Estimating bounds on causal effects in high-dimensional and possibly confounded systems

We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent confounders. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to adjust for) to estimate a set of possible causal effects. Our approach is based on the IDA procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no latent confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm in simulation experiments.