@report {1616725,
	title = {Tensor decompositions for learning latent variable models},
	year = {2014},
	institution = {ArXiv Report},
	address = {JMLR},
	abstract = {This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically, of second- and third-order). Specifically, parameter estimation is reduced to the problem of extracting a certain (orthogonal) decomposition of a symmetric tensor derived from the moments; this decomposition can be viewed as a natural generalization of the singular value decomposition for matrices. Although tensor decompositions are generally intractable to compute, the decomposition of these specially structured tensors can be efficiently obtained by a variety of approaches, including power iterations and maximization approaches (similar to the case of matrices). A detailed analysis of a robust tensor power method is provided, establishing an analogue of Wedin{\textquoteright}s perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.},
	url = {http://arxiv.org/abs/1210.7559},
	author = {Anima Anandkumar and Rong Ge and Daniel Hsu and Sham M. Kakade and Matus Telgarsky}
}
