@inproceedings{f518e3891bf74702a7e370d79964ca2b,

title = "Tensor decompositions for learning latent variable models (A survey for ALT)",

abstract = "This note is a short version of that in [1]. It is intended as a survey for the 2015 Algorithmic Learning Theory (ALT) conference. 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.",

author = "Anima Anandkumar and Rong Ge and Daniel Hsu and Kakade, {Sham M.} and Matus Telgarsky",

year = "2015",

month = jan,

day = "1",

doi = "10.1007/978-3-319-24486-0_2",

language = "English (US)",

isbn = "9783319244853",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "19--38",

editor = "Claudio Gentile and Sandra Zilles and Kamalika Chaudhuri",

booktitle = "Algorithmic Learning Theory - 26th International Conference, ALT 2015",

note = "26th International Conference on Algorithmic Learning Theory, ALT 2015 ; Conference date: 04-10-2015 Through 06-10-2015",

}