论文标题
引导程序正规化单数相关矩阵
Bootstraps Regularize Singular Correlation Matrices
论文作者
论文摘要
我分析地表明，随着$ K $的增加，$ K $ Bootsapped的相关矩阵的平均值迅速变为正定信号，这提供了一种简单的方法，可以使单一的Pearson相关矩阵正常化。如果$ n $是对象的数量和$ t $功能数量，则如果$ k> \ frac {e} {e-1} {e-1} \ frac {n} {t} {t} {t} \ simeq 1.58 \ frac {n} n} n} $ t $ t $ t $ t $ t $ T对于有限的$ n $和$ t $，获得了与$ k $ bootstraps获得正定相关矩阵的可能性。最后，我证明了所需的引导程序的数量总是小于$ n $。此方法在$ n $的数量级比数据点$ t $（例如金融，遗传学，社会科学或图像处理）的数量级大的字段中尤其重要。
I show analytically that the average of $k$ bootstrapped correlation matrices rapidly becomes positive-definite as $k$ increases, which provides a simple approach to regularize singular Pearson correlation matrices. If $n$ is the number of objects and $t$ the number of features, the averaged correlation matrix is almost surely positive-definite if $k> \frac{e}{e-1}\frac{n}{t}\simeq 1.58\frac{n}{t}$ in the limit of large $t$ and $n$. The probability of obtaining a positive-definite correlation matrix with $k$ bootstraps is also derived for finite $n$ and $t$. Finally, I demonstrate that the number of required bootstraps is always smaller than $n$. This method is particularly relevant in fields where $n$ is orders of magnitude larger than the size of data points $t$, e.g., in finance, genetics, social science, or image processing.
