# Set Valued Predictions For Robust Domain Generalization

arXiv: https://arxiv.org/abs/2507.03146 · HTML: https://mlsanity.com/paper/2507.03146/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)
- [On Calibration and Out-of-domain Generalization](https://mlsanity.com/paper/2102.10395/) (2021)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)
- [The Effect of Natural Distribution Shift on Question Answering Models](https://mlsanity.com/paper/2004.14444/) (2020)
- [The iWildCam 2020 Competition Dataset](https://mlsanity.com/paper/2004.10340/) (2020)
- [Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalization](https://mlsanity.com/paper/2202.06856/) (2022)
- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments](https://mlsanity.com/paper/2106.09913/) (2021)
- [Learning Confidence Sets using Support Vector Machines](https://mlsanity.com/paper/1809.10818/) (2018)

## Built on by (most cited first, 1 of 1)

- [Training-Free Model Selection and Domain-Aware Score Calibration for First-Shot Anomalous Sound Detection](https://mlsanity.com/paper/2607.04526/) (2026)

## Abstract (arXiv)

Despite the impressive advancements in modern machine learning, achieving robustness in Domain Generalization (DG) tasks remains a significant challenge. In DG, models are expected to perform well on samples from unseen test distributions (also called domains), by learning from multiple related training distributions. Most existing approaches to this problem rely on single-valued predictions, which inherently limit their robustness. We argue that set-valued predictors could be leveraged to enhance robustness across unseen domains, while also taking into account that these sets should be as small as possible. We introduce a theoretical framework defining successful set prediction in the DG setting, focusing on meeting a predefined performance criterion across as many domains as possible, and provide theoretical insights into the conditions under which such domain generalization is achievable. We further propose a practical optimization method compatible with modern learning architectures, that balances robust performance on unseen domains with small prediction set sizes. We evaluate our approach on several real-world datasets from the WILDS benchmark, demonstrating its potential as a promising direction for robust domain generalization.