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.
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