用自助法提升SGD稳定性，实现无需分布假设的置信区间
Bootstrap SGD: Algorithmic Stability and Robustness
- 基于均值的两种自助SGD方法，从算法稳定性角度分析
- 理论证明可构建中位曲线的点态置信区间，不依赖分布假设
- 适合关注模型鲁棒性与统计推断的研究者
本文从算法稳定性和统计鲁棒性的视角，研究了在可分希尔伯特空间上使用经验自助法改进随机梯度下降（SGD）以最小化经验风险的方法。前两种方法基于平均值，进行了理论分析。基于算法稳定性的通用推广分析被用于类型1和类型2的自助SGD。此外，提出了一种新的自助SGD方法，证明了可在无分布假设条件下，构建中位曲线的点态置信区间。
原文摘要 · Abstract (English)
In this paper some methods to use the empirical bootstrap approach for stochastic gradient descent (SGD) to minimize the empirical risk over a separable Hilbert space are investigated from the view point of algorithmic stability and statistical robustness. The first two types of approaches are based on averages and are investigated from a theoretical point of view. A generalization analysis for bootstrap SGD of Type 1 and Type 2 based on algorithmic stability is done. Another type of bootstrap SGD is proposed to demonstrate that it is possible to construct purely distribution-free pointwise confidence intervals of the median curve using bootstrap SGD.
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