Computing the degrees of freedom of rank-regularized estimators and cousins

DOI10.1214/20-EJS1681zbMath1439.62142arXiv1909.10143MaRDI QIDQ2180064

Haolei Weng, Rahul Mazumder

Publication date: 13 May 2020

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.10143

zbMATH Keywords

regularizationspectral functiondivergencematrix-valued functiondegrees of freedomlow rankStein's unbiased risk sstimate (SURE) framework

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Inference from stochastic processes and spectral analysis (62M15)

Uses Software

• S+WAVELETS
• softImpute
• sparsenet

Cites Work

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• Nearly unbiased variable selection under minimax concave penalty
• Degrees of freedom in lasso problems
• Optimal selection of reduced rank estimators of high-dimensional matrices
• Estimation of the mean of a multivariate normal distribution
• Reduced-rank regression for the multivariate linear model
• Multivariate reduced-rank regression
• On Stein's unbiased risk estimate for reduced rank estimators
• Least angle regression. (With discussion)
• Matrix completion with nonconvex regularization: spectral operators and scalable algorithms
• On the ``degrees of freedom of the lasso
• Nonsmooth analysis of singular values. I: Theory
• Nonsmooth analysis of singular values. II: Applications
• Exact matrix completion via convex optimization
• Degrees of freedom and model search
• SparseNet: Coordinate Descent With Nonconvex Penalties
• Adapting to Unknown Smoothness via Wavelet Shrinkage
• On Measuring and Correcting the Effects of Data Mining and Model Selection
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• Does $\ell _{p}$ -Minimization Outperform $\ell _{1}$ -Minimization?
• Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
• A Statistical View of Some Chemometrics Regression Tools
• Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression
• On the degrees of freedom of reduced-rank estimators in multivariate regression
• Some Comments on C P
• Semismooth Matrix-Valued Functions
• Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems
• Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions
• The elements of statistical learning. Data mining, inference, and prediction

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