We study the problem of choosing algorithm hyper-parameters in unsupervised domain adaptation, i.e., with labeled data in a source domain and unlabeled data in a target domain, drawn from a different input distribution. We follow the strategy to compute several models using different hyper-parameters, and, to subsequently compute a linear aggregation of the models. While several heuristics exist that follow this strategy, methods are still missing that rely on thorough theories for bounding the target error. In this turn, we propose a method that extends weighted least squares to vector-valued functions, e.g., deep neural networks. We show that the target error of the proposed algorithm is asymptotically not worse than twice the error of the unknown optimal aggregation. We also perform a large scale empirical comparative study on several datasets, including text, images, electroencephalogram, body sensor signals and signals from mobile phones. Our method outperforms deep embedded validation (DEV) and importance weighted validation (IWV) on all datasets, setting a new state-of-the-art performance for solving parameter choice issues in unsupervised domain adaptation with theoretical error guarantees. We further study several competitive heuristics, all outperforming IWV and DEV on at least five datasets. However, our method outperforms each heuristic on at least five of seven datasets.

翻译：我们研究了无监督域适应中算法超参数的选择问题，其中带标签数据来自源域，未标签数据来自目标域（两者输入分布不同）。我们采用如下策略：使用不同超参数计算多个模型，随后对这些模型进行线性聚合。尽管存在若干基于该策略的启发式方法，但目前仍缺乏基于严谨理论来限制目标误差的方法。为此，我们提出一种将加权最小二乘法扩展至向量值函数（如深度神经网络）的方法。理论证明，所提算法的目标误差渐近地不超过未知最优聚合误差的两倍。我们还在多个数据集上进行了大规模实证比较研究，涵盖文本、图像、脑电图、身体传感器信号及手机信号。在全部数据集上，我们的方法均优于深度嵌入式验证（DEV）和重要性加权验证（IWV），为在理论误差保证下解决无监督域适应中的参数选择问题确立了新的最优性能。此外，我们研究了多种竞争性启发式方法，其中所有方法至少在五个数据集上优于IWV和DEV。然而，在七个数据集中，我们的方法至少在五个数据集上优于每种启发式方法。