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arXiv 2025年

作者： Zhang, Yimang Wang, Xiaorui Shi, Jian Qing Department of Statistics and Data Science Southern University of Science and Technology China National Center for Applied Mathematics Shenzhen China

Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis model which is more flexible to characterize the relationship between manifest variables and latent factors. The confirmatory identifiability of the latent factor is discussed, ensuring the substantive interpretation of the latent factors. A Bayesian approach with a Gaussian process prior is proposed to estimate the unknown nonlinear function and the unknown parameters. Asymptotic results are established, including structural identifiability of the latent factors, consistency of the estimates of the unknown parameters and the unknown nonlinear function. Simulation studies and a real data analysis are conducted to investigate the performance of the proposed method. Simulation studies show our proposed method performs well in handling nonlinear model and successfully identifies the latent factors. Our analysis incorporates oil flow data, allowing us to uncover the underlying structure of latent nonlinear patterns. © 2025, CC BY-NC-ND.

关键词： Markov processes

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A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION

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Journal of Computational Mathematics 2024年第4期42卷 999-1031页

作者： Jiaofen Li Lingchang Kong Xuefeng Duan Xuelin Zhou Qilun Luo School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuangxi Key Laboratory of Automatic Detecting Technology and InstrumentsGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematical Sciences South China Normal UniversityGuangzhou 510000China School of Mathematics and Computing Science Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematics and Statistics Yunan UniversityKunming 650000China

The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,*** this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et *** presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence *** experiments are provided to illustrate the efficiency of the proposed *** with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.

关键词： Truncated singular value decomposition Riemannian optimization Trust-region method

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Effective Positive Cauchy Combination Test

arXiv

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arXiv 2024年

作者： Ouyang, Yanyan Liu, Xingwei Zhu, Lixing Xu, Wangli Center for Applied Statistics School of Statistics Renmin University of China China School of Science Chang’an University China Center for Statistics and Data Science Beijing Normal University China

In the field of multiple hypothesis testing, combining p-values represents a fundamental statistical method. The Cauchy combination test (CCT) (Liu and Xie, 2020) excels among numerous methods for combining p-values with powerful and computationally efficient performance. However, large p-values may diminish the significance of testing, even extremely small p-values exist. We propose a novel approach named the positive Cauchy combination test (PCCT) to surmount this flaw. Building on the relationship between the PCCT and CCT methods, we obtain critical values by applying the Cauchy distribution to the PCCT statistic. We find, however, that the PCCT tends to be effective only when the significance level is substantially small or the test statistics are strongly correlated. Otherwise, it becomes challenging to control type I errors, a problem that also pertains to the CCT. Thanks to the theories of stable distributions and the generalized central limit theorem, we have demonstrated critical values under weak dependence, which effectively controls type I errors for any given significance level. For more general scenarios, we correct the test statistic using the generalized mean method, which can control the size under any dependence structure and cannot be further optimized. Our method exhibits excellent performance, as demonstrated through comprehensive simulation studies. We further validate the effectiveness of our proposed method by applying it to a genetic dataset. © 2024, CC BY-NC-SA.

关键词： Errors

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ON STOCHASTIC CONTROL PROBLEMS WITH HIGHER-ORDER MOMENTS

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SIAM Journal on Control and Optimization 2025年第3期63卷 1560-1589页

作者： Wang, Yike Liu, Jingzhen Bensoussan, Alain Cedric Yiu, Ka-Fai Wei, Jiaqin School of Finance Chongqing Technology and Business University Chongqing China China Institute for Actuarial Science Central University of Finance and Economics Beijing China SNaveen Jindal School of Management University of Texas at Dallas DallasTX75080 United States Department of Applied Mathematics Hong Kong Polytechnic University Hong Kong Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai China

In this paper, we focus on a class of time-inconsistent stochastic control problems, where the objective function includes the mean and several higher-order central moments of the terminal value of state. To tackle the time-inconsistency, we seek both the closed-loop and the open-loop Nash equilibrium controls as time-consistent solutions. We establish a partial differential equation (PDE) system for deriving a closed-loop Nash equilibrium control, which does not include the equilibrium value function and is different from the extended Hamilton-Jacobi-Bellman (HJB) equations as in Bj\" ork, Khapko, and Murgoci [Finance Stoch., 21 (2017), pp. 331-360]. We show that our PDE system is equivalent to the extended HJB equations that seem difficult to solve for our higher-order moment problems. In deriving an open-loop Nash equilibrium control, due to the nonseparable higher-order moments in the objective function, we make some moment estimates in addition to the standard perturbation argument for developing a maximum principle. Then, the problem is reduced to solving a flow of forward-backward stochastic differential equations. In particular, we investigate linear controlled dynamics and some objective functions affine in the mean. The closed-loop and the open-loop Nash equilibrium controls are identical, which are independent of the state value, the random path, and the preference on the odd-order central moments. By sending the highest order of central moments to infinity, we obtain the time-consistent solutions to some control problems whose objective functions include some penalty functions for deviation. © 2025 Society for Industrial and applied Mathematics.

关键词： Stochastic control systems

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The Optimal Closed-Form Linear Canonical Wigner Distribution 6

The Optimal Closed-Form Linear Canonical Wigner Distribution

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6th International Conference on Information Communication and Signal Processing, ICICSP 2023

作者： Zhang, Zhichao School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing China

ISBN: (纸本)9798350339994

This study devotes to Heisenberg's uncertainty inequalities under the closed-form instantaneous cross-correlation function Wigner distribution (CICFWD), whose generalizability enables it to be a representative Wigner distribution (WD) in the linear canonical transform (LCT) domain. A relation between the spread in the time-CICFWD domain and the spreads and moments in LCT domains is established. We then obtain two versions of lower bounds on the uncertainty product of spreads in time-CICFWD and LCT-CICFWD domains. The first is the tightest universal lower bound for all signals, and the other is a lower bound for complex-valued signals. As a result, uncertainty principles for the traditional WD are revisited. The optimal LCT free parameters selection problems of the CICFWD are also well-addressed from the perspectives of the highest time-frequency resolution and its best estimation accuracy, respectively. © 2023 IEEE.

关键词： linear canonical Wigner distribution lower bound time-frequency resolution uncertainty principle

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Bayesian functional data analysis in astronomy

arXiv

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arXiv 2024年

作者： Loredo, Thomas Budavári, Tamás Kent, David Ruppert, David Cornell Center for Astrophysics and Planetary Science Department of Statistics and Data Science Cornell University United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Department of Statistics and Data Science Cornell University United States School of Operations Research and Information Engineering Department of Statistics and Data Science Cornell University United States

Cosmic demographics—the statistical study of populations of astrophysical objects—has long relied on multivariate statistics, providing methods for analyzing data comprising fixed-length vectors of properties of objects, as might be compiled in a tabular astronomical catalog (say, with sky coordinates, and brightness measurements in a fixed number of spectral passbands). But beginning with the emergence of automated digital sky surveys, ca. 2000, astronomers began producing large collections of data with more complex structure: light curves (brightness time series) and spectra (brightness vs. wavelength). These comprise what statisticians call functional data—measurements of populations of functions. Upcoming automated sky surveys will soon provide astronomers with a flood of functional data. New methods are needed to accurately and optimally analyze large ensembles of light curves and spectra, accumulating information both along and across measured functions. Functional data analysis (FDA) provides tools for statistical modeling of functional data. Astronomical data presents several challenges for FDA methodology, e.g., sparse, irregular, and asynchronous sampling, and heteroscedastic measurement error. Bayesian FDA uses hierarchical Bayesian models for function populations, and is well suited to addressing these challenges. We provide an overview of astronomical functional data, and of some key Bayesian FDA modeling approaches, including functional mixed effects models, and stochastic process models. We briefly describe a Bayesian FDA framework combining FDA and machine learning methods to build low-dimensional parametric models for galaxy spectra. © 2024, CC BY.

关键词： Cosmology

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Non-Regular Pseudo-Differential Operators on Matrix Weighted Besov-Triebel-Lizorkin Spaces

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数学研究（英文） 2024年第1期57卷 84-100页

作者： Tengfei Bai Jingshi Xu School of Mathematics and Statistics Hainan Normal UniversityHaikouHainan 571158China Center for Applied Mathematics of Guangxi Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationSchool of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin 54100China

In this paper we obtain the boundedness of non-regular pseudo-differential operators with symbols in Besov spaces on matrix-weighted Besov-Triebel-Lizorkin *** symbols include the classical Hörmander classes.

关键词： Besov space matrix weight Pseudo-differential operator Triebel-Lizorkin space

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Sorted Minimization for Sparse Signal Recovery

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Journal of Scientific Computing 2024年第2期99卷 1-19页

作者： Wang, Chao Yan, Ming Yu, Junjie Department of Statistics and Data Science Southern University of Science and Technology Shenzhen China National Centre for Applied Mathematics Shenzhen Shenzhen China School of Data Science The Chinese University of Hong Kong Shenzhen (CUHK-Shenzhen) Shenzhen China

This paper introduces a novel approach for recovering sparse signals using sorted $$L_1/L_2$$ minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively preserving the most significant contributions to the signal while promoting sparsity. We present models for both noise-free and noisy scenarios, and rigorously prove the existence of solutions for each case. To solve these models, we adopt a linearization approach inspired by the difference of convex functions algorithm. Our experimental results demonstrate the superiority of our method over state-of-the-art approaches in sparse signal recovery across various circumstances, particularly in support detection.

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Hamiltonian formulations of centroid-based clustering

arXiv

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arXiv 2025年

作者： Seong, Myeonghwan Park, Daniel K. Department of Statistics and Data Science Yonsei University Seoul03722 Korea Republic of Department of Applied Statistics Yonsei University Seoul03722 Korea Republic of

Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given dataset. Traditional clustering methods, such as the k-means algorithm and weighted maximum kcut, focus on specific objectives—typically relying on average or pairwise characteristics of the data—leading to performance that is highly data-dependent. Moreover, incorporating practical constraints into clustering objectives is not straightforward, and these problems are known to be NP-hard. In this study, we formulate the clustering problem as a search for the ground state of a Hamiltonian, providing greater flexibility in defining clustering objectives and incorporating constraints. This approach enables the application of various quantum simulation techniques, including both circuit-based quantum computation and quantum annealing, thereby opening a path toward quantum advantage in solving clustering problems. We propose various Hamiltonians to accommodate different clustering objectives, including the ability to combine multiple objectives and incorporate constraints. We evaluate the clustering performance through numerical simulations and implementations on the D-Wave quantum annealer. The results demonstrate the broad applicability of our approach to a variety of clustering problems on current quantum devices. Furthermore, we find that Hamiltonians designed for specific clustering objectives and constraints impose different requirements for qubit connectivity, indicating that certain clustering tasks are better suited to specific quantum hardware. Our experimental results highlight this by identifying the Hamiltonian that optimally utilizes the physical qubits available in the D-Wave System. Copyright © 2025, The Authors. All rights reserved.

关键词： Qubits

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MODELING THE INTERACTION OF CYTOTOXIC T-LYMPHOCYTES AND ONCOLYTIC VIRUSES IN A TUMOR MICROENVIRONMENT

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SIAM Journal on applied Mathematics 2025年第2期85卷 983-1005页

作者： Zhao, Yan Deng, Qi Qiu, Zhipeng Guo, Ting Ruan, Shigui School of Mathematics and Statistics Nanjing University of Science and Technology Nanjing210094 China Laboratory for Industrial and Applied Mathematics Department of Mathematics and Statistics York University TorontoONM3J1P0 Canada Aliyun School of Big Data Changzhou University Changzhou213164 China Department of Mathematics University of Miami Coral GablesFL33146 United States

Oncolytic virotherapy has become a promising approach in treating cancer. Understanding the mechanism of interaction between oncolytic viruses (OVs) and the immune system is crucial for the interventional diagnosis and therapy of tumors. In this paper, a mathematical model is formulated to understand the interaction among cytotoxic T-lymphocytes (CTLs), OVs, and tumor cells in which the Gompertz curve is used to describe the tumor proliferation. The basic reproductive number (R0) is first derived, and then the local and global dynamics of the system are analyzed mainly in terms of R0 and another threshold R0E, the basic reproductive number of CTLs which determines the number of positive equilibria. The theoretical results suggest that the system may have periodic solutions and backward bifurcation. Furthermore, numerical simulations are explored to evaluate the influence of CTLs on virotherapy. CTL immune response plays an obstructive role on virotherapy, and once the CTL proliferation rate exceeds a threshold, the tumor will escape. In addition, the whole tumor population is inversely proportional to the viral infection rate as well as the tumor proliferation rate. © 2025 Society for Industrial and applied Mathematics.

关键词： Numerical models

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