# Online Time Series Anomaly Detection with State Space Gaussian Processes

arXiv: https://arxiv.org/abs/2201.06763 · HTML: https://mlsanity.com/paper/2201.06763/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 18 Jan 2022.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [Towards a Rigorous Evaluation of Time-series Anomaly Detection](https://mlsanity.com/paper/2109.05257/) (2021)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [RobustTAD: Robust Time Series Anomaly Detection via Decomposition and Convolutional Neural Networks](https://mlsanity.com/paper/2002.09545/) (2020)
- [Multi-View Stereo by Temporal Nonparametric Fusion](https://mlsanity.com/paper/1904.06397/) (2019)
- [Neural Contextual Anomaly Detection for Time Series](https://mlsanity.com/paper/2107.07702/) (2021)
- [Streaming Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1705.07131/) (2017)
- [Automatic Construction and Natural-Language Description of Nonparametric Regression Models](https://mlsanity.com/paper/1402.4304/) (2014)
- [Scalable Exact Inference in Multi-Output Gaussian Processes](https://mlsanity.com/paper/1911.06287/) (2019)
- [Building an Automated and Self-Aware Anomaly Detection System](https://mlsanity.com/paper/2011.05047/) (2020)
- [Online Anomaly Detection with Sparse Gaussian Processes](https://mlsanity.com/paper/1905.05761/) (2019)
- [Monte Carlo EM for Deep Time Series Anomaly Detection](https://mlsanity.com/paper/2112.14436/) (2021)

## Built on by (most cited first, 5 of 5)

- [TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysis](https://mlsanity.com/paper/2210.09693/) (2022)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [A Gaussian Process-based Streaming Algorithm for Prediction of Time Series With Regimes and Outliers](https://mlsanity.com/paper/2406.00570/) (2024)
- [Fourier-KAN-Mamba: A Novel State-Space Equation Approach for Time-Series Anomaly Detection](https://mlsanity.com/paper/2511.15083/) (2025)
- [Sequential Inference for Gaussian Processes: A Signal Processing Perspective](https://mlsanity.com/paper/2604.28163/) (2026)

## Abstract (arXiv)

We propose r-ssGPFA, an unsupervised online anomaly detection model for uni- and multivariate time series building on the efficient state space formulation of Gaussian processes. For high-dimensional time series, we propose an extension of Gaussian process factor analysis to identify the common latent processes of the time series, allowing us to detect anomalies efficiently in an interpretable manner. We gain explainability while speeding up computations by imposing an orthogonality constraint on the mapping from the latent to the observed. Our model's robustness is improved by using a simple heuristic to skip Kalman updates when encountering anomalous observations. We investigate the behaviour of our model on synthetic data and show on standard benchmark datasets that our method is competitive with state-of-the-art methods while being computationally cheaper.