In machine learning, instance weighting is commonly used to control the influence of individual data points in a learning process. The general idea is to improve results (e.g., the accuracy of a predictor) by restricting the influence of training examples that do not appear to be representative and may bias the learner in an undesirable way. The simplest and most common approach is to modulate the influence of each data point through multiplicative scaling. In this paper, we elaborate on the idea of instance weighting through data imprecisiation as a viable alternative to existing methods, and formalize this approach within the framework of superset learning. Roughly speaking, the idea is to reduce the influence of training examples by turning a precise data point into an imprecise observation. Within the framework of optimistic superset learning, a generic approach to superset learning, this effectively comes down to modifying an underlying loss function on a per-instance basis. We illustrate our approach for the case of binary classification with support vector machines, showing that it compares favorably with existing approaches to instance weighting in support vector machines. In a further case study, we demonstrate the usefulness of instance weighting through data imprecisiation for the practical problem of depth estimation in monocular images.

在机器学习中，实例加权通常用于控制学习过程中各个数据点的影响。总体思路是通过限制训练示例的影响来提高结果（例如，预测器的准确性），这些训练示例似乎不具有代表性，并且可能以不希望的方式使学习者产生偏见。最简单，最常见的方法是通过乘法缩放来调制每个数据点的影响。在本文中，我们详细阐述了通过数据不精确性进行实例加权的想法作为现有方法的可行替代方法，并在超集学习的框架内将此方法形式化。粗略地说，其想法是通过将精确的数据点变成不精确的观察结果来减少训练示例的影响。在乐观的超集学习框架（一种超集学习的通用方法）的框架内，这有效地归结为在每个实例的基础上修改基础损失函数。我们说明了使用支持向量机进行二进制分类的情况下的方法，表明该方法与支持向量机中实例加权的现有方法相比具有优势。在进一步的案例研究中，我们证明了通过数据不精确性对单眼图像深度估计的实际问题进行实例加权的有用性。