Learning Instrumental Variables with Non-Gaussianity Assumptions: Theoretical Limitations and Practical Algorithms

Learning a causal effect from observational data is not straightforward, as this is not possible without further assumptions. If hidden common causes between treatment $X$ and outcome $Y$ cannot be blocked by other measurements, one possibility is to use an instrumental variable. In principle, it is possible under some assumptions to discover whether a variable is structurally instrumental to a target causal effect $X \rightarrow Y$, but current frameworks are somewhat lacking on how general these assumptions can be. A instrumental variable discovery problem is challenging, as no variable can be tested as an instrument in isolation but only in groups, but different variables might require different conditions to be considered an instrument. Moreover, identification constraints might be hard to detect statistically. In this paper, we give a theoretical characterization of instrumental variable discovery, highlighting identifiability problems and solutions, the need for non-Gaussianity assumptions, and how they fit within existing methods.