# The Causal Information Bottleneck and Optimal Causal Variable Abstractions

arXiv: https://arxiv.org/abs/2410.00535 · HTML: https://mlsanity.com/paper/2410.00535/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 24 of 24)

- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Nonlinear Information Bottleneck](https://mlsanity.com/paper/1705.02436/) (2017)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Visual Causal Feature Learning](https://mlsanity.com/paper/1412.2309/) (2014)
- [The deterministic information bottleneck](https://mlsanity.com/paper/1604.00268/) (2016)
- [BISCUIT: Causal Representation Learning from Binary Interactions](https://mlsanity.com/paper/2306.09643/) (2023)
- [Caveats for information bottleneck in deterministic scenarios](https://mlsanity.com/paper/1808.07593/) (2018)
- [Multi-Level Cause-Effect Systems](https://mlsanity.com/paper/1512.07942/) (2015)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Unsupervised Discovery of El Nino Using Causal Feature Learning on Microlevel Climate Data](https://mlsanity.com/paper/1605.09370/) (2016)
- [Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions](https://mlsanity.com/paper/2311.02695/) (2023)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [Encoding Causal Macrovariables](https://mlsanity.com/paper/2111.14724/) (2021)
- [Causal Entropy and Information Gain for Measuring Causal Control](https://mlsanity.com/paper/2309.07703/) (2023)
- [Fundamental Properties of Causal Entropy and Information Gain](https://mlsanity.com/paper/2402.01341/) (2024)

## Built on by (most cited first, 4 of 4)

- [Causal Representation Learning for Generalisable Recommendation](https://mlsanity.com/paper/2605.27043/) (2026)
- [Causally-Aware Information Bottleneck for Domain Adaptation](https://mlsanity.com/paper/2601.04361/) (2026)
- [Causal Direction from Convergence Time: Faster Training in the True Causal Direction](https://mlsanity.com/paper/2602.22254/) (2026)
- [Validating Causal Abstraction Metrics on Simulated Complex Systems](https://mlsanity.com/paper/2607.00267/) (2026)

## Abstract (arXiv)

To effectively study complex causal systems, it is often useful to construct abstractions of parts of the system by discarding irrelevant details while preserving key features. The Information Bottleneck (IB) method is a widely used approach to construct variable abstractions by compressing random variables while retaining predictive power over a target variable. Traditional methods like IB are purely statistical and ignore underlying causal structures, making them ill-suited for causal tasks. We propose the Causal Information Bottleneck (CIB), a causal extension of the IB, which compresses a set of chosen variables while maintaining causal control over a target variable. This method produces abstractions of (sets of) variables which are causally interpretable, give us insight about the interactions between the abstracted variables and the target variable, and can be used when reasoning about interventions. We present experimental results demonstrating that the learned abstractions accurately capture causal relations as intended.