Paper Info
Title
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 in a latent tree 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 induce a hierarchical low rank decomposition of the tensor. Exploiting these properties, we derive an optimization problem for estimating the parameters of a latent tree graphical model, i.e., hierarchical decomposion of a tensor which minimizes the Frobenius norm of the difference between the original tensor and its decomposition. When the latent tree graphical models are correctly specified, we show that a global optimum of the optimization problem can be obtained via a recursive decomposition algorithm. This algorithm recovers previous spectral algorithms for hidden Markov models (Hsu et al., 2009; Foster et al., 2012) and latent tree graphical models (Parikh et al., 2011; Song et al., 2011) as special cases, elucidating the global objective these algorithms are optimizing for. When the latent tree graphical models are misspecified, we derive a better decomposition based on our framework, and provide approximation guarantee for this new estimator. In both synthetic and real world data, this new estimator significantly improves over the-state-of-the-art.
Year
Venue
Field
2013
ICML
Tensor,Latent class model,Latent variable,Low-rank approximation,Probabilistic latent semantic analysis,Artificial intelligence,Graphical model,Optimization problem,Machine learning,Marginal distribution,Mathematics
DocType
Citations 
PageRank 
Conference
11
0.85
References 
Authors
9
5
Name
Order
Citations
PageRank
Le Song12437159.27
Mariya Ishteva213011.28
Ankur P. Parikh325018.47
Bo Xing47332471.43
Haesun Park53546232.42