mlsanityData to 7 Oct 2026

backShift: Learning causal cyclic graphs from unknown shift interventions

arXiv 1506.02494 ↗First posted 8 Jun 2015stat.ME stat.MLcited by 37

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Abstract (arXiv)

We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions ("shift interventions"). The location and strength of these interventions do not have to be known and can be estimated from the data. Our method, called backShift, only uses second moments of the data and performs simple joint matrix diagonalization, applied to differences between covariance matrices. We give a sufficient and necessary condition for identifiability of the system, which is fulfilled almost surely under some quite general assumptions if and only if there are at least three distinct experimental settings, one of which can be pure observational data. We demonstrate the performance on some simulated data and applications in flow cytometry and financial time series. The code is made available as R-package backShift.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jun 2015.

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Citing papers per year: 2021: 7; 2022: 5; 2023: 8; 2024: 4; 2025: 5; 2026: 8.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  2. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  3. 2023A Survey on Causal Discovery: Theory and Practicecited by 63
  4. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  5. 2021Causal Inference for Time series Analysis: Problems, Methods and Evaluationcited by 42
  6. 2022Active Learning for Optimal Intervention Design in Causal Modelscited by 30
  7. 2023Causal Modeling with Stationary Diffusionscited by 19
  8. 2021Matching a Desired Causal State via Shift Interventionscited by 16
  9. 2024Amortized Active Causal Induction with Deep Reinforcement Learningcited by 10
  10. 2021Obtaining Causal Information by Merging Datasets with MAXENTcited by 9
  11. 2025When Selection Meets Intervention: Additional Complexities in Causal Discoverycited by 9
  12. 2024Local Causal Discovery with Linear non-Gaussian Cyclic Modelscited by 7
25 more
  1. 2022Learning Relational Causal Models with Cycles through Relational Acyclificationcited by 6
  2. 2022Disentangling Mixtures of Unknown Causal Interventionscited by 6
  3. 2023A Survey of Methods, Challenges and Perspectives in Causalitycited by 6
  4. 2021Variance Minimization in the Wasserstein Space for Invariant Causal Predictioncited by 5
  5. 2023Meaningful Causal Aggregation and Paradoxical Confoundingcited by 5
  6. 2023Establishing Markov Equivalence in Cyclic Directed Graphscited by 5
  7. 2024Generative Intervention Models for Causal Perturbation Modelingcited by 4
  8. 2025Root Cause Analysis of Outliers in Unknown Cyclic Graphscited by 4
  9. 2026Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learningcited by 4
  10. 2021Learning soft interventions in complex equilibrium systemscited by 2
  11. 2022Learning domain-specific causal discovery from time seriescited by 2
  12. 2025Relational Causal Discovery with Latent Confounderscited by 2
  13. 2026Coarsening Linear Non-Gaussian Causal Models with Cyclescited by 2
  14. 2026CausaLab: A Scalable Environment for Interactive Causal Discovery Toward AI Scientistscited by 2
  15. 2021Disentangling Observed Causal Effects from Latent Confounders using Method of Momentscited by 1
  16. 2024Comparative Study of Causal Discovery Methods for Cyclic Models with Hidden Confounderscited by 1
  17. 2023Hypothesis testing on invariant subspaces of non-diagonalizable matrices with applications to network statisticscited by 0
  18. 2023Invariant Probabilistic Predictioncited by 0
  19. 2025On the Identifiability of Causal Graphs with the Invariance Principlecited by 0
  20. 2025Cyclic Counterfactuals under Shift-Scale Interventionscited by 0
  21. 2026Beyond identifiability: Learning causal representations with few environments and finite samplescited by 0
  22. 2026Causal Learning with the Invariance Principlecited by 0
  23. 2026SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targetscited by 0
  24. 2026Tensor-based second-order causal discoverycited by 0
  25. 2026Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent Statescited by 0