大规模经验风险最小化中小数据修正后最优解的有效界
Efficiently Bounding Optimal Solutions after Small Data Modification in Large-Scale Empirical Risk Minimization
摘要：
我们在不断变化的环境中研究大规模的分类问题，其中一小部分数据集被修改，并且数据修改的效果必须快速地并入分类器中。当整个数据集很大时，即使数据修改量相当小，重新训练分类器的计算成本也会非常大。在本文中，我们提出了一种新的方法，有效地将这样的数据修改效果的分类器，而实际上没有重新训练it.The所提出的方法提供了未知的最佳分类器的成本只成比例的数据修改的大小的界限。我们通过数值实验证明，所提出的方法提供了足够紧的界限，可以忽略不计的计算成本，特别是当一小部分的数据集被修改在一个大规模的分类问题。
英文摘要：
We study large-scale classification problems in changing environments where a small part of the dataset is modified, and the effect of the data modification must be quickly incorporated into the classifier. When the entire dataset is large, even if the amount of the data modification is fairly small, the computational cost of re-training the classifier would be prohibitively large. In this paper, we propose a novel method for efficiently incorporating such a data modification effect into the classifier without actually re-training it. The proposed method provides bounds on the unknown optimal classifier with the cost only proportional to the size of the data modification. We demonstrate through numerical experiments that the proposed method provides sufficiently tight bounds with negligible computational costs, especially when a small part of the dataset is modified in a large-scale classification problem.
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