Tensor decompositions for learning latent variable models

摘要: This work considers a computationally and statistically efficient parameter estimation method for wide class of latent variable models--including Gaussian mixture models, hidden Markov Dirichlet allocation--which exploits certain tensor structure in their low-order observable moments (typically, second- third-order). Specifically, is reduced to the problem extracting (orthogonal) decomposition symmetric derived from moments; this can be viewed as natural generalization singular value matrices. Although decompositions are generally intractable compute, these specially structured tensors efficiently obtained by variety approaches, including power iterations maximization approaches (similar case matrices). A detailed analysis robust provided, establishing an analogue Wedin's perturbation theorem vectors implies tractable approach several popular models.