Learning Mixed Latent Forest Models

This paper adopts a latent forest model for mixed data analysis. Unlike traditional latent tree model, the adopted model is more flexible with several trees, and observed variables are allowed to appear as internal nodes. This model can capture more complex potential mechanisms behind data. We address the latent structural learning and the parameter estimation for this model. For structural learning, we propose a consistent bottom-up algorithm and provide a theoretical guarantee on a finite sample size bound for the exact structural recovery. For parameter estimation, we introduce a moment estimator algorithm and demonstrate that the estimator is asymptotically normal. The simulation studies indicate that our algorithms performed well for learning the mixed latent forest model. The real data analysis shows that the learned model captured the hierarchical structure and latent information behind the Changchun mayor hotline data.