We propose an approach to estimate the effect of multiple simultaneous
interventions in the presence of hidden confounders. To overcome the problem of
hidden confounding, we consider the setting where we have access to not only
the observational data but also sets of single-variable interventions in which
each of the treatment variables is intervened on separately. We prove
identifiability under the assumption that the data is generated from a
nonlinear continuous structural causal model with additive Gaussian noise. In
addition, we propose a simple parameter estimation method by pooling all the
data from different regimes and jointly maximizing the combined likelihood. We
also conduct comprehensive experiments to verify the identifiability result as
well as to compare the performance of our approach against a baseline on both
synthetic and real-world data.Comment: Accepted to The Conference on Uncertainty in Artificial Intelligence
(UAI) 202
