Query Training: Learning a Worse Model to Infer Better Marginals in Undirected Graphical Models with Hidden Variables

In the past decades, a great deal of research has focused on learning probabilistic graphical models from data. A serious problem in learning such models is the presence of hidden, or latent, variables. These variables are not observed, yet their interaction with the observed variables has important consequences in terms of representation, inference and prediction. Consequently, numerous works have been directed towards learning probabilistic graphical models with hidden variables. A significantly harder challenge is that of detecting new hidden variables and incorporating them into the network structure. Surprisingly, and despite the recognized importance of hidden variables both in social sciences and the learning community, this problem has received little attention. In this dissertation we explore the problem of learning new hidden variable in real-life domains. We present methods for coping with the different elements that this task encompasses: the detection of new hidden variables; determining the cardinality of new hidden variables; incorporating new hidden variables into learning model. In addition we also address the problem of local maxima that is common in many learning scenarios, and is particularly acute in the presence of hidden variables. We present simple and easy to implement methods that work when training data is relatively plentiful as well as a more elaborate framework that is suitable when the model is particularly complex and the data is sparse. We also consider methods specifically tailored at networks with continuous variables and the added challenges in this scenario. We evaluate all of our methods on both synthetic and real-life data. For the more elaborate methods, we put a particular emphasis on learning complex models with many hidden variables. We demonstrate significant improvement in quantitative prediction on unseen test samples when learning with hidden variables, reaffirming their importance in practice. We also demonstrate that models learned with our methods have hidden variables that are qualitatively appealing and shed light on the learned domain.