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While hidden class models of various types arise in many statisticalapplications, it is often difficult to establish the identifiability of theirparameters. Focusing on models in which there is some structure of independenceof some of the observed variables conditioned on hidden ones, we demonstrate ageneral approach for establishing identifiability utilizing algebraicarguments. A theorem of J. Kruskal for a simple latent-class model with finitestate space lies at the core of our results, though we apply it to a diverseset of models. These include mixtures of both finite and nonparametric productdistributions, hidden Markov models and random graph mixture models, and leadto a number of new results and improvements to old ones. In the parametricsetting, this approach indicates that for such models, the classical definitionof identifiability is typically too strong. Instead generic identifiabilityholds, which implies that the set of nonidentifiable parameters has measurezero, so that parameter inference is still meaningful. In particular, thissheds light on the properties of finite mixtures of Bernoulli products, whichhave been used for decades despite being known to have nonidentifiableparameters. In the nonparametric setting, we again obtain identifiability onlywhen certain restrictions are placed on the distributions that are mixed, butwe explicitly describe the conditions.

Identifiability of parameters in latent structure models with many observed variables