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Simple and Optimal Sublinear Algorithms for Mean Estimation

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arXiv 2024年

作者： Bertolotti, Beatrice Russo, Matteo Schwiegelshohn, Chris Shyam, Sudarshan Department of Computer Science Aarhus University Åbogade 34 Aarhus N8200 Denmark Department of Computer Control Management Engineering Sapienza University of Rome Via Ariosto 25 Rome00185 Italy

We study the sublinear multivariate mean estimation problem in d-dimensional Euclidean space. Specifically, we aim to find the mean µ of a ground point set A, which minimizes the sum of squared Euclidean distances of the points in A to µ. We first show that a multiplicative (1 + Ε) approximation to µ can be found with probability 1 − δ using O(Ε−1 log δ−1) many independent uniform random samples, and provide a matching lower bound. Furthermore, we give two sublinear time algorithms with optimal sample complexity for extracting a suitable approximate mean: 1. A gradient descent approach running in time O((Ε−1 + log log δ−1) · log δ−1 · d). It optimizes the geometric median objective while being significantly faster for our specific setting than all other known algorithms for this problem. 2. An order statistics and clustering approach running in time O ((Ε−1 + logγ δ−1) · log δ−1 · d) for any constant γ > 0. Throughout our analysis, we also generalize the familiar median-of-means estimator to the multivariate case, showing that the geometric median-of-means estimator achieves an optimal sample complexity for estimating µ, which may be of independent interest. © 2024, CC BY.

关键词： Consensus algorithm

A new metric for evaluating the performance and complexity of computer programs: A new approach to the traditional ways of measuring the complexity of algorithms and estimating running times 23

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A new metric for evaluating the performance and complexity o...

23rd International Conference on control Systems and computer science Technologies, CSCS 2021

作者： Folea, Rares Slusanschi, Emil-Ioan University Politehnica of Bucharest Faculty of Automatic Control and Computers Computer Science and Engineering Department Bucharest Romania

ISBN: (纸本)9781665439398

This paper presents a refined complexity calculus model: r-Complexity, a new asymptotic notation that offers better complexity feedback for similar programs than the traditional Bachmann-Landau notation, providing subtle insights even for algorithms that are part of the same conventional complexity class. The architecture-dependent metric represents an enhancement that provides better sensitivity with respect to discrete analysis. © 2021 IEEE.

关键词： Calculations

Resilient distributed optimization under mobile malicious attacks

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IFAC-PapersOnLine 2023年第2期56卷 997-1002页

作者： Yuan Wang Changxin Liu Hideaki Ishii Karl Henrik Johansson Department of Robotics Hunan University Changsha China Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology and Digital Futures Stockholm Sweden Department of Computer Science Tokyo Institute of Technology Yokohama Japan

This article addresses the distributed optimization problem in the presence of malicious adversaries that can move within the network and induce faulty behaviors in the attacked nodes. We first investigate the vulnerabilities of a consensus-based secure distributed optimization protocol under mobile adversaries. Then, a modified resilient distributed optimization algorithm is proposed. We develop conditions on the network structure for both complete and non-complete directed graph cases, under which the proposed algorithm guarantees that the estimates by regular nodes converge to the convex combination of the minimizers of their local functions. Simulations are carried out to verify the effectiveness of our approach.

关键词： Fault-tolerant distributed optimization multi-agent systems network security mobile adversary agents

MRI Brain Tumor Classification Using Optimized APSO-LLRBFNN

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MRI Brain Tumor Classification Using Optimized APSO-LLRBFNN

Machine Learning and Autonomous Systems (ICMLAS), International Conference on

作者： Tiruveedula Gopi Krishna Nune Sreenivas M. Ajay Kumar Chandra Sekhar Reddy Davinder Sing Rathee Teklu Urgessa Department of Computer Science and Engineering College of Electrical Engineering and Computing Adama Science and Technology University Adama Ethiopia Department of Electrical and Electronics Engineering Andhra Loyala institute of Engineering and Technology Vijayawada India Department of Electrical Power and Control Engineering College of Electrical Engineering and Computing Adama Science and Technology University Adama Ethiopia Department of ECE College of Electrical Engineering and Computing Adama Science and Technology University Adama Ethiopia

ISBN: (数字)9798331505745

ISBN: (纸本)9798331505752

The research presents a new efficient machine learning method to classify brain tumors because this task remains vital in fighting the high incidence of brain cancers. The proposed approach unites all its operations including image segmentation with feature extraction and classification into a single processing system. This study uses Particle Swarm Optimization (PSO) and Adaptive PSO (APSO) methodologies to optimize Locally Linear Radial Basis Function Neural Network (LLRBFNN) resulting in PSO-LLRBFNN and APSO-LLRBFNN model implementations. The research examined the optimized APSO-LLRBFNN models against Support Vector Machines (SVM) and Least Mean Squares (LMS) based LLRBFNN classifier methods. Results from experiments show that APSO-LLRBFNN gives superior outcomes with 98.93% accuracy and takes 12.23 seconds for execution, which surpasses currently available methods.

关键词： Support vector machines Image segmentation Adaptation models Accuracy Magnetic resonance imaging Machine learning Feature extraction Brain modeling Data models Numerical models

Out-of-distribution Object Detection through Bayesian Uncertainty Estimation

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arXiv 2023年

作者： Zhang, Tianhao Wang, Shenglin Bouaynaya, Nidhal Calinescu, Radu Mihaylova, Lyudmila Automatic Control and Systems Engineering The University of Sheffield United Kingdom Department of Electrical and Computer Engineering Rowan University United States Department of Computer Science University of York United Kingdom

The superior performance of object detectors is often established under the condition that the test samples are in the same distribution as the training data. However, in many practical applications, out-of-distribution (OOD) instances are inevitable and usually lead to uncertainty in the results. In this paper, we propose a novel, intuitive, and scalable probabilistic object detection method for OOD detection. Unlike other uncertainty-modeling methods that either require huge computational costs to infer the weight distributions or rely on model training through synthetic outlier data, our method is able to distinguish between in-distribution (ID) data and OOD data via weight parameter sampling from proposed Gaussian distributions based on pre-trained networks. We demonstrate that our Bayesian object detector can achieve satisfactory OOD identification performance by reducing the FPR95 score by up to 8.19% and increasing the AUROC score by up to 13.94% when trained on BDD100k and VOC datasets as the ID datasets and evaluated on COCO2017 dataset as the OOD dataset. Copyright © 2023, The Authors. All rights reserved.

关键词： Object detection

Low-Distortion Clustering with Ordinal and Limited Cardinal Information

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arXiv 2024年

作者： Burkhardt, Jakob Caragiannis, Ioannis Fehrs, Karl Russo, Matteo Schwiegelshohn, Chris Shyam, Sudarshan Department of Computer Science Aarhus University Åbogade 34 Aarhus N8200 Denmark Department of Computer Control Management Engineering Sapienza University of Rome Via Ariosto 25 Rome00185 Italy

Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of n agents located in an underlying metric space, our goal is to partition them into k clusters, optimizing some social cost objective. The metric space is defined by a distance function d between the agent locations. Information about d is available only implicitly via n rankings, through which each agent ranks all other agents in terms of their distance from her. Still, even though no cardinal information (i.e., the exact distance values) is available, we would like to evaluate clustering algorithms in terms of social cost objectives that are defined using d. This is done using the notion of distortion, which measures how far from optimality a clustering can be, taking into account all underlying metrics that are consistent with the ordinal information available. Unfortunately, the most important clustering objectives (e.g., those used in the well-known k-median and k-center problems) do not admit algorithms with finite distortion. To sidestep this disappointing fact, we follow two alternative approaches: We first explore whether resource augmentation can be beneficial. We consider algorithms that use more than k clusters but compare their social cost to that of the optimal k-clusterings. We show that using exponentially (in terms of k) many clusters, we can get low (constant or logarithmic) distortion for the k-center and k-median objectives. Interestingly, such an exponential blowup is shown to be necessary. More importantly, we explore whether limited cardinal information can be used to obtain better results. Somewhat surprisingly, for k-median and k-center, we show that a number of queries that is polynomial in k and only logarithmic in n (i.e., only sublinear in the number of agents for the most relevant scenarios in practice) is enough to get constant distortion. © 2024, CC BY.

关键词： Clustering algorithms

Risk-Averse Learning with Delayed feedback

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arXiv 2024年

作者： Wang, Siyi Wang, Zifan Johansson, Karl H. Hirche, Sandra Department of Electrical and Computer Engineering Technical University of Munich Munich80333 Germany Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm10044 Sweden

In real-world scenarios, the impacts of decisions may not manifest immediately. Taking these delays into account facilitates accurate assessment and management of risk in real-world environments, thereby ensuring the efficacy of strategies. In this paper, we investigate risk-averse learning using Conditional Value at Risk (CVaR) as risk measure, while incorporating delayed feedback with unknown but bounded delays. We develop two risk-averse learning algorithms that rely on one-point and two-point zeroth-order optimization approaches, respectively. The regret achieved by the algorithms is analyzed in terms of the cumulative delay and the number of total samplings. The results suggest that the two-point risk-averse learning achieves a smaller regret bound than the one-point algorithm. Furthermore, the one-point risk-averse learning algorithm attains sublinear regret under certain delay conditions, and the two-point risk-averse learning algorithm achieves sublinear regret with minimal restrictions on the delay. We provide numerical experiments on a dynamic pricing problem to demonstrate the performance of the proposed algorithms. © 2024, CC0.

关键词： Adversarial machine learning

Average Communication Rate for Networked Event-Triggered Stochastic control Systems

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IEEE Transactions on control of Network Systems 2025年

作者： Zhang, Zengjie Liu, Qingchen Mamduhi, Mohammad H. Hirche, Sandra Eindhoven University of Technology Department of Electrical Engineering Netherlands University of Science and Technology of China Department of Automation Hefei China University of Birmingham School of Computer Science United Kingdom Technical University of Munich Chair of Information-Oriented Control Munich Germany

Quantifying the average communication rate (ACR) of a networked event-triggered stochastic control system (NET-SCS) with deterministic thresholds is challenging due to the non-stationary nature of the system's stochastic processes. For a NET-SCS, the propagation of nonlinear statistics of the network communication status brought up by deterministic thresholds makes the precise computation of ACR difficult. Previous work used to over-simplify the computation using a Gaussian distribution without incorporating this nonlinearity, leading to sacrificed precision. This paper proposes a novel approach to calculate the exact ACR for a NET-SCS using a recursive model. We use theoretical analysis and a numerical study to qualitatively evaluate the deviation gap of the conventional approach that ignores the side information. The accuracy of our proposed method, alongside its comparison with the simplified results of the conventional approach, is validated by experimental studies. Our work is promising to benefit the efficient resource planning of networked control systems with limited communication resources by providing accurate ACR computation. © 2025 IEEE.

关键词： Networked control systems

Data-Driven Human-Robot Interaction Without Velocity Measurement Using Off-Policy Reinforcement Learning

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IEEE/CAA Journal of Automatica Sinica 2022年第1期9卷 47-63页

作者： Yongliang Yang Zihao Ding Rui Wang Hamidreza Modares Donald C.Wunsch Key Laboratory of Knowledge Automation for Industrial Processes Ministry of Education School of Automation&Electrical EngineeringUniversity of Science and Technology BeijingBeijing 100083China School of Automation Beijng Institute TechnologyBeijing 100081China State Key Laboratory of Management and Control for Complex Systems Institute of AutomationChinese Academy of SciencesBeijing 100190China Mechanical Engineering Department Michigan State UniversityEast LansingMI 48824 USA Department of Electrical&Computer Engineering Missouri University of Science&TechnologyRollaMO 65401 USA

In this paper,we present a novel data-driven design method for the human-robot interaction(HRI)system,where a given task is achieved by cooperation between the human and the *** presented HRI controller design is a two-level control design approach consisting of a task-oriented performance optimization design and a plant-oriented impedance controller *** task-oriented design minimizes the human effort and guarantees the perfect task tracking in the outer-loop,while the plant-oriented achieves the desired impedance from the human to the robot manipulator end-effector in the ***-driven reinforcement learning techniques are used for performance optimization in the outer-loop to assign the optimal impedance *** the inner-loop,a velocity-free filter is designed to avoid the requirement of end-effector velocity *** this basis,an adaptive controller is designed to achieve the desired impedance of the robot manipulator in the task *** simulation and experiment of a robot manipulator are conducted to verify the efficacy of the presented HRI design framework.

关键词： Adaptive impedance control data-driven method human-robot interaction(HRI) reinforcement learning velocity-free