Group invariance principles for causal generative models
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Abstract (arXiv)
The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches. In our setting, the cause-mechanism relationship is assessed by comparing it against a null hypothesis through the application of random generic group transformations. We show that the group theoretic view provides a very general tool to study the structure of data generating mechanisms with direct applications to machine learning.
Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 May 2017.
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Citing papers per year: 2021: 8; 2022: 6; 2023: 4; 2024: 1; 2025: 0; 2026: 1.
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- 2021Towards Causal Representation Learningcited by 209
- 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
- 2021Independent mechanism analysis, a new concept?cited by 97
- 2021Counterfactual Zero-Shot and Open-Set Visual Recognitioncited by 95
- 2021Size-Invariant Graph Representations for Graph Classification Extrapolationscited by 84
- 2022Mechanistic Mode Connectivitycited by 50
- 2023Provably Learning Object-Centric Representationscited by 45
- 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Datacited by 42
- 2022From Statistical to Causal Learningcited by 40
- 2022Mitigating Data Heterogeneity in Federated Learning with Data Augmentationcited by 21
- 2026EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environmentscited by 20
- 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
8 more
- 2021Neural Networks for Learning Counterfactual G-Invariances from Single Environmentscited by 8
- 2023Independent Mechanism Analysis and the Manifold Hypothesiscited by 7
- 2021Demystifying Inductive Biases for β-VAE Based Architecturescited by 5
- 2022Probing the Robustness of Independent Mechanism Analysis for Representation Learningcited by 5
- 2021Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundationscited by 3
- 2023Disentangled Representation Learning with Transmitted Information Bottleneckcited by 3
- 2021Learning soft interventions in complex equilibrium systemscited by 2
- 2024Deep Learning-based Group Causal Inference in Multivariate Time-seriescited by 1
- 2026EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments6 Jul 2026
- 2024Deep Learning-based Group Causal Inference in Multivariate Time-series16 Jan 2024
- 2023Independent Mechanism Analysis and the Manifold Hypothesis20 Dec 2023
- 2023Disentangled Representation Learning with Transmitted Information Bottleneck3 Nov 2023
- 2023Nonparametric Identifiability of Causal Representations from Unknown Interventions1 Jun 2023
- 2023Provably Learning Object-Centric Representations23 May 2023
- 2022Mechanistic Mode Connectivity15 Nov 2022
- 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions25 Jul 2022
- 2022Probing the Robustness of Independent Mechanism Analysis for Representation Learning13 Jul 2022
- 2022Mitigating Data Heterogeneity in Federated Learning with Data Augmentation20 Jun 2022
- 2022From Statistical to Causal Learning1 Apr 2022
- 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data29 Mar 2022
8 more
- 2021Learning soft interventions in complex equilibrium systems10 Dec 2021
- 2021Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundations29 Oct 2021
- 2021Independent mechanism analysis, a new concept?9 Jun 2021
- 2021Neural Networks for Learning Counterfactual G-Invariances from Single Environments20 Apr 2021
- 2021Size-Invariant Graph Representations for Graph Classification Extrapolations8 Mar 2021
- 2021Counterfactual Zero-Shot and Open-Set Visual Recognition1 Mar 2021
- 2021Towards Causal Representation Learning22 Feb 2021
- 2021Demystifying Inductive Biases for β-VAE Based Architectures12 Feb 2021
- 2021Towards Causal Representation Learningcited by 209
- 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
- 2021Independent mechanism analysis, a new concept?cited by 97
- 2021Counterfactual Zero-Shot and Open-Set Visual Recognitioncited by 95
- 2021Size-Invariant Graph Representations for Graph Classification Extrapolationscited by 84
- 2022Mechanistic Mode Connectivitycited by 50
- 2023Provably Learning Object-Centric Representationscited by 45
- 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Datacited by 42
- 2022From Statistical to Causal Learningcited by 40
- 2022Mitigating Data Heterogeneity in Federated Learning with Data Augmentationcited by 21
- 2026EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environmentscited by 20
- 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
12 most cited of 20 All 20 (JSON)
- 2026EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments6 Jul 2026
- 2024Deep Learning-based Group Causal Inference in Multivariate Time-series16 Jan 2024
- 2023Independent Mechanism Analysis and the Manifold Hypothesis20 Dec 2023
- 2023Disentangled Representation Learning with Transmitted Information Bottleneck3 Nov 2023
- 2023Nonparametric Identifiability of Causal Representations from Unknown Interventions1 Jun 2023
- 2023Provably Learning Object-Centric Representations23 May 2023
- 2022Mechanistic Mode Connectivity15 Nov 2022
- 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions25 Jul 2022
- 2022Probing the Robustness of Independent Mechanism Analysis for Representation Learning13 Jul 2022
- 2022Mitigating Data Heterogeneity in Federated Learning with Data Augmentation20 Jun 2022
- 2022From Statistical to Causal Learning1 Apr 2022
- 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data29 Mar 2022
12 newest of 20 All 20 (JSON)