# Evaluating Robustness to Dataset Shift via Parametric Robustness Sets

arXiv: https://arxiv.org/abs/2205.15947 · HTML: https://mlsanity.com/paper/2205.15947/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Leveraging Unlabeled Data to Predict Out-of-Distribution Performance](https://mlsanity.com/paper/2201.04234/) (2022)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [BEGAN: Boundary Equilibrium Generative Adversarial Networks](https://mlsanity.com/paper/1703.10717/) (2017)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Assessing Generalization of SGD via Disagreement](https://mlsanity.com/paper/2106.13799/) (2021)
- [Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Tests](https://mlsanity.com/paper/2106.00545/) (2021)
- [Distributionally Robust Losses for Latent Covariate Mixtures](https://mlsanity.com/paper/2007.13982/) (2020)
- [Causally motivated Shortcut Removal Using Auxiliary Labels](https://mlsanity.com/paper/2105.06422/) (2021)
- [Mandoline: Model Evaluation under Distribution Shift](https://mlsanity.com/paper/2107.00643/) (2021)
- [Out-of-distribution Generalization in the Presence of Nuisance-Induced Spurious Correlations](https://mlsanity.com/paper/2107.00520/) (2021)
- [Regularizing towards Causal Invariance: Linear Models with Proxies](https://mlsanity.com/paper/2103.02477/) (2021)
- [Distributional Anchor Regression](https://mlsanity.com/paper/2101.08224/) (2021)

## Built on by (most cited first, 10 of 10)

- [A Survey on Evaluation of Out-of-Distribution Generalization](https://mlsanity.com/paper/2403.01874/) (2024)
- ["Why did the Model Fail?": Attributing Model Performance Changes to Distribution Shifts](https://mlsanity.com/paper/2210.10769/) (2022)
- [Learning from a Biased Sample](https://mlsanity.com/paper/2209.01754/) (2022)
- [Evaluating ML Robustness in GNSS Interference Classification, Characterization & Localization](https://mlsanity.com/paper/2409.15114/) (2024)
- [Evaluation of (Un-)Supervised Machine Learning Methods for GNSS Interference Classification with Real-World Data Discrepancies](https://mlsanity.com/paper/2503.23775/) (2025)
- [Decision-Focused Evaluation of Worst-Case Distribution Shift](https://mlsanity.com/paper/2407.03557/) (2024)
- [Model Monitoring and Robustness of In-Use Machine Learning Models: Quantifying Data Distribution Shifts Using Population Stability Index](https://mlsanity.com/paper/2302.00775/) (2023)
- [Achievable distributional robustness when the robust risk is only partially identified](https://mlsanity.com/paper/2502.02710/) (2025)
- [Data Heterogeneity Modeling for Trustworthy Machine Learning](https://mlsanity.com/paper/2506.00969/) (2025)
- [Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanisms](https://mlsanity.com/paper/2508.02812/) (2025)

## Abstract (arXiv)

We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where constraints on parameters yield a "robustness set" of plausible distributions and a corresponding worst-case loss over the set. While the loss under an individual parametric shift can be estimated via reweighting techniques such as importance sampling, the resulting worst-case optimization problem is non-convex, and the estimate may suffer from large variance. For small shifts, however, we can construct a local second-order approximation to the loss under shift and cast the problem of finding a worst-case shift as a particular non-convex quadratic optimization problem, for which efficient algorithms are available. We demonstrate that this second-order approximation can be estimated directly for shifts in conditional exponential family models, and we bound the approximation error. We apply our approach to a computer vision task (classifying gender from images), revealing sensitivity to shifts in non-causal attributes.