A Spectral Algorithm for Latent Tree Graphical Models

Ankur P. Parikh, Le Song, Eric P. Xing

Abstract: Latent variable models are powerful tools for probabilistic modeling, and have been successfully applied to various domains, such as speech analysis and bioinformatics. However, parameter learning algorithms for latent variable models have predominantly relied on local search heuristics such as expectation maximization (EM). We propose a fast, local-minimum-free spectral algorithm for learning latent variable models with arbitrary tree topologies, and show that the joint distribution of the observed variables can be reconstructed from the marginals of triples of observed variables irrespective of the maximum degree of the tree. We demonstrate the performance of our spectral algorithm on synthetic and real datasets; for large training sizes, our algorithm performs comparable to or better than EM while being orders of magnitude faster.