1 research outputs found
Cross-covariance modelling via DAGs with hidden variables
DAG models with hidden variables present many difficulties that are not
present when all nodes are observed. In particular, fully observed DAG models
are identified and correspond to well-defined sets ofdistributions, whereas
this is not true if nodes are unobserved. Inthis paper we characterize exactly
the set of distributions given by a class of one-dimensional Gaussian latent
variable models. These models relate two blocks of observed variables, modeling
only the cross-covariance matrix. We describe the relation of this model to the
singular value decomposition of the cross-covariance matrix. We show that,
although the model is underidentified, useful information may be extracted. We
further consider an alternative parametrization in which one latent variable is
associated with each block. Our analysis leads to some novel covariance
equivalence results for Gaussian hidden variable models.Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty
in Artificial Intelligence (UAI2001