Discrete Latent Variables Discovery and Structure Learning in Mixed Bayesian Networks

Latent variables pose a challenge for accurate modelling, experimental design, and inference, since they may cause non-adjustable bias in the estimation of effects. While most of the research regarding latent variables revolves around accounting for their presence and learning how they interact with other variables in the experiment, their bare existence is assumed to be deduced based on domain expertise. In this work we focus on the discovery of such latent variables, utilizing statistical hypothesis testing methods and Bayesian Networks learning. Specifically, we present a novel method for detecting discrete latent factors which affect continuous observed outcomes, in mixed discrete/continuous observed data, and device a structure learning algorithm that adds the detected latent factors to a fully observed Bayesian Network. Finally, we demonstrate the utility of our method with a set of experiments, in both controlled and real-life settings, one of which is a prediction for the outcome of COVID-19 test results.