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Unified Variable Selection for Varying Coefficient Models with Longitudinal Data

Journal of Systems Science & Complexity 2023年第2期36卷 822-842页

作者： XU Xiaoli ZHOU Yan ZHANG Kongsheng ZHAO Mingtao School of Management Science and Engineering Anhui University of Finance and Economics College of Mathematics and Statistics Institute of Statistical SciencesShenzhen Key Laboratory of Advanced Machine Learning and ApplicationsShenzhen University Institute of Statistics and Applied Mathematics Anhui University of Finance and Economics

Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant *** paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal *** proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant *** is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient *** regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant *** obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically ***,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data *** results show that the proposed method performs better than the existing competitor.

关键词： Double-penalized quadratic inference functions longitudinal data variable selection varying coefficient models

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Non-Local and Fully Connected Tensor Network Decomposition for Remote Sensing Image Denoising

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高等学校计算数学学报（英文版） 2024年第2期17卷 379-403页

作者： Zhihui Tu Shunda Chen Jian Lu Lin Li Qingtang Jiang Shenzhen Key Laboratory of Advanced Machine Learning and Applications School of Mathematical SciencesShenzhen UniversityShenzhen 518060China Shenzhen Key Laboratory of Advanced Machine Learning and Applications School of Mathematical SciencesShenzhen UniversityShenzhen 518060China National Center for Applied Mathematics Shenzhen(NCAMS) Shenzhen 518055China Pazhou Lab Guangzhou 510320China School of Electronic Engineering Xidian UniversityXi'an 710071China Department of Mathematics and Statistics University of Missouri-St.LouisSt.LouisMO 63121USA

Remote sensing images(RSIs)encompass abundant spatial and spec-tral/temporal information,finding wide applications in various ***,during image acquisition and transmission,RSI often encounter noise interference,which adversely affects the accuracy of subsequent *** address this is-sue,this paper proposes a novel non-local fully connected tensor network(NLFCTN)decomposition algorithm for denoising RSI,aiming to fully exploit their global cor-relation and non-local self-similarity(NSS)***,as a recently de-veloped tensor decomposition technique,exhibits remarkable capability in captur-ing global correlations and minimizing information *** addition,we introduce an efficient algorithm based on proximal alternating minimization(PAM)to effi-ciently solve the model and prove the *** effectiveness of the pro-posed method is validated through denoising experiments on both simulated and real RSI data,employing objective evaluation metrics and subjective visual *** results of the experiment show that the proposed method outperforms other RSI denoising techniques in terms of denoising performance.

关键词： Remote sensing images denoising tensor decomposition non-local self-similarity

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IMPULSE NOISE REMOVAL BY L1 WEIGHTED NUCLEAR NORM MINIMIZATION

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Journal of Computational Mathematics 2023年第6期41卷 1171-1191页

作者： Jian Lu Yuting Ye Yiqiu Dong Xiaoxia Liu Yuru Zou Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and StatisticsShenzhen UniversityShenzhen 518060China Guangdong Key Laboratory of Intelligent Information Processing Pazhou LabGuangzhou 510335China Department of Applied Mathematics and Computer Science Technical University of Denmark2800 Kgs.LyngbyDenmark

In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research *** assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many ***,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise *** this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from *** apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this *** exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse *** results show that our method can effectively remove impulse noise.

关键词： Image denoising Weighted nuclear norm minimization l 1-data-fidelity term Low rank analysis Impulse noise

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A NONLOCAL KRONECKER-BASIS-REPRESENTATION METHOD FOR LOW-DOSE CT SINOGRAM RECOVERY

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Journal of Computational Mathematics 2024年第4期42卷 1080-1108页

作者： Jian Lu Huaxuan Hu Yuru Zou Zhaosong Lu Xiaoxia Liu Keke Zu Lin Li Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and StatisticsShenzhen UniversityShenzhen 518060China National Center for Applied Mathematics Shenzhen(NCAMS) Shenzhen 518055China Department of Industrial and Systems Engineering University of Minnesota Twin CitiesMinneapolisMN55455USA Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong Kong SARChina School of Electronic Engineering Xidian UniversityXi'an 710071China

Low-dose computed tomography(LDCT)contains the mixed noise of Poisson and Gaus-sian,which makes the image reconstruction a challenging *** order to describe the statistical characteristics of the mixed noise,we adopt the sinogram preprocessing as a stan-dard maximum a posteriori(MAP).Based on the fact that the sinogram of LDCT has non-local self-similarity property,it exhibits low-rank *** conventional way of solving the low-rank problem is implemented in matrix forms,and ignores the correlations among similar patch *** avoid this issue,we make use of a nonlocal Kronecker-Basis-Representation(KBR)method to depict the low-rank problem.A new denoising model,which consists of the sinogram preprocessing for data fidelity and the nonlocal KBR term,is developed in this *** proposed denoising model can better illustrate the generative mechanism of the mixed noise and the prior knowledge of the ***-merical results show that the proposed denoising model outperforms the state-of-the-art algorithms in terms of peak-signal-to-noise ratio(PSNR),feature similarity(FSIM),and normalized mean square error(NMSE).

关键词： Low-dose computed tomography Kronecker-basis-representation Low-rank imation.Noise-generating-mechanism

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Error Estimate for Semi-implicit Method of Sphere-Constrained High-Index Saddle Dynamics

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Chinese Annals of Mathematics,Series B 2023年第5期44卷 765-780页

作者： Lei ZHANG Pingwen ZHANG Xiangcheng ZHENG Beijing International Center for Mathematical Research Center for Machine Learning ResearchCenterfor Quantitative BiologyPeking UniversityBeijing 100871China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China School of MathematicalSciences Laboratory of Mathematics and Applied MathematicsPeking UniversityBeijing 100871China School of Mathematics Shandong UniversityJinan 250100China

The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics,which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems on the high-dimensional *** to the semi-implicit treatment and the novel computational procedure,the orthonormality of numerical solutions at each time step could not be fully employed to simplify the derivations,and the computations of the state variable and directional vectors are coupled with the retraction,the vector transport and the orthonormalization procedure,which significantly complicates the *** address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.

关键词： Saddle point Constrained saddle dynamics Solution landscape Semiimplicit Numerical analysis

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Automating the Selection of Proxy Variables of Unmeasured Confounders 41

Automating the Selection of Proxy Variables of Unmeasured Co...

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41st International Conference on machine learning, ICML 2024

作者： Xie, Feng Chen, Zhengming Luo, Shanshan Miao, Wang Cai, Ruichu Geng, Zhi Department of Applied Statistics Beijing Technology and Business University Beijing China School of Computer Science Guangdong University of Technology Guangzhou510006 China Machine Learning Department Mohamed bin Zayed University of Artificial Intelligence Abu Dhabi United Arab Emirates Department of Probability and Statistics Peking University Beijing China

Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach. Copyright 2024 by the author(s)

关键词： Higher order statistics

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Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere

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Science China Mathematics 2023年第10期66卷 2347-2360页

作者： Lei Zhang Pingwen Zhang Xiangcheng Zheng Beijing International Center for Mathematical Research Center for Machine Learning ResearchCenter for Quantitative BiologyPeking UniversityBeijing 100871China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China School of Mathematical Sciences Laboratory of Mathematics and Applied MathematicsPeking UniversityBeijing 100871China School of Mathematics Shandong UniversityJinan 250100China

We develop and analyze numerical discretization to the constrained high-index saddle dynamics,the dynamics searching for the high-index saddle points confined on the high-dimensional unit *** with the saddle dynamics without constraints,the constrained high-index saddle dynamics has more complex dynamical forms,and additional operations such as the retraction and vector transport are required due to the constraints,which significantly complicate the numerical scheme and the corresponding numerical ***,as the existing numerical analysis results usually depend on the index of the saddle points implicitly,the proved numerical accuracy may be reduced if the index is high in many applications,which indicates the lack of robustness with respect to the *** address these issues,we derive the error estimates for numerical discretization of the constrained high-index saddle dynamics on the high-dimensional sphere and then improve it by providing index-robust error analysis in an averaged norm by adjusting the relaxation *** developed results provide mathematical support for the accuracy of numerical computations.

关键词： saddle dynamics saddle point solution landscape error estimate index-robust

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Risk-based Calibration for Generative Classifiers

arXiv

引用

arXiv 2024年

作者： Pérez, Aritz Echegoyen, Carlos Santafé, Guzmán Machine Learning Basque Center for Applied Mathematics Bilbao Spain Spatial Statistics Group Public University of Navarre Pamplona Spain

Generative classifiers are constructed on the basis of a joint probability distribution and are typically learned using closed-form procedures that rely on data statistics and maximize scores related to data fitting. However, these scores are not directly linked to supervised classification metrics such as the error, i.e., the expected 0-1 loss. To address this limitation, we propose a learning procedure called risk-based calibration (RC) that iteratively refines the generative classifier by adjusting its joint probability distribution according to the 0-1 loss in training samples. This is achieved by reinforcing data statistics associated with the true classes while weakening those of incorrect classes. As a result, the classifier progressively assigns higher probability to the correct labels, improving its training error. Results on 20 heterogeneous datasets using both naïve Bayes and quadratic discriminant analysis show that RC significantly outperforms closed-form learning procedures in terms of both training error and generalization error. In this way, RC bridges the gap between traditional generative approaches and learning procedures guided by performance measures, ensuring a closer alignment with supervised classification objectives. © 2024, CC BY-NC-SA.

关键词： Normal distribution

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A permutation-free kernel independence test

The Journal of Machine Learning Research

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The Journal of machine learning Research 2023年第1期24卷 17707-17774页

作者： Shubhanshu Shekhar Ilmun Kim Aaditya Ramdas Department of Statistics and Data Science Carnegie Mellon University Pittsburgh PA Department of Statistics and Data Science Department of Applied Statistics Yonsei University Seodaemun-gu Seoul Republic of Korea Department of Statistics and Data Science Machine Learning Department Carnegie Mellon University Pittsburgh PA

In nonparametric independence testing, we observe i.i.d. data {(Xi, Yi)}ni=1, where X ∈ Χ, Y ∈ Y lie in any general spaces, and we wish to test the null that X is independent of Y. Modern test statistics such as the kernel Hilbert-Schmidt Independence Criterion (HSIC) and Distance Covariance (dCov) have intractable null distributions due to the degeneracy of the underlying U-statistics. Hence, in practice, one often resorts to using permutation testing, which provides a nonasymptotic guarantee at the expense of recalculating the quadratic-time statistics (say) a few hundred times. In this paper, we provide a simple but nontrivial modification of HSIC and dCov (called xHSIC and xdCov, pronounced "cross" HSIC/dCov) so that they have a limiting Gaussian distribution under the null, and thus do not require permutations. We show that our new tests, like the originals, are consistent against fixed alternatives, and minimax rate optimal against smooth local alternatives. Numerical simulations demonstrate that compared to the permutation tests, our variants have the same power within a constant factor, giving practitioners a new option for large problems or data-analysis pipelines where computation, not sample size, could be the bottleneck.

关键词： independence testing kernel-methods permutation-free tests Hilbert-Schmidt independence critrion (HSIC) distance covariance

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Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data

arXiv

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arXiv 2024年

作者： Gyger, Tim Furrer, Reinhard Sigrist, Fabio Institute of Financial Services Zug Lucerne University of Applied Sciences and Arts Switzerland Department of Mathematical Modeling and Machine Learning University of Zurich Switzerland Seminar for Statistics ETH Zurich Switzerland

Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations (FSAs) combine predictive process methods and covariance tapering, thus approximating both global and local structures. We show how iterative methods can be used to reduce computational costs in calculating likelihoods, gradients, and predictive distributions with FSAs. In particular, we introduce a novel preconditioner and show theoretically and empirically that it accelerates the conjugate gradient method’s convergence speed and mitigates its sensitivity with respect to the FSA parameters and the eigenvalue structure of the original covariance matrix, and we demonstrate empirically that it outperforms a state-of-the-art pivoted Cholesky preconditioner. Furthermore, we introduce an accurate and fast way to calculate predictive variances using stochastic simulation and iterative methods. In addition, we show how our newly proposed FITC preconditioner can also be used in iterative methods for Vecchia approximations. In our experiments, it outperforms existing state-of-the-art preconditioners for Vecchia approximations. All methods are implemented in a free C++ software library with high-level Python and R packages (https://***/fabsig/GPBoost).MSC Codes 62M30, 60G15, 68T09, 62R07, 65F08, 65F10 Copyright © 2024, The Authors. All rights reserved.

关键词： Conjugate gradient method

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