Abstract In the learning using privileged information (LUPI) paradigm, example data cannot always be clean, while the gathered privileged information can be imperfect in practice. Here, imperfect privileged information can refer to auxiliary information that is not always accurate or perturbed by noise, or alternatively to incomplete privileged information, where privileged information is only available for part of the training data. Because of the lack of clear strategies for handling noise in example data and imperfect privileged information, existing learning using privileged information (LUPI) methods may encounter serious issues. Accordingly, in this paper, we propose a Robust SVM+ method to tackle imperfect data in LUPI. In order to make the SVM+ model robust to noise in example data and privileged information, Robust SVM+ maximizes the lower bound of the perturbations that may influence the judgement based on a rigorous theoretical analysis. Moreover, in order to deal with the incomplete privileged information, we use the available privileged information to help us in approximating the missing privileged information of training data. The optimization problem of the proposed method can be efficiently solved by employing a two-step alternating optimization strategy, based on iteratively deploying off-the-shelf quadratic programming solvers and the alternating direction method of multipliers (ADMM) technique. Comprehensive experiments on real-world datasets demonstrate the effectiveness of the proposed Robust SVM+ method in handling imperfect privileged information.

中文翻译：

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具有不完美特权信息的稳健学习

摘要 在使用特权信息学习（LUPI）范式中，示例数据并不总是干净的，而在实践中收集的特权信息可能不完美。在这里，不完美的特权信息可以指不总是准确或受噪声干扰的辅助信息，或者指不完整的特权信息，其中特权信息仅适用于部分训练数据。由于缺乏处理示例数据中的噪声的明确策略和不完善的特权信息，现有的使用特权信息 (LUPI) 方法的学习可能会遇到严重的问题。因此，在本文中，我们提出了一种鲁棒 SVM+ 方法来处理 LUPI 中的不完美数据。为了使 SVM+ 模型对示例数据和特权信息中的噪声具有鲁棒性，Robust SVM+ 基于严格的理论分析，最大化可能影响判断的扰动下限。此外，为了处理不完整的特权信息，我们使用可用的特权信息来帮助我们逼近训练数据中缺失的特权信息。基于迭代部署现成的二次规划求解器和乘法器交替方向法（ADMM）技术，采用两步交替优化策略可以有效地解决所提出方法的优化问题。对真实世界数据集的综合实验证明了所提出的 Robust SVM+ 方法在处理不完美特权信息方面的有效性。