# Exploring Covariate and Concept Shift for Detection and Calibration of Out-of-Distribution Data

arXiv: https://arxiv.org/abs/2110.15231 · HTML: https://mlsanity.com/paper/2110.15231/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 50 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 30 of 35)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Tracking](https://mlsanity.com/paper/1504.06755/) (2015)
- [Multi-Task Curriculum Framework for Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2007.11330/) (2020)
- [Does Your Dermatology Classifier Know What It Doesn't Know? Detecting the Long-Tail of Unseen Conditions](https://mlsanity.com/paper/2104.03829/) (2021)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Decoupled Networks](https://mlsanity.com/paper/1804.08071/) (2018)

## Built on by (most cited first, 7 of 7)

- [Handling Out-of-Distribution Data: A Survey](https://mlsanity.com/paper/2507.21160/) (2025)
- [Unified Out-Of-Distribution Detection: A Model-Specific Perspective](https://mlsanity.com/paper/2304.06813/) (2023)
- [Dissecting Sample Hardness: A Fine-Grained Analysis of Hardness Characterization Methods for Data-Centric AI](https://mlsanity.com/paper/2403.04551/) (2024)
- [Leveraging Intermediate Representations for Better Out-of-Distribution Detection](https://mlsanity.com/paper/2502.12849/) (2025)
- [Defining the boundaries: challenges and advances in identifying cells in microscopy images](https://mlsanity.com/paper/2311.08269/) (2023)
- [AdverX-Ray: Ensuring X-Ray Integrity Through Frequency-Sensitive Adversarial VAEs](https://mlsanity.com/paper/2502.16610/) (2025)
- [ClusterMine: Robust Label-Free Visual Out-Of-Distribution Detection via Concept Mining from Text Corpora](https://mlsanity.com/paper/2511.07068/) (2025)

## Abstract (arXiv)

Moving beyond testing on in-distribution data works on Out-of-Distribution (OOD) detection have recently increased in popularity. A recent attempt to categorize OOD data introduces the concept of near and far OOD detection. Specifically, prior works define characteristics of OOD data in terms of detection difficulty. We propose to characterize the spectrum of OOD data using two types of distribution shifts: covariate shift and concept shift, where covariate shift corresponds to change in style, e.g., noise, and concept shift indicates a change in semantics. This characterization reveals that sensitivity to each type of shift is important to the detection and confidence calibration of OOD data. Consequently, we investigate score functions that capture sensitivity to each type of dataset shift and methods that improve them. To this end, we theoretically derive two score functions for OOD detection, the covariate shift score and concept shift score, based on the decomposition of KL-divergence for both scores, and propose a geometrically-inspired method (Geometric ODIN) to improve OOD detection under both shifts with only in-distribution data. Additionally, the proposed method naturally leads to an expressive post-hoc calibration function which yields state-of-the-art calibration performance on both in-distribution and out-of-distribution data. We are the first to propose a method that works well across both OOD detection and calibration and under different types of shifts. View project page at https://sites.google.com/view/geometric-decomposition.