- Le Song, Mariya Ishteva, Ankur P. Parikh, E. Xing, Haesun Park. 2013. Hierarchical Tensor Decomposition of Latent Tree Graphical Models. Abstract: We approach the problem of estimating the parameters of a latent tree graphical model from a hierarchical tensor decomposition point of view. In this new view, the marginal probability table of the observed variables is treated as a tensor, and we show that: (i) the latent variables induce low rank structures in various matricizations of the tensor; (ii) this collection of low rank matricizations induces a hierarchical low rank decomposition of the tensor. We further derive an optimization problem for estimating (alternative) parameters of a latent tree graphical model, allowing us to represent the marginal probability table of the observed variables in a compact and robust way. The optimization problem aims to find the best hierarchical low rank approximation of a tensor in Frobenius norm. 
