation under Domain Shift](https://mlsanity.com/paper/2306.11180/) (2023)
- [Contracting Skeletal Kinematics for Human-Related Video Anomaly Detection](https://mlsanity.com/paper/2301.09489/) (2023)
- [Hyperbolic Learning with Multimodal Large Language Models](https://mlsanity.com/paper/2408.05097/) (2024)
- [Hyperbolic Metric Learning for Visual Outlier Detection](https://mlsanity.com/paper/2403.15260/) (2024)
- [Graph Inverse Style Transfer for Counterfactual Explainability](https://mlsanity.com/paper/2505.17542/) (2025)
- [AI on the Pulse: Real-Time Health Anomaly Detection with Wearable and Ambient Intelligence](https://mlsanity.com/paper/2508.03436/) (2025)
- [Hyp2Nav: Hyperbolic Planning and Curiosity for Crowd Navigation](https://mlsanity.com/paper/2407.13567/) (2024)
- [A Problem-Oriented Taxonomy of Evaluation Metrics for Time Series Anomaly Detection](https://mlsanity.com/paper/2511.18739/) (2025)
- [Seamless Monitoring of Stress Levels Leveraging a Universal Model for Time Sequences](https://mlsanity.com/paper/2407.03821/) (2024)
- [LADMIM: Logical Anomaly Detection with Masked Image Modeling in Discrete Latent Space](https://mlsanity.com/paper/2410.10234/) (2024)
- [Learning Action Hierarchies via Hybrid Geometric Diffusion](https://mlsanity.com/paper/2601.01914/) (2026)

## Abstract (arXiv)

The progress in modelling time series and, more generally, sequences of structured data has recently revamped research in anomaly detection. The task stands for identifying abnormal behaviors in financial series, IT systems, aerospace measurements, and the medical domain, where anomaly detection may aid in isolating cases of depression and attend the elderly. Anomaly detection in time series is a complex task since anomalies are rare due to highly non-linear temporal correlations and since the definition of anomalous is sometimes subjective. Here we propose the novel use of Hyperbolic uncertainty for Anomaly Detection (HypAD). HypAD learns self-supervisedly to reconstruct the input signal. We adopt best practices from the state-of-the-art to encode the sequence by an LSTM, jointly learned with a decoder to reconstruct the signal, with the aid of GAN critics. Uncertainty is estimated end-to-end by means of a hyperbolic neural network. By using uncertainty, HypAD may assess whether it is certain about the input signal but it fails to reconstruct it because this is anomalous; or whether the reconstruction error does not necessarily imply anomaly, as the model is uncertain, e.g. a complex but regular input signal. The novel key idea is that a detectable anomaly is one where the model is certain but it predicts wrongly. HypAD outperforms the current state-of-the-art for univariate anomaly detection on established benchmarks based on data from NASA, Yahoo, Numenta, Amazon, and Twitter. It also yields state-of-the-art performance on a multivariate dataset of anomaly activities in elderly home residences, and it outperforms the baseline on SWaT. Overall, HypAD yields the lowest false alarms at the best performance rate, thanks to successfully identifying detectable anomalies.