Developments in Statistical Learning Theory from a Perturbation Analysis Perspective

统计学习理论旨在为算法的样本复杂性和准确性提供保证。独立同分布样本的理论已经得到了很好的证实，但与限制性I.I.D.假设被推翻了。我们将特别使用算法稳定性和算法健壮性框架来扩展随机过程统计学习理论中的结果。研究方向是将现有关于混合过程的结果推广到更一般的α-混合情形，发展关于无界损失函数的进一步结果以及关于数据依赖假设集的结果(在非I.I.D.的情况下)。数据)。

Statistical Learning Theory aims to provide guarantees on the sample complexity and accuracy of algorithms. The theory for independent identically distributed samples is well established but less developed in comparison when the restrictive i.i.d. assumption is lifted. We will extend results in Statistical Learning Theory for Stochastic Processes using in particular the algorithmic stability and algorithmic robustness frameworks. The directions of research are the extension of existing results for mixing processes to the more general alpha-mixing case, development of further results for unbounded loss functions as well as results for data-dependent hypothesis sets (in the context of non i.i.d. data).