Heterogeneity across different sub-populations or "homogeneous blocks" can be beneficially exploited for causal inference and novel robustness, with wide-ranging prospects for various applications. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk minimization problem with a corresponding notion of robustness. The novel methodology has connections to instrumental variable regression and robust optimization.

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