  Recently, methods have been proposed that exploit the invariance of
prediction models with respect to changing environments to infer subsets of the
causal parents of a response variable. If the environments influence only few
of the underlying mechanisms, the subset identified by invariant causal
prediction (ICP), for example, may be small, or even empty. We introduce the
concept of minimal invariance and propose invariant ancestry search (IAS). In
its population version, IAS outputs a set which contains only ancestors of the
response and is a superset of the output of ICP. When applied to data,
corresponding guarantees hold asymptotically if the underlying test for
invariance has asymptotic level and power. We develop scalable algorithms and
perform experiments on simulated and real data.
