It is commonplace to encounter heterogeneous data, of which some aspects of
the data distribution may vary but the underlying causal mechanisms remain
constant. When data are divided into distinct environments according to the
heterogeneity, recent invariant learning methods have proposed to learn robust
and invariant models based on this environment partition. It is hence tempting
to utilize the inherent heterogeneity even when environment partition is not
provided. Unfortunately, in this work, we show that learning invariant features
under this circumstance is fundamentally impossible without further inductive
biases or additional information. Then, we propose a framework to jointly learn
environment partition and invariant representation, assisted by additional
auxiliary information. We derive sufficient and necessary conditions for our
framework to provably identify invariant features under a fairly general
setting. Experimental results on both synthetic and real world datasets
validate our analysis and demonstrate an improved performance of the proposed
framework over existing methods. Finally, our results also raise the need of
making the role of inductive biases more explicit in future works, when
considering learning invariant models without environment partition. Codes are
available at this https URL .

本研究提出了一种新框架可以同时学习环境分区和不变的表示，并在合成和真实数据集上进行了实验证明其改进的性能。