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's perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.
Original language | English (US) |
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Pages (from-to) | 2773-2832 |
Number of pages | 60 |
Journal | Journal of Machine Learning Research |
Volume | 15 |
State | Published - Aug 1 2014 |
Keywords
- Latent variable models
- Method of moments
- Mixture models
- Power method
- Tensor decompositions
- Topic models
ASJC Scopus subject areas
- Control and Systems Engineering
- Software
- Statistics and Probability
- Artificial Intelligence