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Demystifying Disagreement-on-the-Line in High Dimensions

2023-01-31 02:31:18
Donghwan Lee, Behrad Moniri, Xinmeng Huang, Edgar Dobriban, Hamed Hassani

Abstract

Evaluating the performance of machine learning models under distribution shift 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 tackle this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have lead 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.

Abstract (translated)

在分布变化下评估机器学习模型的性能是一项挑战,特别是当我们只有来自变化(目标)领域的未标记数据和来自原始(源)领域的标记数据时。最近的研究表明, disagreeing 的概念,即训练使用不同随机性的模型在相同的输入上的差异程度,是解决这个问题的关键。实验表明, disagreeing 和预测错误之间存在强烈的联系,这被用于估计模型性能。实验导致了 disagreeing-on-the-line 现象的发现,即目标领域的分类错误常常是源领域的分类错误的一种线性函数。无论何时 this 属性都存在,源和目标领域的 disagreeing 遵循相同的线性关系。在这项工作中,我们发展了用于分析高维随机特征回归中的 disagreeing 的理论框架;并研究在我们所设定的什么情况下 disagreeing-on-the-line 现象会发生。对 CIFAR-10-C、tiny ImageNet-C 和 Camelyon17 的实验与我们的理论和发现保持一致,并支持其普适性。

URL

https://arxiv.org/abs/2301.13371

PDF

https://arxiv.org/pdf/2301.13371.pdf


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