Invariant Anomaly Detection under Distribution Shifts: A Causal
  Perspective
João B. S. Carvalho Mengtao Zhang Robin Geyer Carlos Cotrini Joachim M. Buhmann
Anomaly detection (AD) is the machine learning task of identifying highly
discrepant abnormal samples by solely relying on the consistency of the normal
training samples. Under the constraints of a distribution shift, the assumption
that training samples and test samples are drawn from the same distribution
breaks down. In this work, by leveraging tools from causal inference we attempt
to increase the resilience of anomaly detection models to different kinds of
distribution shifts. We begin by elucidating a simple yet necessary statistical
property that ensures invariant representations, which is critical for robust
AD under both domain and covariate shifts. From this property, we derive a
regularization term which, when minimized, leads to partial distribution
invariance across environments. Through extensive experimental evaluation on
both synthetic and real-world tasks, covering a range of six different AD
methods, we demonstrated significant improvements in out-of-distribution
performance. Under both covariate and domain shift, models regularized with our
proposed term showed marked increased robustness. Code is available at:
https://github.com/JoaoCarv/invariant-anomaly-detection.