Identifiability of parameters in latent structure models with many observed variables

Details Identifiability of parameters in latent structure models with many observed variables Identifiability of parameters in latent structure models with many observed variables

2008-09-29

arxiv.org/abs/0809.5032v2

Annals of Statistics 2009, Vol. 37, No. 6A, 3099-3132

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS689 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS689

While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent-class model with finite state space lies at the core of our results, though we apply it to a diverse set of models. These include mixtures of both finite and nonparametric product distributions, hidden Markov models and random graph mixture models, and lead to a number of new results and improvements to old ones. In the parametric setting, this approach indicates that for such models, the classical definition of identifiability is typically too strong. Instead generic identifiability holds, which implies that the set of nonidentifiable parameters has measure zero, so that parameter inference is still meaningful. In particular, this sheds light on the properties of finite mixtures of Bernoulli products, which have been used for decades despite being known to have nonidentifiable parameters. In the nonparametric setting, we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed, but we explicitly describe the conditions.

Affiliated with

Also associated with

No associations

Rating

Identifiability of parameters in latent structure models with many observed variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Identifiability of parameters in latent structure models with many observed variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Identifiability of parameters in latent structure models with many observed variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-49774