Some aspects of latent structure analysis
In: Subspace, latent structure and feature selection techniques, 23-25 February 2005, Bohinj, Slovenia.
Latent structure models involve real, potentially observable variables
and latent, unobservable variables. The framework includes
various particular types of model, such as factor analysis, latent class
analysis, latent trait analysis, latent profile models, mixtures of
factor analysers, state-space models and others. The simplest scenario,
of a single discrete latent variable, includes finite mixture models,
hidden Markov chain models and hidden Markov random field models. The
paper gives a brief tutorial of the application of maximum likelihood and
Bayesian approaches to the estimation of parameters within these models,
emphasising especially the fact that computational complexity varies
greatly among the different scenarios. In the case of a single discrete
latent variable, the issue of assessing its cardinality is discussed.
Techniques such as the EM algorithm, Markov chain Monte Carlo methods
and variational approximations are mentioned.