WeSpeR: Computing non-linear shrinkage formulas for the weighted sample covariance
This work addresses a computational bottleneck for researchers and practitioners in statistics and machine learning dealing with high-dimensional covariance estimation, though it appears incremental as it builds on existing non-linear shrinkage methods.
The paper tackles the computational challenge of applying non-linear shrinkage formulas to weighted sample covariance matrices in high dimensions, resulting in the WeSpeR algorithm that significantly speeds up computation for dimensions over 1000, with empirical tests confirming its effectiveness.
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.