Bivariate Causal Discovery using Bayesian Model Selection
This work addresses a key limitation in causal discovery for researchers and practitioners by enabling differentiation in cases where traditional methods fail, though it is incremental as it builds on existing Bayesian approaches.
The paper tackles the problem of distinguishing between Markov equivalent causal structures in bivariate causal discovery by incorporating causal assumptions within a Bayesian framework, resulting in outperformance of previous methods on benchmark datasets.
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.