  Learning under distribution shifts is a challenging task. One principled
approach is to exploit the invariance principle via the structural causal
models. However, the invariance principle is violated when the response is
intervened, making it a difficult setting. In a recent work, the invariant
matching property has been developed to shed light on this scenario and shows
promising performance. In this work, by formulating a high-dimensional problem
with intrinsic sparsity, we generalize the invariant matching property for an
important setting when only the target is intervened. We propose a more robust
and computation-efficient algorithm by leveraging a variant of Lasso, improving
upon the existing algorithms.
