Learning Causal Structure on Mixed Data with Tree-Structured Functional Models

Discovering causal relations from observational data is at the heart of scientific research. Most causal discovery methods assume that the data have only one variable type. In real-world problems, however, data can consist of a mixture of continuous, discrete, and categorical variables. In this paper, we examine the causal discovery problem on mixed data. We introduce a general tree-structured functional causal model, which is well suited for characterizing the generating mechanisms of mixed data by allowing non-differentiability and nonlinearity. We present corresponding identifiability results, showing that under mild conditions, the causal directions can be uniquely determined from observational distributions. Further, we prove that the causal direction between continuous and discrete variables is generally identifiable under a much larger function class. Based on the theoretical findings, we propose an effective causal discovery method leveraging a consistent score function and powerful tree- learning techniques. Experiments on both synthetic and real data verify the effectiveness of our approach.