# Distributionally Robust Post-hoc Classifiers under Prior Shifts

arXiv: https://arxiv.org/abs/2309.08825 · HTML: https://mlsanity.com/paper/2309.08825/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 56 references that are in the map.
- First posted on arXiv 16 Sep 2023.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Just Train Twice: Improving Group Robustness without Training Group Information](https://mlsanity.com/paper/2107.09044/) (2021)
- [BBN: Bilateral-Branch Network with Cumulative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/1912.02413/) (2019)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Improving Calibration for Long-Tailed Recognition](https://mlsanity.com/paper/2104.00466/) (2021)
- [Distribution Alignment: A Unified Framework for Long-tail Visual Recognition](https://mlsanity.com/paper/2103.16370/) (2021)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Simple data balancing achieves competitive worst-group-accuracy](https://mlsanity.com/paper/2110.14503/) (2021)
- [Learning with Instance-Dependent Label Noise: A Sample Sieve Approach](https://mlsanity.com/paper/2010.02347/) (2020)
- [Feature Space Augmentation for Long-Tailed Data](https://mlsanity.com/paper/2008.03673/) (2020)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [Deep Representation Learning on Long-tailed Data: A Learnable Embedding Augmentation Perspective](https://mlsanity.com/paper/2002.10826/) (2020)
- [The Devil is in Classification: A Simple Framework for Long-tail Object Detection and Instance Segmentation](https://mlsanity.com/paper/2007.11978/) (2020)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)
- [A Second-Order Approach to Learning with Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.11854/) (2020)
- [Coping with Label Shift via Distributionally Robust Optimisation](https://mlsanity.com/paper/2010.12230/) (2020)
- [To Smooth or Not? When Label Smoothing Meets Noisy Labels](https://mlsanity.com/paper/2106.04149/) (2021)
- [Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalization](https://mlsanity.com/paper/2202.06856/) (2022)

## Built on by (most cited first, 16 of 16)

- [Group Robust Classification Without Any Group Information](https://mlsanity.com/paper/2310.18555/) (2023)
- [Automatic Dataset Construction (ADC): Sample Collection, Data Curation, and Beyond](https://mlsanity.com/paper/2408.11338/) (2024)
- [GUARD: Generation-time LLM Unlearning via Adaptive Restriction and Detection](https://mlsanity.com/paper/2505.13312/) (2025)
- [Scoring Rules and Calibration for Imprecise Probabilities](https://mlsanity.com/paper/2410.23001/) (2024)
- [Efficient Bias Mitigation Without Privileged Information](https://mlsanity.com/paper/2409.17691/) (2024)
- [Fairness without Sensitive Attributes via Knowledge Sharing](https://mlsanity.com/paper/2409.18470/) (2024)
- [When VLMs Meet Image Classification: Test Sets Renovation via Missing Label Identification](https://mlsanity.com/paper/2505.16149/) (2025)
- [Class Distribution Shifts in Zero-Shot Learning: Learning Robust Representations](https://mlsanity.com/paper/2311.18575/) (2023)
- [Improving Group Robustness on Spurious Correlation via Evidential Alignment](https://mlsanity.com/paper/2506.11347/) (2025)
- [SCENIR: Visual Semantic Clarity through Unsupervised Scene Graph Retrieval](https://mlsanity.com/paper/2505.15867/) (2025)
- [Robust Preference Alignment via Directional Neighborhood Consensus](https://mlsanity.com/paper/2510.20498/) (2025)
- [Robust Representation Learning through Explicit Environment Modeling](https://mlsanity.com/paper/2604.26128/) (2026)
- [Variational Learning of Disentangled Representations](https://mlsanity.com/paper/2506.17182/) (2025)
- [Deep Minimax Classifiers for Imbalanced Datasets with a Small Number of Minority Samples](https://mlsanity.com/paper/2502.16948/) (2025)
- [An Efficient Plugin Method for Metric Optimization of Black-Box Models](https://mlsanity.com/paper/2503.02119/) (2025)
- [Environment-Robust Representation Learning with Empirical Bayes](https://mlsanity.com/paper/2606.05365/) (2026)

## Abstract (arXiv)

The generalization ability of machine learning models degrades significantly when the test distribution shifts away from the training distribution. We investigate the problem of training models that are robust to shifts caused by changes in the distribution of class-priors or group-priors. The presence of skewed training priors can often lead to the models overfitting to spurious features. Unlike existing methods, which optimize for either the worst or the average performance over classes or groups, our work is motivated by the need for finer control over the robustness properties of the model. We present an extremely lightweight post-hoc approach that performs scaling adjustments to predictions from a pre-trained model, with the goal of minimizing a distributionally robust loss around a chosen target distribution. These adjustments are computed by solving a constrained optimization problem on a validation set and applied to the model during test time. Our constrained optimization objective is inspired by a natural notion of robustness to controlled distribution shifts. Our method comes with provable guarantees and empirically makes a strong case for distributional robust post-hoc classifiers. An empirical implementation is available at https://github.com/weijiaheng/Drops.