发表机构
Yunnan University; Chongqing Normal University; Southern University of Science and Technology（云南大学; 重庆师范大学; 南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出数据驱动的垂直分布弹性网支持向量机，通过学习单纯形约束权重优化弹球损失，开发列分区变量分裂求解器，经实验验证其预测性能、数值等价性及多进程可扩展性。
AI 中文摘要
弹球损失支持向量机具有鲁棒性，但其不对称参数通常预先固定。我们提出一种数据驱动的弹性网支持向量机，该方法学习候选弹球损失上的单纯形约束权重，同时保留一个分类器。加权损失等价于具有数据依赖有效参数的弹球损失。经验 oracle 不等式表明，当权重正则化和单纯形截断消失时，全局极小值点的分类器目标不超过最佳固定候选的目标；否则，超出部分有明确界值。针对高维数据，我们开发了一种列分区变量分裂求解器，其以最佳迭代的 O(1/T) 平方步残差速率收敛。在常见初始化和全局参数下，任何列分区在精确算术下产生的迭代和解与集中式训练相同。实验评估了预测性能、数值等价性和多进程可扩展性。
英文摘要
The pinball-loss support vector machine is robust, but its asymmetry parameter is usually fixed in advance. We propose a data-driven elastic-net support vector machine that learns simplex-constrained weights over candidate pinball losses while retaining one classifier. The weighted loss is equivalent to a pinball loss with a data-dependent effective parameter. An empirical oracle inequality shows that, when weight regularization and simplex truncation vanish, the classifier objective at a global minimizer does not exceed that of the best fixed candidate; otherwise, the excess is explicitly bounded. For high-dimensional data, we develop a column-partitioned variable-splitting solver. It converges with a best-iterate $O(1/T)$ squared-step residual rate. Under common initialization and global parameters, any column partition produces, in exact arithmetic, the same iterates and solution as centralized training. Experiments assess predictive behavior, numerical equivalence, and multi-process scalability.
