Generalization bounds for non-stationary mixing processes
Generalization bounds for non-stationary mixing processes
复制标题
非平稳混合过程的泛化界限
DOI：
10.1007/s10994-016-5588-2
复制
发表时间：
2016
期刊：
影响因子：
7.5
通讯作者：
M. Mohri
中科院分区：
文献类型：
--
作者：
Vitaly Kuznetsov;M. Mohri
本文给出了非平稳混合随机过程时间序列预测的第一推广界。我们证明了Rademacher复杂性学习界的平均路径推广与非平稳$$\beta $β-混合过程和路径相关的推广与非平稳$$\phi $混合过程。我们的保证用$$\beta $$β-或$$\phi $-混合系数以及训练和目标分布之间差异的自然度量来表示。他们承认作为特殊情况下以前的Rademacher复杂性界的非i.i.d.平稳分布，对于独立但不相同分布的随机变量，或对于i.i.d.案子我们表明，使用一个新的子样本选择技术，我们介绍，我们的界限可以收紧自然假设下的渐近平稳随机过程。我们还证明了快速的学习率可以通过扩展现有的本地Rademacher复杂性分析的非i.i.d.设置.最后，我们通过提供无限损失和非独立同分布学习的泛化界来总结本文。数据
This paper presents the first generalization bounds for time series prediction with a non-stationary mixing stochastic process. We prove Rademacher complexity learning bounds for both average-path generalization with non-stationary $$\beta $$β-mixing processes and path-dependent generalization with non-stationary $$\phi $$ϕ-mixing processes. Our guarantees are expressed in terms of $$\beta $$β- or $$\phi $$ϕ-mixing coefficients and a natural measure of discrepancy between training and target distributions. They admit as special cases previous Rademacher complexity bounds for non-i.i.d. stationary distributions, for independent but not identically distributed random variables, or for the i.i.d. case. We show that, using a new sub-sample selection technique we introduce, our bounds can be tightened under the natural assumption of asymptotically stationary stochastic processes. We also prove that fast learning rates can be achieved by extending existing local Rademacher complexity analyses to the non-i.i.d. setting. We conclude the paper by providing generalization bounds for learning with unbounded losses and non-i.i.d. data.