# An Invariant Matching Property for Distribution Generalization under Intervened Response

arXiv: https://arxiv.org/abs/2205.09162 · HTML: https://mlsanity.com/paper/2205.09162/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 18 May 2022.

## Builds on (most cited first, 6 of 6)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [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)
- [Estimation of the Evolutionary Spectra with Application to Stationarity Test](https://mlsanity.com/paper/1802.09053/) (2018)

## Built on by (most cited first, 3 of 3)

- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [Generalized Invariant Matching Property via LASSO](https://mlsanity.com/paper/2301.05975/) (2023)
- [Low-Rank Approximation of Structural Redundancy for Self-Supervised Learning](https://mlsanity.com/paper/2402.06884/) (2024)

## Abstract (arXiv)

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the fundamental invariance principle, it is often assumed that the conditional distribution of the response given its predictors remains the same across environments. However, this assumption might be violated in practical settings when the response is intervened. In this work, we investigate a class of model with an intervened response. We identify a novel form of invariance by incorporating the estimates of certain features as additional predictors. Effectively, we show this invariance is equivalent to having a deterministic linear matching that makes the generalization possible. We provide an explicit characterization of the linear matching and present our simulation results under various intervention settings.