Nonparametric Latent Tree Graphical Models: Inference, Estimation, and Structure Learning
This work addresses a restrictive assumption in graphical models for researchers in statistics and machine learning, offering a more flexible approach for applications with non-Gaussian data.
The authors tackled the problem of existing tree-structured graphical models being limited to Gaussian or discrete assumptions, proposing nonparametric methods using reproducing kernel Hilbert space embeddings to handle high-dimensional continuous and non-Gaussian variables, with results validated through numerical experiments.
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for parameter estimation, inference, and structure learning mainly rely on the Gaussian or discrete assumptions, which are restrictive under many applications. In this paper, we propose new nonparametric methods based on reproducing kernel Hilbert space embeddings of distributions that can recover the latent tree structures, estimate the parameters, and perform inference for high dimensional continuous and non-Gaussian variables. The usefulness of the proposed methods are illustrated by thorough numerical results.