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Proceedings of the 41st International Conference on Machine Learning

作者： Konstantinos Ameranis Adela DePavia Lorenzo Orecchia Erasmo Tani Department of Computer Science University of Chicago Chicago Computational and Applied Mathematics University of Chicago Chicago

A fundamental approach to semi-supervised learning is to leverage the structure of the sample space to diffuse label information from annotated examples to unlabeled points. Traditional methods model the input data points as a graph and rely on fast algorithms for solving Laplacian systems of equations, such as those defining PageRank. However, previous work has demonstrated that graph-based models fail to capture higher-order relations, such as group membership, which are better modeled by hypergraphs. Unfortunately, the scalable application of hypergraph models has been hampered by the non-linearity of the hypergraph Laplacian. In this paper, we present highly scalable algorithms for hypergraph primitives, such as hypergraph PageRank vectors and hypergraph Laplacian systems, over general families of hypergraphs. In addition to giving strong theoretical guarantees, we empirically showcase the speed of our algorithms on benchmark instances of semi-supervised learning on categorical data. We exploit their generality to improve semi-supervised manifold clustering via hypergraph models. By providing significant speed-ups on fundamental hypergraph tasks, our algorithms enable the deployment of hypergraph models on a massive scale.

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Neural Estimation of Entropic Optimal Transport

Neural Estimation of Entropic Optimal Transport

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IEEE International Symposium on Information Theory

作者： Tao Wang Ziv Goldfeld Applied Mathematics and Computational Science University of Pennsylvania School of Electrical and Computer Engineering Cornell University

ISBN: (数字)9798350382846

ISBN: (纸本)9798350382853

Optimal transport (OT) serves as a natural frame-work for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances suffer from the curse of dimensionality. To circumvent these issues, entropic regularization has emerged as a remedy that enables parametric estimation rates via plug-in and efficient computation using Sinkhorn iterations. Motivated by further scaling up entropic OT (EOT) to data dimensions and sample sizes that appear in modern machine learning applications, we propose a novel neural estimation approach. Our estimator parametrizes a semi-dual representation of the EOT distance by a neural network, approximates expectations by sample means, and optimizes the resulting empirical objective over parameter space. We establish non-asymptotic error bounds on the EOT neural estimator of the cost and optimal plan. Our bounds characterize the effective error in terms of neural network size and the number of samples, revealing optimal scaling laws that guarantee parametric convergence. The bounds hold for compactly supported distributions, and imply that the proposed estimator is minimax-rate optimal over that class. Numerical experiments validating our theory are also provided.

关键词： Costs Scalability Sociology Estimation Artificial neural networks Machine learning Probability

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Invertibility of Discrete-Time Linear Systems with Sparse Inputs 63

Invertibility of Discrete-Time Linear Systems with Sparse In...

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63rd IEEE Conference on Decision and Control, CDC 2024

作者： Poe, Kyle Mallada, Enrique Vidal, Rene University of Pennsylvania Applied Mathematics and Computational Science Group PA19104 United States Johns Hopkins University Mallada Is with the Department of Electrical and Computer Engineering MD21218 United States University of Pennsylvania Radiology Computer and Information Science Statistics and Data Science Departments of Electrical and Systems Engineering PA19104 United States

ISBN: (纸本)9798350316339

One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics, and spectral structure of a system have been used to characterize the well-posedness of this problem, without assumptions on the inputs. However, certain structural assumptions, such as input sparsity, have been shown to translate to practical gains in the performance of inversion algorithms, surpassing classical guarantees. Establishing necessary and sufficient conditions for left invertibility of systems with sparse inputs is therefore a crucial step toward understanding the performance limits of system inversion under structured input assumptions. In this work, we provide the first necessary and sufficient characterizations of left invertibility for linear systems with sparse inputs, echoing classic characterizations for standard linear systems. The key insight in deriving these results is in establishing the existence of two novel geometric invariants unique to the sparseinput setting, the weakly unobservable and strongly reachable subspace arrangements. By means of a concrete example, we demonstrate the utility of these characterizations. We conclude by discussing extensions and applications of this framework to several related problems in sparse control. © 2024 IEEE.

关键词： State space methods

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computer Network Technology in Big Data Distributed Cloud Storage Platform

Computer Network Technology in Big Data Distributed Cloud St...

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作者： Xu, Yuelin Wang, Yuran Wan, Baiyang Khan, Ahthasham Ullah Department of Computational Mathematics and Cybernetics Mathematics and Applied Mathematics Shenzhen MSU-BIT University Guangdong Shenzhen518172 China Faculty of Economics Shenzhen MSU-BIT University Guangdong Shenzhen518172 China Institute of IT and Computer Science Afghanistan Kabul Afghanistan

In the era of big data, distributed cloud storage platforms are widely used to store massive amounts of data and information. Compared with traditional storage methods, distributed cloud storage platforms can provide flexible storage space to ensure the security and speed of platform operating data. This article uses computer network technology to design a distributed cloud storage platform, test platform file upload and download time and user login platform success rate to verify the reliability of platform operation, and realize the feasibility of user login function module operation, I hope this article distributed cloud storage platform can help people process data efficiently and realize the safe preservation of data and information. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Distributed cloud

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Adaptive energy-preserving algorithms for guiding center system

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Plasma science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

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A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

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computers, Materials & Continua 2022年第12期73卷 4611-4626页

作者： Pramote Charongrattanasakul Wimonmas Bamrungsetthapong Poom Kumam Division of Mathematics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology KrungthepBangkok10120Thailand Division of Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiPathum Thani12110Thailand Center of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research Laboratory Room SCL 802 Fixed Point LaboratoryScience Laboratory BuildingDepartments of MathematicsFaculty of ScienceKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand

The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull *** achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot *** optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve *** addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling *** results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.

关键词： Adaptive version of multiple dependent state sampling plan time truncated life test quality level weibull distribution mean lifetime

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Fuzzy Rough Choquet Distances for Classification

arXiv

引用

arXiv 2024年

作者： Theerens, Adnan Cornelis, Chris Computational Web Intelligence Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium

This paper introduces a novel Choquet distance using fuzzy rough set based measures. The proposed distance measure combines the attribute information received from fuzzy rough set theory with the flexibility of the Choquet integral. This approach is designed to adeptly capture non-linear relationships within the data, acknowledging the interplay of the conditional attributes towards the decision attribute and resulting in a more flexible and accurate distance. We explore its application in the context of machine learning, with a specific emphasis on distance-based classification approaches (e.g. k-nearest neighbours). The paper examines two fuzzy rough set based measures that are based on the positive region. Moreover, we explore two procedures for monotonizing the measures derived from fuzzy rough set theory, making them suitable for use with the Choquet integral, and investigate their differences. © 2024, CC BY-NC-ND.

关键词： Machine learning

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Finite Basis Physics-Informed Neural Networks as a Schwarz Domain Decomposition Method 27th

Finite Basis Physics-Informed Neural Networks as a Schwarz D...

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27th International Conference on Domain Decomposition Methods in science and Engineering, DD 2022

作者： Dolean, Victorita Heinlein, Alexander Mishra, Siddhartha Moseley, Ben University of Strathclyde 26 Richmond Street GlasgowG1 1XH United Kingdom Faculty of Electrical Engineering Mathematics & Computer Science Delft University of Technology Delft Institute of Applied Mathematics Mekelweg 4 Delft2628 CD Netherlands Computational and Applied Mathematics Laboratory/ETH AI Center ETH Zurich Ramistrasse 101 Zurich8092 Switzerland

The success and advancement of machine learning (ML) in fields such as image recognition and natural language processing has lead to the development of novel methods for the solution of problems in physics and enginee... 详细信息

ISBN: (纸本)9783031507687

关键词： Domain decomposition methods

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ON THE SPECIALIZATION OF NEURAL MODULES 11

ON THE SPECIALIZATION OF NEURAL MODULES

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11th International Conference on Learning Representations, ICLR 2023

作者： Jarvis, Devon Klein, Richard Rosman, Benjamin Saxe, Andrew M. School of Computer Science and Applied Mathematics University of the Witwatersrand South Africa Gatsby Computational Neuroscience Unit Sainsbury Wellcome Centre UCL United Kingdom CIFAR Azrieli Global Scholar CIFAR United Kingdom

A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional architectures which aim to learn specialized modules dedicated to structures in a task that can be composed to solve novel problems with similar structures. While the compositionality of these architectures is guaranteed by design, the modules specializing is not. Here we theoretically study the ability of network modules to specialize to useful structures in a dataset and achieve systematic generalization. To this end we introduce a minimal space of datasets motivated by practical systematic generalization benchmarks. From this space of datasets we present a mathematical definition of systematicity and study the learning dynamics of linear neural modules when solving components of the task. Our results shed light on the difficulty of module specialization, what is required for modules to successfully specialize, and the necessity of modular architectures to achieve systematicity. Finally, we confirm that the theoretical results in our tractable setting generalize to more complex datasets and non-linear architectures. © 2023 11th International Conference on Learning Representations, ICLR 2023. All rights reserved.

关键词： Network architecture

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Predicting the friction angle of clays using a multi-layer perceptron neural network enhanced by yeo-johnson transformation and coral reefs optimization

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Journal of Rock Mechanics and Geotechnical Engineering 2024年第10期16卷 3982-4003页

作者： Libing Yang Trung Nguyen-Thoi Trung-Tin Tran College of Civil Engineering and Architecture Hunan Institute of Science and TechnologyYueyang414006China Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh CityViet Nam Faculty of Mechanical-Electrical and Computer Engineering School of TechnologyVan Lang UniversityHo Chi Minh CityViet Nam Department of Information Technology Greenwich VietnamFPT UniversityDa Nang550000Viet Nam

The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering *** study addresses the importance of estimating the friction angle and presents the development of four soft computing models:YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and *** of all,the Yeo-Johnson(YJ)transformation technique was used to stabilize the variance of data and make it more suitable for parametric statistical models that assume normality and equal *** technique is expected to improve the accuracy of friction angle prediction *** friction angle prediction models then utilized multi-layer perceptron neural networks(MLPnet)and metaheuristic optimization algorithms to further enhance performance,including flower pollination algorithm(FPA),coral reefs optimization(CRO),ant colony optimization continuous(ACOC),and cuckoo search algorithm(CSA).The prediction models without the YJ technique,***-MLPnet,CRO-MLPnet,ACOC-MLPnet,and CSA-MLPnet,were then compared to those with the YJ technique,***-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and *** these,the YJ-CRO-MLPnet model demonstrated superior reliability,achieving an accuracy of up to 83%in predicting the friction angle of clay in practical engineering *** improvement is significant,as it represents an increase from 1.3%to approximately 20%compared to the models that did not utilize the YJ transformation technique.

关键词： Natural hazards Slope stability Friction angle Clay Soft computing models Geotechnical engineering

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