Anomaly detection

I don’t define what is abnormal, but I know it when I see it

2015-10-06 — 2022-10-19

Wherein anomaly detection is considered, with emphasis on high-dimensional and time-series methods, and an ocean-hydrology model outlier shaped like a distended whale is examined.

probability
statistics
Figure 1: An outlier in my ocean hydrology model.

Working out when something you see is not what you expect, especially when you’re not quite sure how to quantify your expectations. Detecting black swans, for example.

Nuit Blanche rounds up methods for high dimensional statistics.

1 Trend detection

e.g. Gnip Trend detection Nikolov (2012) looks fun and comes with a cute explanation of how you might do this nonparametrically.

2 Incoming

Sevvandi Kandanaarachchi is presenting some methods in a seminar right now: (Kandanaarachchi and Hyndman 2021; Kandanaarachchi, Hyndman, and Smith-Miles 2020; Kandanaarachchi 2021; Sevvandi Kandanaarachchi and Hyndman 2021; Talagala et al. 2020).

Related software:

3 References

Ahmad, Lavin, Purdy, et al. 2017. “Unsupervised Real-Time Anomaly Detection for Streaming Data.” Neurocomputing, Online Real-Time Learning Strategies for Data Streams,.
Chalapathy, and Chawla. 2019. “Deep Learning for Anomaly Detection: A Survey.” arXiv:1901.03407 [Cs, Stat].
Dauncey, Holmes, Williams, et al. 2024. “Approximations to the Fisher Information Metric of Deep Generative Models for Out-Of-Distribution Detection.”
Henrickson, Kolb, Lehmann, et al. 2015. “Trend Detection in Social Data.”
Kandanaarachchi. 2021. “Unsupervised Anomaly Detection Ensembles Using Item Response Theory.” arXiv:2106.06243 [Cs, Stat].
Kandanaarachchi, and Hyndman. 2021. “Dimension Reduction for Outlier Detection Using DOBIN.” Journal of Computational and Graphical Statistics.
Kandanaarachchi, Hyndman, and Smith-Miles. 2020. “Early Classification of Spatio-Temporal Events Using Partial Information.” PLOS ONE.
Kandanaarachchi, Munoz, Hyndman, et al. 2018. “On Normalization and Algorithm Selection for Unsupervised Outlier Detection.” 16/18. Monash Econometrics and Business Statistics Working Papers.
Kristiadi, Hein, and Hennig. 2022. “Being a Bit Frequentist Improves Bayesian Neural Networks.” In CoRR.
Kulinski, and Inouye. 2022. “Towards Explaining Distribution Shifts.”
Lopez, Camps, and Sznaier. 2015. “Robust Anomaly Detection Using Semidefinite Programming.” arXiv:1504.00905 [Cs, Math].
Ming, Fan, and Li. 2022. “POEM: Out-of-Distribution Detection with Posterior Sampling.”
Nikolov. 2012. “Trend or no trend : a novel nonparametric method for classifying time series.”
Ovadia, Fertig, Ren, et al. 2019. “Can You Trust Your Model’s Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift.” In Proceedings of the 33rd International Conference on Neural Information Processing Systems.
Pang, Shen, Cao, et al. 2021. “Deep Learning for Anomaly Detection: A Review.” ACM Computing Surveys.
Sevvandi Kandanaarachchi, and Hyndman. 2021. “Leave-One-Out Kernel Density Estimates for Outlier Detection.”
She, and Owen. 2010. “Outlier Detection Using Nonconvex Penalized Regression.”
Talagala, Hyndman, Smith-Miles, et al. 2020. “Anomaly Detection in Streaming Nonstationary Temporal Data.” Journal of Computational and Graphical Statistics.