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

    USA

Created

November 5, 2013

Last update

November 5, 2013

Software

Matlab

Ranking

85

Visits

3062

Downloads

95

Description

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)

Empirical likelihood inference for longitudinal data with covariate measurement errors: an application to the LEAN study

Working Paper (2021)

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

Principal componentsof spatial, rank and Kendalls tau-covariance matrices for the population, randomsamples, real and simulated data

Working Paper (2021)

Koch Inge and Naito Kanta

2021-03-12

Zip Archive

954

257

11

Testing the first-order separability hypothesis for spatio-temporal point patterns

Computational Statistics & Data Analysis (2021)

Ghorbani Mohammad, Vafaei Nafiseh, Dvořák Jiří, and Myllymäki Mari

Ensemble Sparse Estimation of Covariance Structure for Exploring Genetic Disease Data

Computational Statistics & Data Analysis (2021)

Kang Xiaoning and Wang Mingqiu

A Mapping-based Universal Kriging Model for Order-of addition Problems in Drug Combination Studies

Computational Statistics & Data Analysis (2021)

Xiao Qian and Xu Hongquan

Inference for partially observed epidemic dynamics guided by Kalman filtering techniques

Working Paper (2020)

Delattre Maud, Larédo Catherine, and Vergu Elisabeta

Estimating Robot Strengths with Application to Selection of Alliance Members in FIRST Robotics Competitions

Computational Statistics and Data Analysis (2021)

Lim Alejandro, Chiang Chin-Tsang, and Teng Jen-Chieh

A New Nonlinear Wavelet-Based Unit Root Test with Structural Breaks

Munich Personal RePEc Archive (2019)

Aydin Mucahit

Are shocks to disaggregated renewable energy consumption permanent or temporary for the USA? Wavelet based unit root test with smooth structural shifts

Energy (2020)

Aydin Mucahit

0 comment

Add comment

You need to log in to post a comment.