Asymptotic Inference for Eigenvectors

Asymptotic Eigenvectors, Topological Patterns and Recurrent Networks

The notions of asymptotic eigenvectors and asymptotic eigenvalues are defined. Based on these notions a special probability rule for pattern selection in a Hopfield type dynamics is introduced. The underlying network is considered to be a d -regular graph, where d is an integer denoting the number of nodes connected to each neuron. It is shown that as far as the degree d is less than a critical...

Asymptotic Inference

Inference for Eigenvalues and Eigenvectors of Gaussian Symmetric Matrices

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic backgroun...

Inference for Eigenvalues and Eigenvectors of Gaussian Symmetric Matrices By

This article presents maximum likelihood estimators (MLEs) and loglikelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background...

Factorized Asymptotic Bayesian Inference for Mixture Modeling

This paper proposes a novel Bayesian approximation inference method for mixture modeling. Our key idea is to factorize marginal log-likelihood using a variational distribution over latent variables. An asymptotic approximation, a factorized information criterion (FIC), is obtained by applying the Laplace method to each of the factorized components. In order to evaluate FIC, we propose factorize...