Thread by @charlinelelan

New insights about the limitations of density-based anomaly detection!
With @laurent_dinh, we show that perfect density model *cannot* guarantee anomaly detection.
📜Paper: arxiv.org/abs/2012.03808
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https://twitter.com/laurent_dinh/status/1335819731799056385

We demonstrate that the widespread intuition that an anomaly should have low density does not quite apply in general, irrespective of the dimension of the data or the inductive bias of the model.
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We deconstruct this expectation through the lens of invertible reparametrizations (e.g., Cartesian to polar coordinates). While density changes with the underlying representation, the status of inlier/outlier *does not*.
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In particular, it is possible to impose an arbitrary score to any point in a new representation of the same problem, which can mislead density-based anomaly detection methods into wrong anomaly detection results.
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What if we consider a fixed distribution (eg. the 2d gaussian below) which regular regions are known?🤔
Even in this case, we find that the status of inlier/outlier of two points can be swapped with a continuous invertible map.
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Density only conveys meaningful information for anomaly detection in a particular representation space. Density-based methods therefore need to make this underlying hypothesis explicit for reliable anomaly detection.
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We cannot fix density-based anomaly detection with more data 📊 or capacity 🗄 but we might require additional *prior knowledge*, e.g., about the task or meaning of the data.
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Excited to talk about our work at ICBINB @ #NeurIPS2020 workshop this Saturday!🌟
Poster: bit.ly/37LaUme
Slides: bit.ly/3gtGDMs
Workshop: neurips.cc/virtual/2020/p…
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