# Bivariate Causal Discovery using Bayesian Model Selection

arXiv: https://arxiv.org/abs/2306.02931 · HTML: https://mlsanity.com/paper/2306.02931/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Gaussian Process Conditional Density Estimation](https://mlsanity.com/paper/1810.12750/) (2018)
- [Causal Inference via Kernel Deviance Measures](https://mlsanity.com/paper/1804.04622/) (2018)
- [A Bayesian Approach to Learning Causal Networks](https://mlsanity.com/paper/1302.4958/) (2013)
- [Gaussian Process Networks](https://mlsanity.com/paper/1301.3857/) (2013)
- [Conditional distribution variability measures for causality detection](https://mlsanity.com/paper/1601.06680/) (2016)
- [Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means](https://mlsanity.com/paper/1401.4788/) (2014)
- [On the Generalization and Adaption Performance of Causal Models](https://mlsanity.com/paper/2206.04620/) (2022)
- [Generalised Gaussian Process Latent Variable Models (GPLVM) with Stochastic Variational Inference](https://mlsanity.com/paper/2202.12979/) (2022)
- [A Bayesian Model for Bivariate Causal Inference](https://mlsanity.com/paper/1812.09895/) (2018)

## Built on by (most cited first, 12 of 12)

- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (2024)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Use What You Know: Causal Foundation Models with Partial Graphs](https://mlsanity.com/paper/2602.14972/) (2026)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [Algorithmic causal structure emerging through compression](https://mlsanity.com/paper/2502.04210/) (2025)
- [Identifying Causal Direction via Variational Bayesian Compression](https://mlsanity.com/paper/2505.07503/) (2025)
- [Skewness-Robust Causal Discovery in Location-Scale Noise Models](https://mlsanity.com/paper/2511.14441/) (2025)
- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)
- [Finding Structure in Continual Learning](https://mlsanity.com/paper/2602.04555/) (2026)
- [Causal Discovery via Transformed Low-Rank Quantile Surfaces](https://mlsanity.com/paper/2609.16931/) (2026)
- [CIDER-FM: Foundation Models for Causal Inference from Diverse Experimental Regimes](https://mlsanity.com/paper/2609.39523/) (2026)
- [Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2610.03647/) (2026)

## Abstract (arXiv)

Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in real-world datasets, ultimately limiting the usability of these methods. Building on previous attempts, we show how to incorporate causal assumptions within the Bayesian framework. Identifying causal direction then becomes a Bayesian model selection problem. This enables us to construct models with realistic assumptions, and consequently allows for the differentiation between Markov equivalent causal structures. We analyse why Bayesian model selection works in situations where methods based on maximum likelihood fail. To demonstrate our approach, we construct a Bayesian non-parametric model that can flexibly model the joint distribution. We then outperform previous methods on a wide range of benchmark datasets with varying data generating assumptions.