检索结果-内蒙古大学图书馆

A Fast Smoothing Newton Method for Bilevel Hyperparameter Optimization for SVC with Logistic Loss

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Wang, Yixin Li, Qingna School of Mathematics and Statistics Beijing Institute of Technology Beijing China Beijing Key Laboratory on MCAACI Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing China

Support Vector Classification with logistic loss has excellent theoretical properties in classification problems where the label values are not continuous. In this paper, we reformulate the hyperparameter selection for SVC with logistic loss as a bilevel optimization problem in which the upper-level problem and the lower-level problem are both based on logistic loss. The resulting bilevel optimization model is converted to a single-level nonlinear programming (NLP) problem based on the KKT conditions of the lower-level problem. Such NLP contains a set of nonlinear equality constraints and a simple lower bound constraint. The second-order sufficient condition is characterized, which guarantees that the strict local optimizers are obtained. To solve such NLP, we apply the smoothing Newton method proposed in [32] to solve the KKT conditions, which contain one pair of complementarity constraints. We show that the smoothing Newton method has a superlinear convergence rate. Extensive numerical results verify the efficiency of the proposed approach and strict local minimizers can be achieved both numerically and theoretically. In particular, compared with other methods, our algorithm can achieve competitive results while consuming less time than other methods. Copyright © 2023, The Authors. All rights reserved.

关键词： Nonlinear programming

A COMPOSITION METHOD FOR NEAT FORMULAS OF CHROMATIC SYMMETRIC FUNCTIONS

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Wang, David G.L. Zhou, James Z.F. School of Mathematics and Statistics MIIT Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing102400 China School of Mathematics and Statistics Beijing Institute of Technology Beijing102400 China

We develop a composition method to unearth positive eI-expansions of chromatic symmetric functions XG, where the subscript I stands for compositions rather than integer partitions. Using this method, we derive positive and neat eI-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the e-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of *** Codes 05E05, 05A15 Copyright © 2024, The Authors. All rights reserved.

关键词： Choquet integral

CHROMATIC SYMMETRIC FUNCTIONS OF CONJOINED GRAPHS

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Qi, E.Y.J. Tang, D.Q.B. Wang, D.G.L. School of Mathematics and Statistics Beijing Institute of Technology Beijing102400 China School of Mathematics and Statistics MIIT Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing102400 China

We introduce path-conjoined graphs defined for two rooted graphs by joining their roots with a path, and investigate the chromatic symmetric functions of its two generalizations: spider-conjoined graphs and chain-conjoined graphs. By using the composition method developed by Zhou and the third author recently, we obtain neat positive eI-expansions for the chromatic symmetric functions of clique-path-cycle graphs, path-clique-path graphs, and clique-clique-path graphs. We pose the e-positivity conjecture for *** Codes 05E05, 05A15 © 2024, CC BY-NC-ND.

关键词： Graphic methods

Global relaxation-based LP–Newton method for multiple hyperparameter selection in support vector classification with feature selection

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Li, Qingna Qian, Yaru Zemkoho, Alain School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Key Laboratory of Mathematical Theory and Computation in Information Security Beijing Institute of Technology Beijing100081 China School of Mathematical Sciences University of Southampton SouthamptonSO17 1BJ United Kingdom

Support vector classification (SVC) is an effective tool for classification tasks in machine learning. Its performance relies on the selection of appropriate hyperparameters. In this paper, our focus is on identifying the optimal value for the regularization hyperparameter C, as well as determining the bounds on the features in a SVC problem. This implies that the number of hyperparameters in our SVC can potentially be very large. It is very well-known in machine learning that this could lead to the so-called curse of dimensionality. To address this challenge of multiple hyperparameter selection, the problem is formulated as a bilevel optimization problem, which is then transformed into a mathematical program with equilibrium constraints (MPEC). Our first contribution involves proving the fulfillment of a Mangasarian–Fromovitz constraint qualification tailored to the latter reformulation of the problem. Furthermore, we introduce a novel linear programming (LP)-Newton-based global relaxation method (GRLPN) for solving this problem and provide corresponding convergence results. Typically, in global relaxation methods for MPECs, the algorithm for the corresponding subproblem is treated as a blackbox. Possibly for the first time in the literature, the subproblem is specifically studied in detail. Numerical experiments substantiate the superiority of GRLPN over grid search and the global relaxation solved by the well-known nonlinear programming solver SNOPT. © 2023, CC BY.

关键词： Linear programming

Improved security of a Data Truthfulness and Privacy Preservation Scheme in Data Markets

学校读者我要写书评

暂无评论

SSRN

SSRN 2024年

作者： Duan, Meijiao Sun, Yujiao Sui, Zhiyuan Qin, Haimiao School of Information Central University of Finance and Economics Beijing China Department of Engineering Research Center of State Financial Security Ministry of Education Central University of Finance and Economics Beijing China MIIT Key Laboratory of Mathematical Theory and Computation in Information Security School of Mathematics and Statistics Beijing Institute of Technology Beijing China

Data Market, which has emerged in recent years, can carry out efficient data trading and further enhance the utility of data. However, there are many potential security risks in Data Market, and scholars have conducted numerous studies on related topics. Niu et al. proposed a TPDM scheme that claimed to achieve data truthfulness and privacy preservation. However, their solution relies heavily on tamper-proof devices and suffers a single point of failure. To solve the dependence issue, we develop a formal security model and a new signature method that provides necessary security guarantees against single points of failure. Finally, the performance analysis shows that the improved scheme achieves higher signing efficiency and less storage space. © 2024, The Authors. All rights reserved.

关键词： Cybersecurity

DISPERSIVE DECAY FOR THE MASS-CRITICAL NONLINEAR SCHRÖDINGER EQUATION

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Fan, Chenjie Killip, Rowan Visan, Monica Zhao, Zehua Academy of Mathematics and Systems Science Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing China Department of Mathematics UCLA Los Angeles United States Department of Mathematics and Statistics Beijing Institute of Technology MIIT Key Laboratory of Mathematical Theory and Computation in Information Security Beijing China

关键词：

ON HECKE ALGEBRAS AND Z-GRADED TWISTING, SHUFFLING AND ZUCKERMAN FUNCTORS

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Fang, Ming Hu, Jun Sun, Yujiao Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences 100190 Beijing100049 China Key Laboratory of Algebraic Lie Theory and Analysis of Ministry of Education School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China Key Laboratory of Mathematical Theory and Computation in Information Security School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China

Let g be a complex semisimple Lie algebra with Weyl group W. Let H(W) be the Iwahori-Hecke algebra associated to W. For each w ∈ W, let Tw and Cw be the corresponding Z-graded twisting functor and Z-graded shuffling functor respectively. In this paper we present a categorical action of H(W) on the derived category Db(OZ0 ) of the Z-graded BGG category OZ0 via derived twisting functors as well as a categorical action of H(W) on Db(OZ0 ) via derived shuffling functors. As applications, we get graded character formulae for TsL(x) and CsL(x) for each simple reflection s. We describe the graded shifts occurring in the action of the Z-graded twisting and shuffling functors on dual Verma modules and simple modules. We also characterize the action of the derived Z-graded Zuckerman functors on simple modules. Copyright © 2024, The Authors. All rights reserved.

关键词： Lie groups

Input-to-state stabilization for a 2 × 2 hyperbolic system cascaded with an ODE 37

学校读者我要写书评

暂无评论

Input-to-state stabilization for a 2 × 2 hyperbolic system ...

37th Youth Academic Annual Conference of Chinese Association of Automation, YAC 2022

作者： Zhang, Han-Wen Wang, Jun-Min Wang, Jing Shanxi University School of Automation and Software Engineering Shanxi Taiyuan030006 China Theory and Computation in Information Security Beijing Institute of Technology School of Mathematics and Statistics Key Laboratory of Mathematical Beijing100081 China Delft Institute of Applied Mathematics Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands

ISBN: (纸本)9781665465366

The paper deals with the input-to-state stabilization for the 2×2 system of first-order hyperbolic equations, which convect in opposite directions cascaded with an unstable ODE equation. First, an inverse backstepping transformation is introduced to obtain a target system. Then, by active disturbance rejection control (ADRC) method, the disturbance is estimated via a disturbance estimator with time-varying gain. When the unmatched disturbances are absent, the disturbance estimator is exponentially convergent to the matched disturbance. Furthermore, in order to reject the matched disturbance and obtain the input-to-state stability of the system, the controller is proposed by using the disturbance estimator. Finally, numerical simulations are presented to validate theoretical results. © 2022 IEEE.

关键词： Backstepping

ON the CENTER CONJECTURE for the CYCLOTOMIC KLR ALGEBRAS

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Hu, Jun Lin, Huang MIIT Key Laboratory of Mathematical Theory and Computation in Information Security School of Mathematical and Statistics Beijing Institute of Technology Beijing100081 China School of Mathematical Sciences Zhejiang University Hangzhou310027 China

The center conjecture for the cyclotomic KLR algebras RβΛasserts that the center of RβΛconsists of symmetric elements in its KLR x and e(ν) gen-erators. In this paper we show that this conjecture is equivalent to the injectivity of some natural map ιβΛ,1from the cocenter of RβΛto the cocenter of RβΛ+Λifor all i ϵ I and Λ ϵ P+. We prove that the map ιβΛ,1is given by multiplication with a center element z(i, β) ϵ RβΛ+Λiand we explicitly calculate the element z(i, β) in terms of the KLR x and e(ν) generators. We present an explicit monomial basis for certain bi-weight spaces of the defining ideal of RβΛand of RβΛ. For β = Σj=1nαijwith αi1, · · · , αinpairwise distinct, we construct an explicit monomial basis of RβΛ, prove the map ιβΛ,1is injective and thus verify the center conjecture for these RβΛ Copyright © 2022, The Authors. All rights reserved.

关键词：