Invariant Causal Prediction with Local Models (2401.05218v2)
Abstract: We consider the task of identifying the causal parents of a target variable among a set of candidates from observational data. Our main assumption is that the candidate variables are observed in different environments which may, under certain assumptions, be regarded as interventions on the observed system. We assume a linear relationship between target and candidates, which can be different in each environment with the only restriction that the causal structure is invariant across environments. Within our proposed setting we provide sufficient conditions for identifiability of the causal parents and introduce a practical method called L-ICP ($\textbf{L}$ocalized $\textbf{I}$nvariant $\textbf{Ca}$usal $\textbf{P}$rediction), which is based on a hypothesis test for parent identification using a ratio of minimum and maximum statistics. We then show in a simplified setting that the statistical power of L-ICP converges exponentially fast in the sample size, and finally we analyze the behavior of L-ICP experimentally in more general settings.
- Invariant risk minimization. CoRR, abs/1907.02893, 2019.
- Multi-task learning of order-consistent causal graphs. In Advances in Neural Information Processing Systems 34, pages 11083–11095, 2021.
- R. Christiansen and J. Peters. Switching regression models and causal inference in the presence of discrete latent variables. Journal of Machine Learning Research, 21:41:1–41:46, 2020.
- The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26:404–413, 1934.
- D. Constales. A closed formula for the Moore-Penrose generalized inverse of a complex matrix of given rank. Acta Mathematica Hungarica, 80:83–88, 1998.
- S. Dasgupta and A. Gupta. An elementary proof of a theorem of johnson and lindenstrauss. Random Structures and Algorithms, 22:60–65, 2003.
- D. Donoho and J. Jin. Higher criticism for detecting sparse heterogeneous mixtures. Annals of Statistics, 32:962–994, 2004.
- Modelling extremal events: for insurance and finance, volume 33. Springer Science & Business Media, 2013.
- Extremes of independent chi-square random vectors. Extremes, 15, 03 2012.
- Journal of Causal Inference, 6:20170016, 2018.
- Causal discovery and forecasting in nonstationary environments with state-space models. In Proceedings of the 36th International Conference on Machine Learning, pages 2901–2910, 2019.
- Causal discovery from heterogeneous/nonstationary data. Journal of Machine Learning Research, 21:1–53, 2020.
- Y. I. Ingster. Some problems of hypothesis testing leading to infinitely divisible distributions. Mathematical Methods of Statistics, 6:47–69, 1997.
- Invariant ancestry search. In Proceedings of the 39th International Conference on Machine Learning, pages 15832–15857, 2022.
- Joint causal inference from multiple contexts. Journal of Machine Learning Research, 21:1–108, 2020.
- Regularizing towards causal invariance: Linear models with proxies. In Proceedings of the 38th International Conference on Machine Learning, volume 139, pages 8260–8270, 2021.
- Information-theoretic causal discovery and intervention detection over multiple environments. In Proceedings of the 37th AAAI Conference on Artificial Intelligence, pages 9171–9179, 2023.
- J. Pearl. Causal inference in statistics : a primer. Chichester, West Sussex, 2016.
- R. Penrose. A generalized inverse for matrices. Mathematical Proceedings of the Cambridge Philosophical Society, 51:406–413, 1955.
- J. Peters and P. Bühlmann. Identifiability of gaussian structural equation models with equal error variances. Biometrika, 101:219–228, 2014.
- Causal inference by using invariant prediction: identification and confidence intervals. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 78:947–1012, 2016.
- Invariant causal prediction for sequential data. Journal of the American Statistical Association, 114:1264–1276, 2019.
- Identifying the causes of pyrocumulonimbus (pyrocb). CoRR, abs/2211.08883, 2022.
- B.-W. Shen. Nonlinear feedback in a five-dimensional lorenz model. Journal of the Atmospheric Sciences, 71:1701 – 1723, 2014.
- S. Shimizu. Joint estimation of linear non-gaussian acyclic models. Neurocomputing, 81:104–107, 2012.
- A linear non-gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7:2003–2030, 2006.
- P. Spirtes. An anytime algorithm for causal inference. In Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, pages 278–285, 2001.
- Anomaly detection for a large number of streams: A permutation-based higher criticism approach. 2021.
- On calibration and out-of-domain generalization. In Advances in Neural Information Processing Systems 34, pages 2215–2227, 2021.
- Causal discovery with heterogeneous observational data. In Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, pages 2383–2393, 2022.