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Evaluating the performance of machine learning models under distribution shifts is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackling this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain; and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression; and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings. 

In modern machine learning, users often have to collaborate to learn distributions that generate the data. Communication can be a significant bottleneck. Prior work has studied homogeneous users—i.e., whose data follow the same discrete distribution—and has provided optimal communication-efficient methods. How- ever, these methods rely heavily on homogeneity, and are less applicable in the common case when users’ discrete distributions are heterogeneous. Here we consider a natural and tractable model of heterogeneity, where users’ discrete distributions only vary sparsely, on a small number of entries. We propose a novel two-stage method named SHIFT: First, the users collaborate by communicating with the server to learn a central distribution; relying on methods from robust statistics. Then, the learned central distribution is fine-tuned to estimate the indi- vidual distributions of users. We show that our method is minimax optimal in our model of heterogeneity and under communication constraints. Further, we provide experimental results using both synthetic data and n-gram frequency estimation in the text domain, which corroborate its efficiency.