A Bayesian Model for Bivariate Causal Inference

Area of Science:

• Causal Inference
• Machine Learning
• Statistical Modeling

Background:

• Inferring causal relationships from observational data is challenging due to the absence of interventions.
• Existing methods for two-variable causal discovery often struggle with noisy, discretized, or sparse data.
• Structural properties of data are key for solving this ill-posed problem.

Purpose of the Study:

• To introduce a novel method, Bayesian Causal Inference (BCI), for two-variable causal discovery without interventions.
• To evaluate BCI's performance against state-of-the-art methods under challenging data conditions.
• To provide a generative model for creating synthetic data for benchmarking.

Main Methods:

• Developed a generative Bayesian hierarchical model for Bayesian model selection.
• Utilized a Poisson lognormal distribution for the cause variable to handle discrete data and parameter correlations.
• Assumed Fourier diagonal Field covariance operators.
• Benchmarked BCI against LiNGAM, ANM-HSIC, ANM-MML, IGCI, and CGNN using synthetic and real-world (TCEP) data.

Main Results:

• BCI demonstrates reliable performance on synthetic and real-world datasets.
• The method achieves accuracy comparable to existing state-of-the-art algorithms.
• Performance was evaluated under high noise, strong discretization, and sparse data conditions.

Conclusions:

• Bayesian Causal Inference (BCI) is a robust method for two-variable causal discovery from observational data.
• BCI shows competitive accuracy against established methods, particularly in challenging data scenarios.
• Future work will focus on further developing the BCI framework.