# Identifying Causal Direction via Variational Bayesian Compression

arXiv: https://arxiv.org/abs/2505.07503 · HTML: https://mlsanity.com/paper/2505.07503/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 69 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Information-Theoretic Probing with Minimum Description Length](https://mlsanity.com/paper/2003.12298/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Bayesian Compression for Deep Learning](https://mlsanity.com/paper/1705.08665/) (2017)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [The Description Length of Deep Learning Models](https://mlsanity.com/paper/1802.07044/) (2018)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Wide Mean-Field Bayesian Neural Networks Ignore the Data](https://mlsanity.com/paper/2202.11670/) (2022)
- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (2024)
- [Telling Cause from Effect using MDL-based Local and Global Regression](https://mlsanity.com/paper/1709.08915/) (2017)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [Heteroscedastic Causal Structure Learning](https://mlsanity.com/paper/2307.07973/) (2023)
- [A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery](https://mlsanity.com/paper/2410.06407/) (2024)
- [Robust Estimation of Causal Heteroscedastic Noise Models](https://mlsanity.com/paper/2312.10102/) (2023)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [Differentiable Bayesian Structure Learning with Acyclicity Assurance](https://mlsanity.com/paper/2309.01392/) (2023)

## Built on by (most cited first, 3 of 3)

- [Topological Residual Asymmetry for Bivariate Causal Direction](https://mlsanity.com/paper/2602.00427/) (2026)
- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)

## Abstract (arXiv)

Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic Markov condition, which postulates that the joint distribution, when factorized according to the causal direction, yields a more succinct codelength compared to the anti-causal direction. Previous approaches approximate these codelengths by relying on simple functions or Gaussian processes (GPs) with easily evaluable complexity, compromising between model fitness and computational complexity. To address these limitations, we propose leveraging the variational Bayesian learning of neural networks as an interpretation of the codelengths. This allows the improvement of model fitness, while maintaining the succinctness of the codelengths, and the avoidance of the significant computational complexity of the GP-based approaches. Extensive experiments on both synthetic and real-world benchmarks in cause-effect identification demonstrate the effectiveness of our proposed method, showing promising performance enhancements on several datasets in comparison to most related methods.