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。在这种情况下，主动学习能够发挥重要作用，它有助于选择最具信息量的数据点用于模型拟合。减少模型开发所需的观测数量，既能减轻训练所需的计算负担，也能降低与数据标注相关的运营成本。特别是在大规模生产过程中，在线主动学习具有显著优势，因为在这些场景中，需要在极短的时间内决定是否为某个数据点获取标签。然而，尽管近年来在线主动学习策略的开发取得了进展，这些方法在存在异常值情况下的行为尚未得到深入研究。在本研究中，我们探讨了在线主动线性回归在受污染数据流中的表现。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。为解决这一问题，我们提出了一种新方法，该方法限制了条件D最优算法的搜索范围，并采用了稳健估计器。我们的方法在探索输入空间的未知区域与抵御异常值之间取得了平衡。通过数值模拟，我们证明了所提方法在存在异常值时能有效提升在线主动学习的性能，从而扩展了这一强大工具的潜在应用范围。