Quartet-Based Learning of Shallow Latent Variables

Hierarchical latent class(HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are hidden. We explore the following two-stage approach for learning HLC models: One first identifies the shallow latent variables – latent variables adjacent to observed variables – and then determines the structure among the shallow and possibly some other “deep” latent variables. This paper is concerned with the first stage. In earlier work, we have shown how shallow latent variables can be correctly identified from quartet submodels if one could learn them without errors. In reality, one does make errors when learning quartet submodels. In this paper, we study the probability of such errors and propose a method that can reliably identify shallow latent variables despite of the errors.