# Group invariance principles for causal generative models

arXiv: https://arxiv.org/abs/1705.02212 · HTML: https://mlsanity.com/paper/1705.02212/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2017.

## Built on by (most cited first, 20 of 20)

- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
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- [Mechanistic Mode Connectivity](https://mlsanity.com/paper/2211.08422/) (2022)
- [Provably Learning Object-Centric Representations](https://mlsanity.com/paper/2305.14229/) (2023)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Mitigating Data Heterogeneity in Federated Learning with Data Augmentation](https://mlsanity.com/paper/2206.09979/) (2022)
- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions](https://mlsanity.com/paper/2207.12067/) (2022)
- [Neural Networks for Learning Counterfactual G-Invariances from Single Environments](https://mlsanity.com/paper/2104.10105/) (2021)
- [Independent Mechanism Analysis and the Manifold Hypothesis](https://mlsanity.com/paper/2312.13438/) (2023)
- [Demystifying Inductive Biases for β-VAE Based Architectures](https://mlsanity.com/paper/2102.06822/) (2021)
- [Probing the Robustness of Independent Mechanism Analysis for Representation Learning](https://mlsanity.com/paper/2207.06137/) (2022)
- [Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundations](https://mlsanity.com/paper/2110.15595/) (2021)
- [Disentangled Representation Learning with Transmitted Information Bottleneck](https://mlsanity.com/paper/2311.01686/) (2023)
- [Learning soft interventions in complex equilibrium systems](https://mlsanity.com/paper/2112.05729/) (2021)
- [Deep Learning-based Group Causal Inference in Multivariate Time-series](https://mlsanity.com/paper/2401.08386/) (2024)

## 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.