We study the problem of domain adaptation under distribution shift, where the
shift is due to a change in the distribution of an unobserved, latent variable
that confounds both the covariates and the labels. In this setting, neither the
covariate shift nor the label shift assumptions apply. Our approach to
adaptation employs proximal causal learning, a technique for estimating causal
effects in settings where proxies of unobserved confounders are available. We
demonstrate that proxy variables allow for adaptation to distribution shift
without explicitly recovering or modeling latent variables. We consider two
settings, (i) Concept Bottleneck: an additional ''concept'' variable is
observed that mediates the relationship between the covariates and labels; (ii)
Multi-domain: training data from multiple source domains is available, where
each source domain exhibits a different distribution over the latent
confounder. We develop a two-stage kernel estimation approach to adapt to
complex distribution shifts in both settings. In our experiments, we show that
our approach outperforms other methods, notably those which explicitly recover
the latent confounder.

我们研究了领域适应问题，该问题是由于未观察到的潜在变量分布改变所导致的分布偏移。我们的适应方法采用了近端因果学习，一种用于估计因果效应的技术，适用于存在未观察到的混淆变量代理的情况。我们证明了代理变量允许在不明确恢复或建模潜在变量的情况下适应分布偏移。我们考虑了两种情况：（i）概念瓶颈：观察到一个额外的 “概念” 变量，它介导了协变量和标签之间的关系；（ii）多领域：有来自多个源领域的训练数据，其中每个源领域对潜在混淆变量有不同的分布。我们在这两种情况下开发了一种两阶段核估计方法，以适应复杂的分布偏移。在我们的实验证明，我们的方法优于其他方法，尤其是那些明确恢复潜在混淆变量的方法。