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Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent

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arXiv 2024年

作者： Cai, HanQin Huang, Longxiu Lu, Xiliang You, Juntao Department of Statistics and Data Science Department of Computer Science University of Central Florida OrlandoFL32816 United States Department of Computational Mathematics Science and Engineering Department of Mathematics Michigan State University East LansingMI48823 United States School of Mathematics and Statistics Hubei Key Laboratory of Computational Science Wuhan University Wuhan430072 China School of Artificial Intelligence Wuhan University National Center for Applied Mathematics in Hubei Hubei Key Laboratory of Computational Science Wuhan China Institute for Advanced Study Shenzhen University Shenzhen518000 China

This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a novel non-convex algorithm, coined Hankel Structured Newton-Like Descent (HSNLD), to tackle the robust Hankel recovery problem. HSNLD is highly efficient with linear convergence, and its convergence rate is independent of the condition number of the underlying Hankel matrix. The recovery guarantee has been established under some mild conditions. Numerical experiments on both synthetic and real datasets show the superior performance of HSNLD against state-of-the-art *** Codes 15A29, 15A83, 47B35, 90C17, 90C26, 90C53 Copyright © 2024, The Authors. All rights reserved.

关键词： Recovery

Trustworthy Actionable Perturbations

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arXiv 2024年

作者： Friedbaum, Jesse Adiga, Sudarshan Tandon, Ravi Program in Applied Mathematics University of Arizona TucsonAZ United States Department of Electrical and Computer Engineering University of Arizona TucsonAZ United States

Counterfactuals, or modified inputs that lead to a different outcome, are an important tool for understanding the logic used by machine learning classifiers and how to change an undesirable classification. Even if a counterfactual changes a classifier’s decision, however, it may not affect the true underlying class probabilities, i.e. the counterfactual may act like an adversarial attack and "fool" the classifier. We propose a new framework for creating modified inputs that change the true underlying probabilities in a beneficial way which we call Trustworthy Actionable Perturbations (TAP). This includes a novel verification procedure to ensure that TAP change the true class probabilities instead of acting adversarially. Our framework also includes new cost, reward, and goal definitions that are better suited to effectuating change in the real world. We present PAClearnability results for our verification procedure and theoretically analyze our new method for measuring reward. We also develop a methodology for creating TAP and compare our results to those achieved by previous counterfactual methods. © 2024, CC BY.

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Multilevel Monte Carlo Methods for the Grad-Shafranov Free Boundary Problem

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SSRN

SSRN 2023年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Applied Mathematics & Statistics and Scientific Computing Program University of Maryland College Park United States Department of Mathematics The University of Arizona United States

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costsby performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductionstypically on the order of 60 or more and possibly as large as 200. Adaptive gridding results in more accurate computation of geometric quantities such as x-points associated with the model. © 2023, The Authors. All rights reserved.

关键词： Monte Carlo methods

Impact of Filter-Based Feature Selection on Prediction Model Performance for Early Detection of Stunting 9

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Impact of Filter-Based Feature Selection on Prediction Model...

9th International Conference on Informatics and Computing, ICIC 2024

作者： Widiastuti, Sri Handani Purwanto Wibowo, Adi Wisnuwardani, Ratih Wirapuspita Sekolah Tinggi Teknologi Informatics Engineering Study Program Bontang Indonesia Diponegoro Univercity School of Postgraduate Studies Indonesia Diponegoro Univercity Faculty of Engineering Department of Chemical Engineering Semarang Indonesia Diponegoro Univercity Faculty of Science and Mathematics Department of Informatics Semarang Indonesia Mulawarman Univercity Faculty of Public Health Samarinda Indonesia

ISBN: (纸本)9798331517601

This study investigates the impact of feature selection results using the filter method on the performance of predictive models for the nutritional status of children aged 0-23 months. This study aimed to understand how correlation-based feature selection methods affect the efficiency and accuracy of predictive models. The dataset comes from the Basic Health Research survey, which consists of 84 variables and around 130,000 data, including anthropometric, family, socioeconomic, and environmental information. In this study, various filter-based feature selection methods were applied to evaluate and identify features that have significant relationships with children's nutritional status, both linearly and non-linearly. The mutual information method was used to identify complex relationships between features and target variables, while the Pearson Correlation Coefficient and information gain were used to assess the relevance of numerical and categorical features. Of the 84 variables in the dataset, 37 features were selected after the selection process. The model performance evaluation was carried out using the Random Forest (RF) and Gradient Boosting (GB) algorithms, by comparing the results between the dataset that had been selected and without feature selection. The RF model without feature selection produces accuracy: 0,84600, precision: 0,83958, recall: 0,84600, F1-score: 0,78962, and a computation time of 9 seconds. The GB model without feature selection produces accuracy: 0,86330, precision: 0,84722, recall: 0,86330, F1-score: 0,84925, and a computation time of 2 minutes 50 seconds. After feature selection and cross-validation, the RF model shows accuracy: 0,85701, precision: 0,83599, recall: 0,85701, and F1 score: 0,83484. The GB model shows accuracy at 0,86124, precision at 0,84226, recall at 0,86130, and F1 score at 0,84120. © 2024 IEEE.

关键词： feature selection information gain machine learning Pearson Correlation prediction stunting

Prioritization of AI-based material handling approaches for smart logistics in sustainable warehouses: A q-rung orthopair fuzzy CoCoSo methodology with consensus reaching

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Environment, Development and Sustainability 2025年 1-39页

作者： Saha, Abhijit Simic, Vladimir Dabic-Miletic, Svetlana Senapati, Tapan Pamucar, Dragan Arya, Leena Tirkolaee, Erfan Babaee Department of Computing Technologies SRM Institute of Science and Technology (SRMIST) Kattankulathur India Chief Research Fellow Faculty of Fundamental Sciences Department of Information Technologies Vilnius Gediminas Technical University Vilnius Lithuania Faculty of Transport and Traffic Engineering University of Belgrade Belgrade Serbia College of Engineering Department of Industrial Engineering and Management Yuan Ze University Taoyuan City Taiwan Department of Computer Science and Engineering College of Informatics Korea University Seoul Republic of Korea Department of Mathematics SIMATS Engineering Saveetha Institute of Mechanical and Technical Sciences Chennai India School of Mathematics and Statistics Southwest University Chongqing China Széchenyi István University Győr Hungary Department of Computer Science and Engineering College of Engineering Koneru Lakshmiah Education Foundation Vaddeswaram India Department of Industrial Engineering Istinye University Istanbul Turkey Department of Mechanics and Mathematics Western Caspian University Baku Azerbaijan

This study aims to address the artificial intelligence-based material handling approach selection problem under circular economy to contribute the smart and sustainable business management in logistics systems. The "consensus-reaching process" for experts is not emphasized in the current decision-making procedures with q-rung orthopair fuzzy data. Experts working on group decision-making challenges may hold views that are very dissimilar from one another as a result of their knowledge and experiences. In order for experts to increase the amount of consensus, a consensus-building process is needed. Besides, the ranking results provided by "combined compromise for ideal solution" do not change dramatically in line with the changing weight distributions of characteristics. So, q-rung orthopair fuzzy-based combined compromise for ideal solution methodology with consensus reaching is introduced for solving the addressed emerging problem of logistics companies. This robust and logical decision-making method can comprehensively analyze the advantages, disadvantages, and potential barriers to the acceptance of artificial intelligence-based material handling approaches. The real-life study is offered for a logistics company that plans to invest in robotic solutions based on artificial intelligence. The findings show that autonomous mobile robots represent the best artificial intelligence-based material handling approach. Recommendations for adopting alternative solutions are provided to assist in the efficient completion of smart logistics activities.

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On the Effectiveness of Text and Image Embeddings in Multimodal Hate Speech Detection

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On the Effectiveness of Text and Image Embeddings in Multimo...

IEEE International Conference on Big Data

作者： Nora Lewis Charles C. Cavalcante Zois Boukouvalas Roberto Corizzo Department of Computer Science American University Washington DC USA Department of Teleinformatics Engineering Federal University of Ceará Fortaleza Ceará Brazil Department of Mathematics and Statistics American University Washington DC USA

ISBN: (数字)9798350362480

ISBN: (纸本)9798350362497

Social media content is increasingly subject to hate speech towards specific demographic groups. In this context, machine learning approaches appear relevant to detect malicious contents and support moderators in mitigation initiatives. However, many of the existing approaches are exclusively focused on the analysis of textual contents. On the other hand, studies that address multiple data modalities often rely on a single feature representation and a fully supervised learning setting. In this paper, we tackle multimodal hate speech detection resorting to different learning settings (one-class learning and binary classification). We also investigate the effectiveness of multiple deep learning model backbones and language models to extract embedding feature representations for text and image modalities. Our experiments with a real-world hate speech dataset show that there is a significant performance gap between one-class learning and binary classification, and that the choice of embedding representations for image and text modalities can impact the detection performance for different predictive models.

关键词： Deep learning Radio frequency Social networking (online) Prevention and mitigation Hate speech Supervised learning Predictive models Nearest neighbor methods Feature extraction Vectors

Sensitivity to control signals in triphasic rhythmic neural systems: a comparative mechanistic analysis via infinitesimal local timing response curves

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arXiv 2022年

作者： Yu, Zhuojun Rubin, Jonathan E. Thomas, Peter J. Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University ClevelandOH44106 United States Department of Mathematics University of Pittsburgh PittsburghPA15260 United States Department of Mathematics Applied Mathematics and Statistics Department of Biology Department of Electrical Control and Systems Engineering Case Western Reserve University ClevelandOH44106 United States

Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and, specifically, to tuning of inputs that represent control signals. In this work, we analyze the responses resulting from modulation of a localized input in each of three classes of model neural networks that have been recognized in the literature for their capacity to produce robust three-phase rhythms: coupled fast-slow oscillators, near-heteroclinic oscillators, and threshold-linear networks. Triphasic rhythms, in which each phase consists of a prolonged activation of a corresponding subgroup of neurons followed by a fast transition to another phase, represent a fundamental activity pattern observed across a range of central pattern generators underlying behaviors critical to survival, including respiration, locomotion, and feeding. To perform our analysis, we extend the recently developed local timing response curve (lTRC), which allows us to characterize the timing effects due to perturbations, and we complement our lTRC approach with model-specific dynamical systems analysis. Interestingly, we observe disparate effects of similar perturbations across distinct model classes. Thus, this work provides an analytical framework for studying control of oscillations in nonlinear dynamical systems, and may help guide model selection in future efforts to study systems exhibiting triphasic rhythmic activity. Copyright © 2022, The Authors. All rights reserved.

关键词： Linear networks

A numerical treatment through Bayesian regularization neural network for the chickenpox disease model

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Computers in Biology and Medicine 2025年 187卷 109807-109807页

作者： Sabir, Zulqurnain Mehmood, Muhammad Athar Umar, Muhammad Salahshour, Soheil Altun, Yener Arbi, Adnène Ali, Mohamed R. Department of Mathematics and Statistics Hazara University Mansehra Pakistan Department of Mathematics University of Gujrat Pakistan Faculty of Engineering and Natural Sciences Istanbul Okan University Istanbul Turkey Faculty of Engineering and Natural Sciences Bahcesehir University Istanbul Turkey Faculty of Economics and Administrative Sciences Department of Business Administration Yuzuncu Yil University Van Turkey EPT University of Carthage Carthage Tunisia Faculty of Engineering Benha National University Obour Campus Egypt Basic Engineering Science Department Benha Faculty of Engineering Benha University Benha Egypt

Objectives: The current research investigations designates the numerical solutions of the chickenpox disease model by applying a proficient optimization framework based on the artificial neural network. The mathematical form of the chickenpox disease model is divided into different categories of individuals, susceptible, vaccinated, infected, exposed, recovered, and infected with/without complications. Method: The construction of neural network is performed by using the single hidden layer and the optimization of Bayesian regularization. A dataset is assembled using the explicit Runge-Kutta technique for reducing the mean square error using the training 76 %, while 12 %, 12 % for validation and testing. The whole stochastic procedure is based on logistic sigmoid fitness function, single hidden layer structure with thirty neurons, along with the optimization capability of Bayesian regularization. Finding: The designed procedure's correctness and reliability is observed by results matching, negligible absolute error around 10−04 to 10−06, regression, error histogram, and state transmission. Moreover, the best performance values based on the mean square error are performed as 10−09 to 10−11. Novelty: The current neural network framework using the construction of a single hidden layer and the optimization of Bayesian regularization is applied first time to solve the chickenpox disease model. © 2025 Elsevier Ltd

关键词： Neural network models

Universality of max-margin classifiers

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arXiv 2023年

作者： Montanari, Andrea Ruan, Feng Saeed, Basil Sohn, Youngtak Department of Electrical Engineering Department of Statistics Stanford University United States Department of Statistics and Data Science Northwestern University United States Department of Electrical Engineering Stanford University United States Department of Mathematics Massachusetts Institute of Technology United States

Maximum margin binary classification is one of the most fundamental algorithms in machine learning, yet the role of featurization maps and the high-dimensional asymptotics of the misclassification error for non-Gaussian features are still poorly understood. We consider settings in which we observe binary labels yi and either d-dimensional covariates zi that are mapped to a p-dimension space via a randomized featurization map φ: d → p, or p-dimensional features of non-Gaussian independent entries. In this context, we study two fundamental questions: (i) At what overparametrization ratio p/n do the data become linearly separable? (ii) What is the generalization error of the max-margin classifier? Working in the high-dimensional regime in which the number of features p, the number of samples n and the input dimension d (in the nonlinear featurization setting) diverge, with ratios of order one, we prove a universality result establishing that the asymptotic behavior is completely determined by the expected covariance of feature vectors and by the covariance between features and labels. In particular, the overparametrization threshold and generalization error can be computed within a simpler Gaussian model. The main technical challenge lies in the fact that max-margin is not the maximizer (or minimizer) of an empirical average, but the maximizer of a minimum over the samples. We address this by representing the classifier as an average over support vectors. Crucially, we find that in high dimensions, the support vector count is proportional to the number of samples, which ultimately yields universality. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning