提出新型凸损失函数，提升SVM与神经网络泛化能力
Convex losses and their applications to SVM, SVR, and Shallow Neural Networks
- 设计可推广标准损失的新型凸损失函数
- 在小数据集上实验，泛化性能未显著提升
- 适合研究损失函数设计与优化算法的学者
我们为SVM和神经网络提出了多个新的凸损失函数，应用于二分类任务。尽管这些损失函数在对偶SVM模型中存在实际限制，但可在SVM原始形式和神经网络中使用。具体而言，采用粒子群优化算法求解改进损失下的原始SVM问题。我们证明了所提损失是标准损失的推广，并在多个小型数据集上进行了实验。初步研究表明，在损失函数中引入模式相关性理论上可能提升某些数据集的泛化性能。为评估各损失表现，采用嵌套交叉验证方法。结果表明，使用新损失与否，泛化度量无明显差异。
原文摘要 · Abstract (English)
We propose multiple new convex losses for SVM and Neural Networks, applied to binary classification tasks. While there are practical limitations in exploiting them with the dual SVM models, we are able to use them with SVM primal formulation and Neural Networks. In detail, the primal SVM problem with the modified losses has been solved with the Particle Swarm Optimization algorithm. We prove that the proposed losses are a generalization of the standard loss, and we experiment them with several small data-sets. This preliminary study shows that using pattern correlations inside the loss function could in theory enhance the generalization performances on some data-sets. To evaluate the performance of each loss, we adopt a Nested Cross-Validation procedure. Results show that generalization measures are the same with or without the new losses.
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