arXiv:2410.14413math.STcs.LG2024-10
高效计算高维加权样本协方差的非线性收缩公式
WeSpeR: Computing non-linear shrinkage formulas for the weighted sample covariance
- 基于渐近样本谱理论推导新算法
- 在维度超1000时速度显著提升
- 适合高维金融或生物数据建模
我们解决高维情况下加权样本协方差的非线性收缩公式计算问题。利用渐近样本谱的理论性质，推导出WeSpeR算法，显著加速维度高于1000时的非线性收缩计算。实证测试验证了WeSpeR算法的良好性能。我们提供了基于PyTorch的实现。
原文摘要 · Abstract (English)
We address the issue of computing the non-linear shrinkage formulas for the weighted sample covariance in high dimension. We use theoretical properties of the asymptotic sample spectrum in order to derive the \textit{WeSpeR} algorithm and significantly speed up non-linear shrinkage in dimension higher than $1000$. Empirical tests confirm the good properties of the \textit{WeSpeR} algorithm. We provide the implementation in PyTorch for it.
协方差估计高维统计算法优化
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