# Causality-oriented robustness: exploiting general noise interventions

arXiv: https://arxiv.org/abs/2307.10299 · HTML: https://mlsanity.com/paper/2307.10299/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 18 Jul 2023.

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

- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [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)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Gradient Matching for Domain Generalization](https://mlsanity.com/paper/2104.09937/) (2021)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Extending the WILDS Benchmark for Unsupervised Adaptation](https://mlsanity.com/paper/2112.05090/) (2021)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [Distributionally Robust Losses for Latent Covariate Mixtures](https://mlsanity.com/paper/2007.13982/) (2020)
- [When is invariance useful in an Out-of-Distribution Generalization problem ?](https://mlsanity.com/paper/2008.01883/) (2020)
- [Stabilizing Variable Selection and Regression](https://mlsanity.com/paper/1911.01850/) (2019)
- [CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Data](https://mlsanity.com/paper/2210.17283/) (2022)
- [Environment Invariant Linear Least Squares](https://mlsanity.com/paper/2303.03092/) (2023)
- [Causal Dantzig: fast inference in linear structural equation models with hidden variables under additive interventions](https://mlsanity.com/paper/1706.06159/) (2017)
- [Causal Regularization: On the trade-off between in-sample risk and out-of-sample risk guarantees](https://mlsanity.com/paper/2205.01593/) (2022)

## Built on by (most cited first, 5 of 5)

- [Multi-Domain Empirical Bayes for Linearly-Mixed Causal Representations](https://mlsanity.com/paper/2603.18404/) (2026)
- [Representation-Aware Distributionally Robust Optimization: A Knowledge Transfer Framework](https://mlsanity.com/paper/2509.09371/) (2025)
- [Anti-causal domain generalization: Leveraging unlabeled data](https://mlsanity.com/paper/2602.17187/) (2026)
- [2D Stability Selection: Design Jittering for Doubly Stable Feature Selection](https://mlsanity.com/paper/2605.02205/) (2026)
- [Prediction-Intervention Games and Invariant Sets](https://mlsanity.com/paper/2605.16828/) (2026)

## Abstract (arXiv)

Since distribution shifts are common in real-world applications, there is a pressing need to develop prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust optimization, either lack generalizability for unseen distributions or rely on postulated distance measures. Alternatively, causality offers a data-driven and structural perspective to robust predictions. However, the assumptions necessary for causal inference can be overly stringent, and the robustness offered by such causal models often lacks flexibility. In this paper, we focus on causality-oriented robustness and propose Distributional Robustness via Invariant Gradients (DRIG), a method that exploits general noise interventions in training data for robust predictions against unseen interventions, and naturally interpolates between in-distribution prediction and causality. In a linear setting, we prove that DRIG yields predictions that are robust among a data-dependent class of distribution shifts. Furthermore, we show that our framework includes anchor regression as a special case, and that it yields prediction models that protect against more diverse perturbations. We establish finite-sample results and extend our approach to semi-supervised domain adaptation to further improve prediction performance. Finally, we empirically validate our methods on synthetic simulations and on single-cell and intensive health care datasets.