Scalable Latent Tree Model and its Application to Health Analytics

Latent tree graphical models are a popular class of latent variable models, where a probability distribution involving observed and hidden variables are Markovian on a tree. Due to the fact that structure of (observable and hidden) variable interactions are approximated as a tree, inference on latent trees can be carried out exactly through a simple belief propagation [Pea88]. Therefore, latent tree graphical models present a good tradeoff between model accuracy and computational complexity. They are applicable in many domains, where it is natural to expect hierarchical or sequential relationships among the variables (through a hidden-Markov model). For instance, latent tree models have been employed for phylogenetic reconstruction [DEKM99], object recognition [CTW12a, CTW12b] and human pose estimation [WL13]. In this paper, we use latent tree model for discovering a hierarchy among diseases based on comorbidities exhibited in patients' health records, i.e. co-occurrences of diseases in patients. In particular, two large healthcare datasets of 30K and 1.6M patients are used to build the latent disease trees, where clinically meaningful disease clusters are identified as shown in fig 3 and 4. The task of learning a latent tree models consists of two parts: learning the tree structure, and learning the parameters of the tree. There exist many challenges which prohibit efficient or guaranteed learning of the latent tree graphical model, which will be addressed in this paper: 1. The location and the number of latent variables are hidden and the marginalized graph over the observable variables no longer conforms to a tree structure.