scholarly journals Eigenvalue Distribution of a High-Dimensional Distance Covariance Matrix With Application

2023 ◽  
Author(s):  
Weiming Li ◽  
Qinwen Wang ◽  
Jianfeng Yao
Keyword(s):  
Covariance Matrix ◽  
Eigenvalue Distribution ◽  
High Dimensional ◽  
Distance Covariance

scholarly journals ON DETERMINING THE NUMBER OF SPIKES IN A HIGH-DIMENSIONAL SPIKED POPULATION MODEL

2012 ◽  
Vol 01 (01) ◽  
pp. 1150002 ◽  
Author(s):  
DAMIEN PASSEMIER ◽  
JIAN-FENG YAO
Keyword(s):  
Covariance Matrix ◽  
Population Model ◽  
Factor Model ◽  
Fundamental Problem ◽  
High Dimensional ◽  
Sample Covariance ◽  
Or Economics ◽  
Linear Mixture Model ◽  
The Difference ◽  
Scientific Fields

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific fields, including signal processing (linear mixture model) or economics (factor model). Several recent papers studied the asymptotic behavior of the eigenvalues of the sample covariance matrix (sample eigenvalues) when the dimension of the observations and the sample size both grow to infinity so that their ratio converges to a positive constant. Using these results, we propose a new estimator based on the difference between two consecutive sample eigenvalues.

scholarly journals On eigenvalues of a high-dimensional spatial-sign covariance matrix

Bernoulli ◽  
2022 ◽  
Vol 28 (1) ◽  
Author(s):  
Weiming Li ◽  
Qinwen Wang ◽  
Jianfeng Yao ◽  
Wang Zhou
Keyword(s):  
Covariance Matrix ◽  
High Dimensional

scholarly journals Mirrored Orthogonal Sampling for Covariance Matrix Adaptation Evolution Strategies

2019 ◽  
Vol 27 (4) ◽  
pp. 699-725 ◽  
Author(s):  
Hao Wang ◽  
Michael Emmerich ◽  
Thomas Bäck
Keyword(s):  
Convergence Rate ◽  
Covariance Matrix ◽  
Sampling Technique ◽  
Black Box ◽  
Evolution Strategies ◽  
High Dimensional ◽  
Major Purpose ◽  
Search Spaces ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution

Generating more evenly distributed samples in high dimensional search spaces is the major purpose of the recently proposed mirrored sampling technique for evolution strategies. The diversity of the mutation samples is enlarged and the convergence rate is therefore improved by the mirrored sampling. Motivated by the mirrored sampling technique, this article introduces a new derandomized sampling technique called mirrored orthogonal sampling. The performance of this new technique is both theoretically analyzed and empirically studied on the sphere function. In particular, the mirrored orthogonal sampling technique is applied to the well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The resulting algorithm is experimentally tested on the well-known Black-Box Optimization Benchmark (BBOB). By comparing the results from the benchmark, mirrored orthogonal sampling is found to outperform both the standard CMA-ES and its variant using mirrored sampling.

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