  Unobserved confounding is the main obstacle to causal effect estimation from
observational data. Instrumental variables (IVs) are widely used for causal
effect estimation when there exist latent confounders. With the standard IV
method, when a given IV is valid, unbiased estimation can be obtained, but the
validity requirement on a standard IV is strict and untestable. Conditional IVs
have been proposed to relax the requirement of standard IVs by conditioning on
a set of observed variables (known as a conditioning set for a conditional IV).
However, the criterion for finding a conditioning set for a conditional IV
needs a directed acyclic graph (DAG) representing the causal relationships of
both observed and unobserved variables. This makes it challenging to discover a
conditioning set directly from data. In this paper, by leveraging maximal
ancestral graphs (MAGs) for causal inference with latent variables, we study
the graphical properties of ancestral IVs, a type of conditional IVs using
MAGs, and develop the theory to support data-driven discovery of the
conditioning set for a given ancestral IV in data under the pretreatment
variable assumption. Based on the theory, we develop an algorithm for unbiased
causal effect estimation with a given ancestral IV and observational data.
Extensive experiments on synthetic and real-world datasets demonstrate the
performance of the algorithm in comparison with existing IV methods.

Artificial Intelligence