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Optimal Estimation of High-Dimensional Covariance Matrices with missing and Noisy data

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Advances in Pure Mathematics 2024年第4期14卷 214-227页

作者： Meiyin Wang Wanzhou Ye Department of Mathematics College of Science Shanghai University Shanghai China

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

关键词： High-Dimensional Covariance Matrix missing data Sub-Gaussian Noise Optimal Estimation

data-driven fault diagnosis of control valve with missing data based on modeling and deep residual shrinkage network

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2022年第4期23卷 303-313页

作者： Feng SUN He XU Yu-han ZHAO Yu-dong ZHANG College of Mechanical and Electrical Engineering Harbin Engineering UniversityHarbin150001China

A control valve is one of the most widely used machines in hydraulic ***,it often works in harsh environments and failure occurs from time to *** intelligent and robust control valve fault diagnosis is therefore important for operation of the *** this study,a fault diagnosis based on the mathematical model(MM)imputation and the modified deep residual shrinkage network(MDRSN)is proposed to solve the problem that data-driven models for control valves are susceptible to changing operating conditions and missing *** multiple fault time-series samples of the control valve at different openings are collected for fault diagnosis to verify the effectiveness of the proposed *** effects of the proposed method in missing data imputation and fault diagnosis are *** with random and k-nearest neighbor(KNN)imputation,the accuracies of MM-based imputation are improved by 17.87%and 21.18%,in the circumstances of a20.00%data missing rate at valve opening from 10%to 28%.Furthermore,the results show that the proposed MDRSN can maintain high fault diagnosis accuracy with missing data.

关键词： Control valve missing data Fault diagnosis Mathematical model(MM) Deep residual shrinkage network(DRSN)

New Chain Imputation Methods for Estimating Population Mean in the Presence of missing data Using Two Auxiliary Variables

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Communications in Mathematics and Statistics 2023年第2期11卷 325-340页

作者： Shashi Bhushan Abhay Pratap Pandey Department of Mathematics and Statistics Dr.Shakuntala Misra National Rehabilitation UniversityLucknowIndia Department of Statistics Ramanujan College University of DelhiNew DelhiIndia

This article deals with some new chain imputation methods by using two auxiliary variables under missing completely at random(MCAR)*** proposed generalized classes of chain imputation methods are tested from the viewpoint of optimality in terms of *** proposed imputation methods can be considered as an efficient extension to the work of Singh and Horn(Metrika 51:267-276,2000),Singh and Deo(Stat Pap 44:555-579,2003),Singh(Stat A J Theor Appl Stat 43(5):499-511,2009),Kadilar and Cingi(Commun Stat Theory Methods 37:2226-2236,2008)and Diana and Perri(Commun Stat Theory Methods 39:3245-3251,2010).The performance of the proposed chain imputation methods is investigated relative to the conventional chain-type imputation *** theoretical results are derived and comparative study is conducted and the results are found to be quite encouraging providing the improvement over the discussed work.

关键词： missing data Imputation MCAR

Comparison of missing data Imputation Methods in Time Series Forecasting

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Computers, Materials & Continua 2022年第1期70卷 767-779页

作者： Hyun Ahn Kyunghee Sun Kwanghoon Pio Kim Division of Software Convergence Hanshin UniversityGyeonggi18101Korea Contents Convergence Software Research Institute Kyonggi UniversityGyeonggi16227Korea Division of AI Computer Science and Engineering Kyonggi UniversityGyeonggi16227Korea

Time series forecasting has become an important aspect of data analysis and has many real-world ***,undesirable missing values are often encountered,which may adversely affect many forecasting *** this study,we evaluate and compare the effects of imputationmethods for estimating missing values in a time *** approach does not include a simulation to generate pseudo-missing data,but instead perform imputation on actual missing data and measure the performance of the forecasting model created *** an experiment,therefore,several time series forecasting models are trained using different training datasets prepared using each imputation ***,the performance of the imputation methods is evaluated by comparing the accuracy of the forecasting *** results obtained from a total of four experimental cases show that the k-nearest neighbor technique is the most effective in reconstructing missing data and contributes positively to time series forecasting compared with other imputation methods.

关键词： missing data imputation method time series forecasting LSTM

Unsupervised learning of Dirichlet process mixture models with missing data

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Science China(Information Sciences) 2016年第1期59卷 161-174页

作者： Xunan ZHANG Shiji SONG Lei ZHU Keyou YOU Cheng WU Department of Automation Tsinghua University China Ocean Mineral Resources R&D Association

This study presents a novel approach to unsupervised learning for clustering with missing *** first extend a finite mixture model to the infinite case by considering Dirichlet process mixtures, which can automatically determine the number of mixture components or clusters. Furthermore, we view the missing features as latent variables and compute the posterior distributions using the variational Bayesian expectation maximization algorithm, which optimizes the evidence lower bound on the complete-data log marginal likelihood. We demonstrate the performance on several artificial data sets with missing values. The experimental results indicate that the proposed method outperforms some classic imputation methods. We finally present an application to seabed hydrothermal sulfide color images analysis problem.

关键词： Dirichlet processes missing data clustering variational Bayesian image analysis

Semi-empirical Likelihood Confidence Intervals for the Differences of Quantiles with missing data

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Acta Mathematica Sinica,English Series 2009年第5期25卷 845-854页

作者： Yong Song QIN Jun Chao ZHANG School of Mathematical Sciences Guangxi Normal University Guilin 541004 P. R. China Department of Mathematics Harbin University Harbin 150086 P. R. China

Detecting population （group） differences is useful in many applications, such as medical research. In this paper, we explore the probabilistic theory for identifying the quantile differences .between two populations. Suppose that there are two populations x and y with missing data on both of them, where x is nonparametric and y is parametric. We are interested in constructing confidence intervals on the quantile differences of x and y. Random hot deck imputation is used to fill in missing data. Semi-empirical likelihood confidence intervals on the differences are constructed.

关键词： empirical likelihood confidence interval quantile missing data hot deck imputation

Empirical Likelihood Confidence Intervals for the Differences of Quantiles with missing data

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Acta Mathematicae Applicatae Sinica 2009年第1期25卷 105-116页

作者： Yong-song Qin Yong-jiang Qian School of Mathematical Sciences Guangxi Normal University Guilin Guangxi 541004 China

Suppose that there are two nonparametric populations x and y with missing data on both of them. We are interested in constructing confidence intervals on the quantile differences of x and y. Random imputation is used.... 详细信息

关键词： Empirical likelihood confidence Interval quantile missing data imputation

Stochastic Gradient Descent for Linear Systems with missing data

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 1-20页

作者： Anna Ma Deanna Needell Claremont Graduate University ClaremontCA 91711USA University of California Los AngelesLos Angeles CA 90095USA

Traditional methods for solving linear systems have quickly become imprac-tical due to an increase in the size of available *** massive amounts of data is further complicated when the data is incomplete or has missing *** this work,we address the obstacles presented when working with large data and incom-plete data *** particular,we propose to adapt the Stochastic Gradient Descent method to address missing data in linear *** proposed algorithm,the Stochastic Gradient Descent for missing data method(mSGD),is introduced and theoretical convergence guarantees are *** addition,we include numerical experiments on simulated and real world data that demonstrate the usefulness of our method.

关键词： Linear systems missing data iterative methods least squares problems

A Practical Approach for missing Wireless Sensor Networks data Recovery

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China Communications 2024年第5期21卷 202-217页

作者： Song Xiaoxiang Guo Yan Li Ning Ren Bing The College of Communications Engineering Army Engineering University of PLANanjing 210007China The 63891 Unit of PLA Luoyang 471000China

In wireless sensor networks(WSNs),the performance of related applications is highly dependent on the quality of data ***,missing data is almost inevitable in the process of data acquisition and *** methods often rely on prior information such as low-rank characteristics or spatiotemporal correlation when recovering missing WSNs ***,in realistic application scenarios,it is very difficult to obtain these prior information from incomplete data ***,we aim to recover the missing WSNs data effectively while getting rid of the perplexity of prior *** designing the corresponding measurement matrix that can capture the position of missing data and sparse representation matrix,a compressive sensing(CS)based missing data recovery model is ***,we design a comparison standard to select the best sparse representation basis and introduce average cross-correlation to examine the rationality of the established ***,an improved fast matching pursuit algorithm is proposed to solve the *** results show that the proposed method can effectively recover the missing WSNs data.

关键词： average cross correlation matching pursuit missing data wireless sensor networks