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，获取标注数据并非易事，因为这通常需要人类专家的介入或使用昂贵的测试设备。在此类场景下，主动学习极具价值，它能推荐最具信息量的数据点用于模型拟合。减少模型开发所需的数据量，既能缓解训练的计算负担，又能降低标注相关的运营成本。特别是在高产量生产过程中，在线主动学习尤为重要，因为针对数据点是否获取标签的决策需要在极短时间内完成。然而，尽管近年来在线主动学习策略的研究取得进展，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。研究表明，当前可用的查询策略倾向于采样离群值，而将离群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，该方案通过约束条件D-最优算法的搜索区域并采用鲁棒估计器，在探索输入空间的未知区域与抵御离群值影响之间取得平衡。数值模拟结果表明，所提方法能有效提升存在离群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。