# Invariant Anomaly Detection under Distribution Shifts: A Causal Perspective

arXiv: https://arxiv.org/abs/2312.14329 · HTML: https://mlsanity.com/paper/2312.14329/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 62 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Builds on (most cited first, 30 of 41)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [Contrastive Adaptation Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1901.00976/) (2019)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Learning Memory-guided Normality for Anomaly Detection](https://mlsanity.com/paper/2003.13228/) (2020)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Representation Learning via Invariant Causal Mechanisms](https://mlsanity.com/paper/2010.07922/) (2020)
- [PANDA: Adapting Pretrained Features for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2010.05903/) (2020)
- [Quantifying the effects of data augmentation and stain color normalization in convolutional neural networks for computational pathology](https://mlsanity.com/paper/1902.06543/) (2019)
- [Student-Teacher Feature Pyramid Matching for Anomaly Detection](https://mlsanity.com/paper/2103.04257/) (2021)
- [Causality Inspired Representation Learning for Domain Generalization](https://mlsanity.com/paper/2203.14237/) (2022)
- [CFA: Coupled-hypersphere-based Feature Adaptation for Target-Oriented Anomaly Localization](https://mlsanity.com/paper/2206.04325/) (2022)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Improving Robustness Without Sacrificing Accuracy with Patch Gaussian Augmentation](https://mlsanity.com/paper/1906.02611/) (2019)
- [Mean-Shifted Contrastive Loss for Anomaly Detection](https://mlsanity.com/paper/2106.03844/) (2021)
- [A Mutual Information Maximization Perspective of Language Representation Learning](https://mlsanity.com/paper/1910.08350/) (2019)
- [Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Tests](https://mlsanity.com/paper/2106.00545/) (2021)

## Built on by (most cited first, 8 of 8)

- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [Subject Information Extraction for Novelty Detection with Domain Shifts](https://mlsanity.com/paper/2504.21247/) (2025)
- [DP-DGAD: A Generalist Dynamic Graph Anomaly Detector with Dynamic Prototypes](https://mlsanity.com/paper/2508.00664/) (2025)
- [When Unsupervised Domain Adaptation meets One-class Anomaly Detection: Addressing the Two-fold Unsupervised Curse by Leveraging Anomaly Scarcity](https://mlsanity.com/paper/2502.21022/) (2025)
- [Out of Context: Reliability in Multimodal Anomaly Detection Requires Contextual Inference](https://mlsanity.com/paper/2604.13252/) (2026)
- [ShiftSplit-AD: Separating Domain Shift from Defects in Foundation-Feature Visual Anomaly Detection](https://mlsanity.com/paper/2608.27610/) (2026)
- [When Identical Rows Disagree: From Benchmark Identifiability to Replication-Robust Anomaly Detection](https://mlsanity.com/paper/2609.29580/) (2026)
- [MAADBench: The Refreshable Paradigm for Anomaly Detection in Multi-Agent Systems](https://mlsanity.com/paper/2609.36556/) (2026)

## Abstract (arXiv)

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.