Diagnosing and Rectifying Fake OOD Invariance: A Restructured Causal
  Approach
Ziliang Chen Yongsen Zheng Zhao-Rong Lai Quanlong Guan Liang Lin
Invariant representation learning (IRL) encourages the prediction from
invariant causal features to labels de-confounded from the environments,
advancing the technical roadmap of out-of-distribution (OOD) generalization.
Despite spotlights around, recent theoretical results verified that some causal
features recovered by IRLs merely pretend domain-invariantly in the training
environments but fail in unseen domains. The \emph{fake invariance} severely
endangers OOD generalization since the trustful objective can not be diagnosed
and existing causal surgeries are invalid to rectify. In this paper, we review
a IRL family (InvRat) under the Partially and Fully Informative Invariant
Feature Structural Causal Models (PIIF SCM /FIIF SCM) respectively, to certify
their weaknesses in representing fake invariant features, then, unify their
causal diagrams to propose ReStructured SCM (RS-SCM). RS-SCM can ideally
rebuild the spurious and the fake invariant features simultaneously. Given
this, we further develop an approach based on conditional mutual information
with respect to RS-SCM, then rigorously rectify the spurious and fake invariant
effects. It can be easily implemented by a small feature selection subnet
introduced in the IRL family, which is alternatively optimized to achieve our
goal. Experiments verified the superiority of our approach to fight against the
fake invariant issue across a variety of OOD generalization benchmarks.