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，获取标注观测值并非易事，因为通常需要人类专家的干预或使用昂贵的测试设备。在此情况下，主动学习能够极大发挥作用，它可建议在模型拟合时使用最具信息量的数据点。减少模型开发所需观测数量可同时缓解训练所需的计算负担和与标注相关的运营费用。尤其对于大规模生产流程，在线主动学习具有重要价值，因为此类流程中需在极短时间内决定是否对数据点进行标签获取。然而，尽管近期为开发在线主动学习策略做出了诸多努力，但这些方法在存在离群值时的表现尚未得到深入探究。本研究考察了在线主动线性回归在受污染数据流中的性能表现。研究显示，当前可用的查询策略易受离群值影响，将此类离群值纳入训练集最终会降低模型的预测性能。针对此问题，我们提出了一种解决方案：该方案通过限定条件D最优算法的搜索区域并采用稳健估计器，在探索输入空间未知区域与抵御离群值之间取得平衡。数值模拟结果表明，所提方法能有效提升在线主动学习在离群值存在时的性能表现，从而拓展了这一强大工具的潜在应用场景。