## Learning Instrumental Variables with Structural and Non-Gaussianity Assumptions

*Ricardo Silva, Shohei Shimizu*; 18(120):1−49, 2017.

### Abstract

Learning a causal effect from observational data requires strong
assumptions. One possible method is to use instrumental
variables, which are typically justified by background
knowledge. It is possible, under further assumptions, to
discover whether a variable is structurally instrumental to a
target causal effect $X \rightarrow Y$. However, the few
existing approaches are lacking on how general these assumptions
can be, and how to express possible equivalence classes of
solutions. We present instrumental variable discovery methods
that systematically characterize which set of causal effects can
and cannot be discovered under local graphical criteria that
define instrumental variables, without reconstructing full
causal graphs. We also introduce the first methods to exploit
non-Gaussianity assumptions, highlighting identifiability
problems and solutions. Due to the difficulty of estimating such
models from finite data, we investigate how to strengthen
assumptions in order to make the statistical problem more
manageable.

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