基于多类体积近似的直推学习
Transductive Learning with Multi-class Volume Approximation
摘要：
给定一个假设空间，弗拉基米尔·瓦普尼克（Vladimir Vapnik）的大体积原则根据等价类在假设空间中的体积来确定等价类的优先级。体积近似迄今已成功地应用于二进制学习问题。在本文中，我们自然地将其扩展到一个更一般的定义，可以应用于几个转导的问题设置，如多类，多标签和偶然学习。即使结果学习方法涉及非凸优化问题，全局最优解几乎肯定是唯一的，并且可以在O（n^3）时间内获得。我们从理论上提供的稳定性和误差分析所提出的方法，然后实验表明，它是有前途的。
英文摘要：
Given a hypothesis space, the large volume principle by Vladimir Vapnik prioritizes equivalence classes according to their volume in the hypothesis space. The volume approximation has hitherto been successfully applied to binary learning problems. In this paper, we extend it naturally to a more general definition which can be applied to several transductive problem settings, such as multi-class, multi-label and serendipitous learning. Even though the resultant learning method involves a non-convex optimization problem, the globally optimal solution is almost surely unique and can be obtained in O(n^3) time. We theoretically provide stability and error analyses for the proposed method, and then experimentally show that it is promising.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
