Pairwise cluster comparison for learning latent variable models

Learning a latent variable model (LVM) exploits values of the measured variables as manifested in the data to causal discovery. Because the challenge in learning an LVM is similar to that faced in unsupervised learning, where the number of clusters and the classes that are represented by these clusters are unknown, we link causal discovery and clustering. We propose the concept of pairwise cluster comparison (PCC), by which clusters of data points are compared pairwise to associate changes in the observed variables with changes in their ancestor latent variables and thereby to reveal these latent variables and their causal paths of influence, and the learning PCC (LPCC) algorithm that identifies PCCs and uses them to learn an LVM. LPCC is not limited to linear or latent-tree models. It returns a pattern of the true graph or the true graph itself if the graph has serial connections or not, respectively. The complete theoretical foundation to PCC, the LPCC algorithm, and its experimental evaluation are given in [Asbeh and Lerner, 2016a,b], whereas, here, we only introduce and promote them. The LPCC code and evaluation results are available online.