Estimating multivariate latent-structure models
arXiv:1603.09141 · doi:10.1214/15-AOS1376
Abstract
A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same nonorthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this joint-diagonalization problem. Algorithms are available for computation and we derive distribution theory. We further develop asymptotic theory for orthogonal-series estimators of component densities in mixture models and emission densities in hidden Markov models.
Published at http://dx.doi.org/10.1214/15-AOS1376 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (6)
- Identifiability of parameters in latent structure models with many observed variables
- Canonical polyadic decomposition of third-order tensors: reduction to generalized eigenvalue decomposition
- Inference for mixtures of symmetric distributions
- An algorithm for generic and low-rank specific identifiability of complex tensors
- Generic uniqueness conditions for the canonical polyadic decomposition and INDSCAL
- Estimating multivariate latent-structure models