Publications [#302371] of Rong Ge

Papers Published

1. Anandkumar, A; Ge, R; Hsu, D; Kakade, SM; Telgarsky, M, Tensor decompositions for learning latent variable models, Journal of Machine Learning Research, vol. 15 (August, 2014), pp. 2773-2832, ISSN 1532-4435
   (last updated on 2026/01/16)

   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.