  Discovering the complete set of causal relations among a group of variables
is a challenging unsupervised learning problem. Often, this challenge is
compounded by the fact that there are latent or hidden confounders. When only
observational data is available, the problem is ill-posed, i.e. the causal
relationships are non-identifiable unless strong modeling assumptions are made.
When interventions are available, we provide guarantees on identifiability and
learnability under mild assumptions. We assume a linear structural equation
model (SEM) with independent latent factors and directed acyclic graph (DAG)
relationships among the observables. Since the latent variable inference is
based on independent component analysis (ICA), we call this model SEM-ICA. We
use the method of moments principle to establish model identifiability. We
develop efficient algorithms based on coupled tensor decomposition with linear
constraints to obtain scalable and guaranteed solutions. Thus, we provide a
principled approach to tackling the joint problem of causal discovery and
latent variable inference.
