Integrated Structure and Parameter Learning in Latent Tree Graphical Models

We present an integrated approach to structure and parameter estimation in latent tree graphical models, where some nodes are hidden. Our approach follows a “divide-and-conquer ” strategy, and learns models over small groups of variables (where the grouping is obtained through preprocessing). A global solution is obtained in the end through simple merge steps. Our structure learning procedure involves simple combinatorial operations such as minimum spanning tree construction and local recursive group-ing, and our parameter learning is based on the method of moments and involves tensor decompositions. Our method is guaranteed to correctly recover the unknown tree structure and the model parameters with low sample complexity for the class of linear multivariate latent tree models which includes discrete and Gaussian distributions, and Gaussian mixtures. Our method can be implemented in parallel with computational complexity per worker scaling only logarithmically in the number of observed variables, and linearly in the dimensionality of each variable. Our experiments confirm our theoretical guarantees and show a high degree of efficiency and accuracy.