检索结果-内蒙古大学图书馆

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

来源：评论

学校读者我要写书评

暂无评论

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

引用

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

来源：评论

学校读者我要写书评

暂无评论

Multivariate response directional regression: a projective resampling approach

引用

Journal of Big data 2025年第1期12卷 1-30页

作者： Lee, Ahreum Kim, Kyongwon Department of Statistics Ewha Womans University 52 Ewhayeodae-gil Seodaemum-gu Seoul 03760 South Korea Department of Applied Statistics Department of Statistics and Data Science Yonsei University 50 Yonsei-ro Seodaemun-gu Seoul 03722 South Korea

In high dimensional data analysis, directional regression is a widely used method for implementing linear sufficient dimension reduction by extracting core information from the complex data structure. However, extending sufficient dimension reduction techniques to handle multivariate response data remains a relatively challenging task. In this paper, we propose a novel method that integrates directional regression with the projective resampling framework to tackle the multivariate response regression problem. Our method, called projective resampling directional regression, not only improves estimation accuracy of the dimension reduction subspace but also offers greater flexibility of directional regression across diverse datasets. We establish theoretical properties of our method, including consistency and convergence rates. Comprehensive simulation studies under various scenarios, along with analyses of two real-world datasets, demonstrate the effectiveness and competitiveness of our approach. © The Author(s) 2025.

关键词： Directional regression High dimensional data analysis Multivariate analysis Projective resampling Sufficient dimension reduction

来源：评论

学校读者我要写书评

暂无评论

On sufficient dimension reduction methods based on a graphical model with non-concave penalty

引用

statistics and Computing 2025年第4期35卷 1-30页

作者： Park, Yujin Kim, Kyongwon Yoo, Jae Keun Department of Statistics Ewha Womans University 52 Ewhayeodae-gil Seodaemun-gu Seoul 03760 South Korea Department of Applied Statistics Department of Statistics and Data Science Yonsei University 50 Yonsei-ro Seodaemun-gu Seoul 03722 South Korea

Ultra high-dimensional datasets, which refer to scenarios where the number of covariates grows at an exponential rate relative to the sample size, are frequently encountered in modern data analysis across fields such as genomics, finance, and social sciences. These datasets pose significant challenges due to the large number of variables relative to the number of observations, potentially resulting in issues such as multicollinearity, overfitting, and computational difficulties. Traditional sufficient dimension reduction (SDR) methods struggle with these challenges, making it necessary to develop new approaches. To address these limitations, we introduce a graphical model-based SDR method that incorporates a smoothly clipped absolute deviation (SCAD) penalty. This method effectively reduces dimensionality while managing sparsity in the dataset. Additionally, we extend directional regression for high-dimensional data by integrating them with graphical LASSO, which enhances the model’s ability to estimate sparse precision matrices. This combined approach not only mitigates computational infeasibility in estimating covariance matrices but also helps avoid overfitting, making it particularly suitable for high-dimensional contexts. Through extensive simulation studies and real-world data analyses, we validate the robustness and effectiveness of our proposed methods. Moreover, we provide a theoretical framework that discusses the convergence rate of these methods, offering insights into their performance under various conditions. Finally, we outline potential avenues for future research, including exploring alternative penalty functions and expanding the applicability of these methods to other types of data structures. © The Author(s), under exclusive licence to Springer science+Business Media, LLC, part of Springer Nature 2025.

关键词： graphical LASSO graphical model precision matrix SCAD sufficient dimension reduction

来源：评论

学校读者我要写书评

暂无评论

Hamiltonian formulations of centroid-based clustering

引用

Frontiers in Physics 2025年 13卷

作者： Seong, Myeonghwan Park, Daniel Kyungdeock Department of Statistics and Data Science Yonsei University Seoul Korea Republic of Department of Applied Statistics Yonsei University Seoul 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 (Formula presented.) -means algorithm and weighted maximum (Formula presented.) -cut, 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 Seong and Park.

关键词： Qubits

来源：评论

学校读者我要写书评

暂无评论

A trust-region approach for iteration solution of the direct fitting metric MDS

引用

BIT Numerical Mathematics 2025年第2期65.0卷 1-37页

作者： Li, Jiao-Fen Zhou, Jing Zhou, Xue-Lin Li, Chao-Qian Song, Jia-Shuo School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin 541004 China Center for Applied Mathematics of Guangxi (GUET) Guilin 541004 China School of Mathematics and Statistics Yunan University Kunming 650000 China School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin 541004 China

Multidimensional scaling (MDS) serves as a widely adopted methodology for projecting data on a finite metric space onto a lower-dimensional Euclidean space, with the goal of preserving pairwise distances as accurately as possible. While the classical metric MDS model typically involves fitting double-centered squared dissimilarity, Browne (1987) advocated for the direct fitting of original squared dissimilarity, suggesting potentially superior outcomes. This study redefines and investigates the problem of directly fitting the metric MDS model to the data as a matrix optimization problem over the product of the Stiefel sub-manifold of matrices with zero column sums and the linear sub-space comprising all r×r diagonal matrices. We introduce an effective algorithm, drawing upon the generic Riemannian trust-region method developed by Absil et al., to address this problem, offering both global convergence and local superlinear convergence rates. Numerical experiments demonstrate that direct fitting yields a Euclidean distance matrix with reduced error. Additionally, we provide numerical comparisons with the projected gradient flow method, as well as several existing Riemannian first and second-order algorithms in the Riemannian optimization toolbox Manopt, to highlight the merits of our proposed approach. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.

关键词： Metric multidimensional scaling Riemannian optimization Trust-region method

来源：评论

学校读者我要写书评

暂无评论

Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes

arXiv

引用

arXiv 2025年

作者： Fan, Zhou Ko, Justin Loureiro, Bruno Lu, Yue M. Shen, Yandi Department of Statistics and Data Science Yale University United States Department of Statistics and Actuarial Science University of Waterloo Canada Departement d’Informatique École Normale Supérieure PSL & CNRS France Departments of Electrical Engineering and Applied Mathematics Harvard University United States Department of Statistics and Data Science Carnegie Mellon University United States

In many applications of statistical estimation via sampling, one may wish to sample from a high-dimensional target distribution that is adaptively evolving to the samples already seen. We study an example of such dynamics, given by a Langevin diffusion for posterior sampling in a Bayesian linear regression model with i.i.d. regression design, whose prior continuously adapts to the Langevin trajectory via a maximum marginal-likelihood scheme. Results of dynamical mean-field theory (DMFT) developed in our companion paper establish a precise high-dimensional asymptotic limit for the joint evolution of the prior parameter and law of the Langevin sample. In this work, we carry out an analysis of the equations that describe this DMFT limit, under conditions of approximate time-translation-invariance which include, in particular, settings where the posterior law satisfies a log-Sobolev inequality. In such settings, we show that this adaptive Langevin trajectory converges on a dimension-independent time horizon to an equilibrium state that is characterized by a system of scalar fixed-point equations, and the associated prior parameter converges to a critical point of a replica-symmetric limit for the model free energy. As a by-product of our analyses, we obtain a new dynamical proof that this replica-symmetric limit for the free energy is exact, in models having a possibly misspecified prior and where a log-Sobolev inequality holds for the posterior law. © 2025, CC0.

关键词： Mean field theory

来源：评论

学校读者我要写书评

暂无评论

Task Diversity in Bayesian Federated Learning: Simultaneous Processing of Classification and Regression 25

Task Diversity in Bayesian Federated Learning: Simultaneous ...

引用

Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and data Mining V.1

作者： Junliang Lyu Yixuan Zhang Xiaoling Lu Feng Zhou Center for Applied Statistics and School of Statistics Renmin University of China Beijing China School of Statistics and Data Science Southeast University Nanjing China Center for Applied Statistics and School of Statistics Renmin University of China Beijing China & Innovation Platform Renmin University of China Beijing China Center for Applied Statistics and School of Statistics Renmin University of China Beijing China & Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing Beijing China

ISBN: (纸本)9798400712456

This work addresses a key limitation in current federated learning approaches, which predominantly focus on homogeneous tasks, neglecting the task diversity on local devices. We propose a principled integration of multi-task learning using multi-output Gaussian processes (MOGP) at the local level and federated learning at the global level. MOGP handles correlated classification and regression tasks, offering a Bayesian non-parametric approach that naturally quantifies uncertainty. The central server aggregates the posteriors from local devices, updating a global MOGP prior redistributed for training local models until convergence. Challenges in performing posterior inference on local devices are addressed through the Polya-Gamma augmentation technique and mean-field variational inference, enhancing computational efficiency and convergence rate. Experimental results on both synthetic and real data demonstrate superior predictive performance, OOD detection, uncertainty calibration and convergence rate, highlighting the method's potential in diverse applications. Our code is publicly available at https://***/JunliangLv/task_diversity_BFL.

关键词： bayesian federated learning

来源：评论

学校读者我要写书评

暂无评论

Improved Image Classification with Manifold Neural Networks

Improved Image Classification with Manifold Neural Networks

引用

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Caio F. Deberaldini Netto Zhiyang Wang Luana Ruiz Department of Applied Mathematics and Statistics Mathematical Institute for Data Science (MINDS) Data Science and Artificial Intelligence Institute (DSAI) Johns Hopkins University Baltimore USA Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia USA

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting from GNNs’ message-passing framework. However, the potential of GNNs in more general data representations, especially in the image domain, remains underexplored. Leveraging the manifold hypothesis, which posits that high-dimensional data lies in a low-dimensional manifold, we explore GNNs’ potential in this context. We construct an image manifold using variational autoencoders, then sample the manifold to generate graphs where each node is an image. This approach reduces data dimensionality while preserving geometric information. We then train a GNN to predict node labels corresponding to the image labels in the classification task, and leverage convergence of GNNs to manifold neural networks to analyze GNN generalization. Experiments on MNIST and CIFAR10 datasets demonstrate that GNNs generalize effectively to unseen graphs, achieving competitive accuracy in classification tasks.

关键词： Manifolds Electric potential High dimensional data Autoencoders Transportation Signal processing Graph neural networks Molecular biology Speech processing Image classification

来源：评论

学校读者我要写书评

暂无评论

Analyzing Classroom Interaction data Using Prompt Engineering and Network Analysis

arXiv

引用

arXiv 2025年

作者： Kim, Gwanghee Jin, Ick Hoon Jeon, Minjeong Department of Statistics and Data Science Yonsei University Korea Republic of Department of Applied Statistics Yonsei University Korea Republic of School of Education and Information Studies University of California Los Angeles United States

Classroom interactions play a vital role in developing critical thinking, collaborative problem-solving abilities, and enhanced learning outcomes. While analyzing these interactions is crucial for improving educational practices, the examination of classroom dialogues presents significant challenges due to the complexity and high-dimensionality of conversational data. This study presents an integrated framework that combines prompt engineering with network analysis to investigate classroom interactions comprehensively. Our approach automates utterance classification through prompt engineering, enabling efficient and scalable dialogue analysis without requiring pre-labeled datasets. The classified interactions are subsequently transformed into network representations, facilitating the analysis of classroom dynamics as structured social networks. To uncover complex interaction patterns and how underlying interaction structures relate to student learning, we utilize network mediation analysis. In this approach, latent interaction structures, derived from the additive and multiplicative effects network (AMEN) model that places students within a latent social space, act as mediators. In particular, we investigate how the gender gap in mathematics performance may be mediated by students’ classroom interaction structures. Copyright © 2025, The Authors. All rights reserved.

关键词： Students

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：