High dimensional regression and matrix estimation without tuning parameters

2015/10/25 by Sourav Chatterjee, Chatterjee, Sourav
Computer Science · Engineering · Mathematics · #62F10 #62F12 #62F30 #62J05 #Control Systems and Identification #Distributed Sensor Networks and Detection Algorithms #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST #msc:62F10 #msc:62F12 #msc:62F30 #msc:62J05 #stat.TH

paper · pdf · doi:10.48550/arxiv.1510.07294

23 pages, 1 figure. Minor corrections in this revision

openalex publication_date 2015/10/25 · arxiv created 2015/11/28 · arxiv updated 2015/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A general theory for Gaussian mean estimation that automatically adapts to unknown sparsity under arbitrary norms is proposed. The theory is applied to produce adaptively minimax rate-optimal estimators in high dimensional regression and matrix estimation that involve no tuning parameters.

Citations

• Various thresholds for ℓ₁-optimization in compressed sensing
• SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax
• Atomic Decomposition by Basis Pursuit
• Estimation of the Mean of a Multivariate Normal Distribution
• Least angle regression
• Adapting to unknown sparsity by controlling the false discovery rate
• Nuclear norm penalization and optimal rates for noisy low rank matrix\n completion

Related

• Adaptive estimation of High-Dimensional Signal-to-Noise Ratios
• TIGER: A Tuning-Insensitive Approach for Optimally Estimating Gaussian Graphical Models
• Flat Minima in Linear Estimation and an Extended Gauss Markov Theorem
• Minimax-optimal nonparametric regression in high dimensions
• Interplay of minimax estimation and minimax support recovery under sparsity