Heuristic Greedy Search Algorithms for Latent Variable Models

Abstract

There has recently been significant progress in the development of algorithms for learning the directed acyclic graph (DAG) part of a Bayesian network without latent variables from data and optional background knowledge. However, the problem of learning the DAG part of a Bayesian network with latent (unmeasured) variables is much more difficult for two reasons: first the number of possible models is infinite, and second, calculating scores for latent variables models is generally much slower than calculating scores for models without latent variables. In this paper we will describe how to extend search algorithms developed for non-latent variable DAG models to the case of DAG models with latent variables. We will introduce two generalizations of DAGs, called mixed ancestor graphs (or MAGs) and partial ancestor graphs (or PAGs), and briefly describe how they can be used to search for latent variable DAG models, to classify, and to predict the effects of interventions in causal systems.