The program provided calculates the asymptotic minimax MSE, and the asymptotic minimax tuning threshold, of matrix denoising by Singular Value Thresholding: lim_{N->\infty} inf_lambda sup_{rank(X)<= M*rho} MSE ||Xhat_lambda - X||^2_F /MN ... Here: (*) Xhat_lambda is the Singular Value Thresholding denoiser (applying soft thresholding with threshold lambda to each singular value of the data) (*) rho is the asymptotic rank fraction (*) M/N -> beta (the asymptotic aspect ratio) (*) X is an M-by-N matrix, M<=N (*) ||.||_F denotes the Frobenius matrix norm (sum of squares of matrix entries)

Working Paper (2021)

Zhang Yuexia, Qin Guoyou, Zhu Zhongyi, and Zhang Jiajia