Learning Semi-Parametric Tree Models from Mixed Data

Causal discovery and representation involving latent variables and structures have attracted growing interest in the era of artificial intelligence, particularly for their critical role in understanding real-world data. While many existing methods focus exclusively on either purely continuous or purely discrete data, this paper addresses the challenge of learning latent structures from mixed data. We propose a novel semi-parametric tree model capable of handling mixed data and develop an algorithm for learning the structure of this model using additive information distances. We demonstrate that this algorithm efficiently and accurately recovers the true structure, given the information distances. Additionally, the sample-based version of the structural learning algorithm achieves probabilistic approximate correctness, with a finite sample bound established for exact structural recovery. Both simulated and real data are used to assess the performance of our proposed algorithm, with experimental results showing that our algorithm can effectively discover latent hierarchical structures behind mixed data.