Estimating multivariate latent-structure models

TL;DR

This paper presents a constructive proof for identifying multivariate latent-structure models, such as finite-mixture and hidden Markov models, using joint diagonalization techniques and develops related estimation algorithms and asymptotic theory.

Contribution

It introduces a new proof method for model identification and provides algorithms and theoretical analysis for estimating complex multivariate latent structures.

Findings

Successful joint diagonalization approach for model identification

Development of estimation algorithms with distribution theory

Asymptotic analysis for component density estimators

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.