Tensor decompositions for learning latent variable models
Journal Article (Journal Article)
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