# Invariant Causal Prediction for Sequential Data

arXiv: https://arxiv.org/abs/1706.08058 · HTML: https://mlsanity.com/paper/1706.08058/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2017.

## Built on by (most cited first, 30 of 63)

- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalization](https://mlsanity.com/paper/2105.05612/) (2021)
- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [Out-of-distribution Generalization with Causal Invariant Transformations](https://mlsanity.com/paper/2203.11528/) (2022)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Alleviating Structural Distribution Shift in Graph Anomaly Detection](https://mlsanity.com/paper/2401.14155/) (2024)
- [Assumption violations in causal discovery and the robustness of score matching](https://mlsanity.com/paper/2310.13387/) (2023)
- [Predicting is not Understanding: Recognizing and Addressing Underspecification in Machine Learning](https://mlsanity.com/paper/2207.02598/) (2022)
- [Invariant Learning via Probability of Sufficient and Necessary Causes](https://mlsanity.com/paper/2309.12559/) (2023)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Invariant Policy Learning: A Causal Perspective](https://mlsanity.com/paper/2106.00808/) (2021)
- [Environment Invariant Linear Least Squares](https://mlsanity.com/paper/2303.03092/) (2023)
- [Optimization-based Causal Estimation from Heterogenous Environments](https://mlsanity.com/paper/2109.11990/) (2021)
- [Equivariance and Invariance Inductive Bias for Learning from Insufficient Data](https://mlsanity.com/paper/2207.12258/) (2022)
- [Meta-Causal Feature Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2208.10156/) (2022)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [Granger causal inference on DAGs identifies genomic loci regulating transcription](https://mlsanity.com/paper/2210.10168/) (2022)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Class Is Invariant to Context and Vice Versa: On Learning Invariance for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2208.03462/) (2022)
- [Understanding and Testing Generalization of Deep Networks on Out-of-Distribution Data](https://mlsanity.com/paper/2111.09190/) (2021)
- [Invariant Ancestry Search](https://mlsanity.com/paper/2202.00913/) (2022)
- [Structural restrictions in local causal discovery: identifying direct causes of a target variable](https://mlsanity.com/paper/2307.16048/) (2023)
- [Causal Discovery using Model Invariance through Knockoff Interventions](https://mlsanity.com/paper/2207.04055/) (2022)
- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [Out-of-Variable Generalization for Discriminative Models](https://mlsanity.com/paper/2304.07896/) (2023)
- [Multi-Domain Causal Discovery in Bijective Causal Models](https://mlsanity.com/paper/2504.21261/) (2025)
- [Scalable Causal Domain Adaptation](https://mlsanity.com/paper/2103.00139/) (2021)

## Abstract (arXiv)

We investigate the problem of inferring the causal predictors of a response Y from a set of d explanatory variables (X1,dots,Xd). Classical ordinary least squares regression includes all predictors that reduce the variance of Y. Using only the causal predictors instead leads to models that have the advantage of remaining invariant under interventions, loosely speaking they lead to invariance across different "environments" or "heterogeneity patterns". More precisely, the conditional distribution of Y given its causal predictors remains invariant for all observations. Recent work exploits such a stability to infer causal relations from data with different but known environments. We show that even without having knowledge of the environments or heterogeneity pattern, inferring causal relations is possible for time-ordered (or any other type of sequentially ordered) data. In particular, this allows detecting instantaneous causal relations in multivariate linear time series which is usually not the case for Granger causality. Besides novel methodology, we provide statistical confidence bounds and asymptotic detection results for inferring causal predictors, and present an application to monetary policy in macroeconomics.