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，获取带标签的观测数据并非易事，因为这通常需要人类专家的干预或使用昂贵的测试设备。在此情况下，主动学习能够有效建议用于模型拟合时最具信息量的数据点。减少模型开发所需的观测数量，既可缓解训练过程中的计算负担，又能降低与标注相关的运营成本。尤其在高产量生产流程中，在线主动学习具有重要意义，因为此类场景要求在极短时间内决定是否为某个数据点获取标签。然而，尽管近年来在开发在线主动学习策略方面做出了努力，但这些方法在存在异常值时的表现尚未得到深入研究。本文研究了在线主动线性回归在受污染数据流中的性能。我们的研究表明，现有的查询策略容易采样异常值，而这些异常值被纳入训练集后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，该方法通过限制条件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异常值之间取得平衡。通过数值模拟，我们证明了所提方法在异常值存在时能有效提升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场景。