Graphical models of Bayesian networks and structural equation models are widely used as a representation for probabilistic distributions and causal relations. Their representational power can be vastly increased if one includes variables that connot be measured directly. Such "latent" variables are able to explain situations in which two measured variables are correlated but no causation exists between them, and no other observed variable is a common cause of such pair. For probabilistic modeling, latent variables often allow the representation of a probabilistic distribution with fewer parameters than in models composed only of observed variables. One useful category of latent variable graphs is the measurement/structural model in which all observed variables are measurements of some latent variable, and there are causal relationships among the unobserved variables that explain the correlation of the observed ones. In this work, we introduce and evaluate principled strategies for clustering measurements and discovering probabilistic independences among latents in order to reconstruct the causal relations of the unobserved variables.

31 pages

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