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It is commonplace to encounter heterogeneous data, of which some aspects ofthe data distribution may vary but the underlying causal mechanisms remainconstant. When data are divided into distinct environments according to theheterogeneity, recent invariant learning methods have proposed to learn robustand invariant models based on this environment partition. It is hence temptingto utilize the inherent heterogeneity even when environment partition is notprovided. Unfortunately, in this work, we show that learning invariant featuresunder this circumstance is fundamentally impossible without further inductivebiases or additional information. Then, we propose a framework to jointly learnenvironment partition and invariant representation, assisted by additionalauxiliary information. We derive sufficient and necessary conditions for ourframework to provably identify invariant features under a fairly generalsetting. Experimental results on both synthetic and real world datasetsvalidate our analysis and demonstrate an improved performance of the proposedframework over existing methods. Finally, our results also raise the need ofmaking the role of inductive biases more explicit in future works, whenconsidering learning invariant models without environment partition. Codes areavailable at https://github.com/linyongver/ZIN_official .

ZIN: When and How to Learn Invariance Without Environment Partition?