Tensor decompositions for learning latent variable models

Published

Journal Article

© 2014 Animashree Anandkumar, Rong Ge, Daniel Hsu, Sham M. Kakade, and Matus Telgarsky. 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's perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.

Duke Authors

Cited Authors

  • Anandkumar, A; Ge, R; Hsu, D; Kakade, SM; Telgarsky, M

Published Date

  • August 1, 2014

Published In

Volume / Issue

  • 15 /

Start / End Page

  • 2773 - 2832

Electronic International Standard Serial Number (EISSN)

  • 1533-7928

International Standard Serial Number (ISSN)

  • 1532-4435

Citation Source

  • Scopus