Bayesian learning of measurement and structural models

We present a Bayesian search algorithm for learning the structure of latent variable models of continuous variables. We stress the importance of applying search operators designed especially for the parametric family used in our models. This is performed by searching for subsets of the observed variables whose covariance matrix can be represented as a sum of a matrix of low rank and a diagonal matrix of residuals. The resulting search procedure is relatively efficient, since the main search operator has a branch factor that grows linearly with the number of variables. The resulting models are often simpler and give a better fit than models based on generalizations of factor analysis or those derived from standard hill-climbing methods.