分析在线线性回归中高斯近似的收敛速度。
On the Rate of Gaussian Approximation for Linear Regression Problems
- 基于固定学习率推导出高斯近似率
- 近似误差为√(log n/n)，需样本量足够大
- 揭示维度d与设计矩阵对收敛的影响
本文研究在线线性回归任务中的高斯近似问题。针对固定学习率设置，推导出相应的高斯近似速率，并分析收敛速率在问题维度d及设计矩阵相关量上的显式依赖关系。当迭代次数n已知且足够大时，所得高斯近似阶数为√(log n/n)。
原文摘要 · Abstract (English)
In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield the rate of normal approximation of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enough.
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