The Phase Transition of Matrix Recovery from Gaussian Measurements Matches the Minimax MSE of Matrix Denoising

By Gavish Matan, Donoho David, and Montanari Andrea
Working Paper Stanford University (2013)

  • Matan Gavish

    Stanford University



November 5, 2013

Last update

November 5, 2013










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)

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