# Generalized Invariant Matching Property via LASSO

arXiv: https://arxiv.org/abs/2301.05975 · HTML: https://mlsanity.com/paper/2301.05975/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 14 Jan 2023.

## Builds on (most cited first, 13 of 13)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Domain Adaptation for Visual Applications: A Comprehensive Survey](https://mlsanity.com/paper/1702.05374/) (2017)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [Stabilizing Variable Selection and Regression](https://mlsanity.com/paper/1911.01850/) (2019)
- [Causal Inference from Slowly Varying Nonstationary Processes](https://mlsanity.com/paper/2012.13025/) (2020)
- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [An Invariant Matching Property for Distribution Generalization under Intervened Response](https://mlsanity.com/paper/2205.09162/) (2022)

## Built on by (most cited first, 2 of 2)

- [Low-Rank Approximation of Structural Redundancy for Self-Supervised Learning](https://mlsanity.com/paper/2402.06884/) (2024)
- [Mining Invariance from Nonlinear Multi-Environment Data: Binary Classification](https://mlsanity.com/paper/2404.15245/) (2024)

## Abstract (arXiv)

Learning under distribution shifts is a challenging task. One principled approach is to exploit the invariance principle via the structural causal models. However, the invariance principle is violated when the response is intervened, making it a difficult setting. In a recent work, the invariant matching property has been developed to shed light on this scenario and shows promising performance. In this work, by formulating a high-dimensional problem with intrinsic sparsity, we generalize the invariant matching property for an important setting when only the target is intervened. We propose a more robust and computation-efficient algorithm by leveraging a variant of Lasso, improving upon the existing algorithms.