Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This note is a short version of that in [1]. It is intended as a survey for the 2015 Algorithmic Learning Theory ALT conference.#R##N##R##N#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 vied 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 por iterations and maximization approaches similar to the case of matrices. A detailed analysis of a robust tensor por method is provided, establishing an analogue of din's perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.
['Anima Anandkumar', 'Rong Ge', 'Daniel J. Hsu', 'Sham M. Kakade', 'Matus Telgarsky']
I am writing a research paper on a idea Tensor Decompositions for Learning Latent Variable Models A Survey for ALT
[{"from": "human", "value": "I am writing a research paper on a idea Tensor Decompositions for Learning Latent Variable Models A Survey for ALT"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This note is a short version of that in [1]. It is intended as a survey for the 2015 Algorithmic Learning Theory ALT conference.#R##N##R##N#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 vied 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 por iterations and maximization approaches similar to the case of matrices. A detailed analysis of a robust tensor por method is provided, establishing an analogue of din's perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models."}]