In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high-volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D-optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool.

翻译：在许多工业应用中，获取标注观测数据并非易事，因为这通常需要人类专家的干预或使用昂贵的测试设备。在此类情形下，主动学习极具价值，它能够建议在模型拟合时使用最具信息量的数据点。减少模型开发所需的观测数量，既减轻了训练中的计算负担，也降低了与标注相关的运营开销。特别是在高产量生产流程中，在线主动学习十分有用，因为在这些流程中，决定是否为某个数据点获取标注必须在极短的时间框架内作出。然而，尽管近期在开发在线主动学习策略方面有所努力，但这些方法在存在异常值时的行为尚未得到深入检验。在本工作中，我们研究了受污染数据流中在线主动线性回归的性能表现。我们的研究表明，当前可用的查询策略容易采样到异常值，而将这些异常值纳入训练集会最终降低模型的预测性能。为解决此问题，我们提出了一种解决方案，该方案限定了条件D-最优算法的搜索区域，并使用鲁棒估计器。我们的方法在探索输入空间未观测区域与抵御异常值之间取得了平衡。通过数值模拟，我们证明所提方法能有效提升存在异常值时在线主动学习的性能，从而拓展了这一强大工具的潜在应用范围。