Structural Equation Modeling with Latent Variables

Discovering causal relationships between variables is a difficult unsupervised learning task, which becomes more challenging if there are unobserved common causes between pairs of variables. Often it is not feasible to uniquely recover causal relations when only observational data is available. When experimental data is obtainable through interventions, we present a method for guaranteed identification under mild assumptions. We consider a linear structural equation model where there are independent unobserved common causes between pairs of observed variables. The generative process of latent effects is given by the mixing method of blind source separation problem. Our objective is to disentangle the observed causal effects from latent confounders and learn the model parameters that are consistent with observational and experimental data. By exploiting the invariance of latent factors across various interventions, we present matching methods as a way to combine the information across various interventions. Finally, we propose an identification algorithm that uses efficient tensor decomposition for a unique recovery of model parameters and disentangling the latent confounders from observed causal effects