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Optimal rates of convergence for covariance matrix estimation
Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covarianceExpand
OPTIMAL RATES OF CONVERGENCE FOR SPARSE COVARIANCE MATRIX ESTIMATION
This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is onExpand
Rate-optimal graphon estimation
Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzingExpand
Minimax Rates of Community Detection in Stochastic Block Models
TLDR
In this paper, we provide a general minimax theory for community detection for the stochastic block model. Expand
Sparse CCA: Adaptive Estimation and Computational Barriers
Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originatedExpand
Achieving Optimal Misclassification Proportion in Stochastic Block Models
TLDR
In this paper, we present a computationally feasible two-stage method that achieves optimal statistical performance in misclassification proportion for stochastic block model under weak regularity conditions. Expand
MINIMAX ESTIMATION OF LARGE COVARIANCE MATRICES UNDER ℓ1-NORM
Driven by a wide range of applications in high-dimensional data analy- sis, there has been significant recent interest in the estimation of large covariance matrices. In this paper, we considerExpand
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation
This is an expository paper that reviews recent developments on optimal estimation of structured high-dimensional covariance and precision matrices. Minimax rates of convergence for estimatingExpand
A data-driven block thresholding approach to wavelet estimation
A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size andExpand
Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants
  • Yu Lu, H. Zhou
  • Mathematics, Computer Science
  • ArXiv
  • 7 December 2016
TLDR
We investigate the performance of Lloyd's algorithm on clustering sub-Gaussian mixtures. Expand
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