Abstract
Statistical uncertainties are rarely incorporated into machine learning algorithms, especially for anomaly detection. Here we present the Bayesian Anomaly Detection And Classification (BADAC) formalism, which provides a unified statistical approach to classification and anomaly detection within a hierarchical Bayesian framework. BADAC deals with uncertainties by marginalising over the unknown, true, value of the data. Using simulated data with Gaussian noise as an example, BADAC is shown to be superior to standard algorithms in both classification and anomaly detection performance in the presence of uncertainties. Additionally, BADAC provides well-calibrated classification probabilities, valuable for use in scientific pipelines.
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Notes
- 1.
It is worth noting that this method of modeling the uncertainty fails when the measurement errors are zero, since the probability of classifying data \(\{d\}\) into a known class vanishes almost everywhere. In this case one could account for intraclass variability by modelling \(\mathbf{F}_{\tau }\) and \(\theta ^i_\tau \) explicitly.
- 2.
Strictly speaking we should write \(n_{\tau }\) since the number of samples in each class will be different but we suppress this to keep the notation relatively simple.
- 3.
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Acknowledgements
We thank Alireza Vafaei Sadr, Martin Kunz and Boris Leistedt for discussions and comments. We acknowledge the financial assistance of the National Research Foundation (NRF).
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Roberts, E., Bassett, B.A., Lochner, M. (2021). Bayesian Anomaly Detection and Classification for Noisy Data. In: Abraham, A., Siarry, P., Ma, K., Kaklauskas, A. (eds) Intelligent Systems Design and Applications. ISDA 2019. Advances in Intelligent Systems and Computing, vol 1181. Springer, Cham. https://doi.org/10.1007/978-3-030-49342-4_41
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