标题： 稀疏协方差和稀疏Wigner模型的Gram-Schmidt扰动计算等价性 显示英文标题

标题： Computational Equivalence of Spiked Covariance and Spiked Wigner Models via Gram-Schmidt Perturbation

摘要： 在这项工作中，我们展示了第一个平均情况下的约简，该约简将稀疏尖峰协方差模型转化为稀疏尖峰Wigner模型，并因此获得了两个被广泛研究的高维统计模型之间的第一个计算等价性结果。 我们的方法利用了Gram-Schmidt正交化的一种新的扰动等变性质，从而在移除噪声依赖性的同时保留信号。 显示英文摘要

摘要： In this work, we show the first average-case reduction transforming the sparse Spiked Covariance Model into the sparse Spiked Wigner Model and as a consequence obtain the first computational equivalence result between two well-studied high-dimensional statistics models. Our approach leverages a new perturbation equivariance property for Gram-Schmidt orthogonalization, enabling removal of dependence in the noise while preserving the signal.