Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Data
This addresses a specific challenge in causal inference for researchers dealing with mixed data types, though it is incremental as it builds on existing causal discovery methods.
The paper tackles the problem of causal discovery for mixed bivariate data with one continuous and one discrete variable by proposing a method that uses the monotonicity of the conditional density ratio to determine causal direction, achieving superior accuracy in experiments.
We propose a causal discovery method for mixed bivariate data consisting of one continuous and one discrete variable. Existing approaches either impose strong distributional assumptions or face challenges in fairly comparing causal directions between variables of different types, due to differences in their information content. We introduce a novel approach that determines causal direction by analyzing the monotonicity of the conditional density ratio of the continuous variable, conditioned on different values of the discrete variable. Our theoretical analysis shows that the conditional density ratio exhibits monotonicity when the continuous variable causes the discrete variable, but not in the reverse direction. This property provides a principled basis for comparing causal directions between variables of different types, free from strong distributional assumptions and bias arising from differences in their information content. We demonstrate its effectiveness through experiments on both synthetic and real-world datasets, showing superior accuracy compared to existing methods.