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Linear expectile regression under massive data

Fundamental Research 2021年第5期1卷 574-585页

作者： Shanshan Song Yuanyuan Lin Yong Zhou Department of Statistics Chinese University of Hong KongHongKongChina Academy of Statistics and Interdisciplinary Sciences East China Normal UniversityShanghaiChina

In this paper,we study the large-scale inference for a linear expectile regression *** mitigate the computational challenges in the classical asymmetric least squares(ALS)estimation under massive data,we propose a communication-efficient divide and conquer algorithm to combine the information from sub-machines through confidence *** resulting pooled estimator has a closed-form expression,and its consistency and asymptotic normality are established under mild ***,we derive the Bahadur representation of the ALS estimator,which serves as an important tool to study the relationship between the number of submachines K and the sample *** studies including both synthetic and real data examples are presented to illustrate the finite-sample performance of our method and support the theoretical results.

关键词： divide and conquer algorithm Expectile regression (Asymptotic)confidence distribution Massive data

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Nonlinear waves in a two-ring network with a transverse coupling

Nonlinear waves in a two-ring network with a transverse coup...

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IUTAM Symposium on Nonlinear and Delayed Dynamics of Mechatronic Systems

作者： Yu, Dongyuan Ding, Nan Zhou, Jing Xu, Xu Jilin Univ Coll Math 2699 Qianjin St Changchun 130012 Jilin Peoples R China Jilin Agr Univ Coll Informat Technol 2888 Xincheng St Changchun 130012 Jilin Peoples R China

A two-ring network coupling by a transverse link is considered in this paper. divide and conquer algorithm is used to analyze the stability and Hopf bifurcation values. Nonlinear waves (such as synchronization and reflection waves) are studied using the center manifold theorem and normal form theory. It is shown that appropriate settings of transverse coupling can guarantee the backup of the complicated dynamics from one ring to the other. (C) 2017 The Authors. Published by Elsevier B.V.

关键词： Complex network divide and conquer algorithm nonlinear waves Hopf bifurcation spatio-temporal dynamics

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On the square-based montgomery multiplier for a class of type C.2 Pentanomial 19

On the square-based montgomery multiplier for a class of typ...

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2019 International Conference on Artificial Intelligence, Information Processing and Cloud Computing, AIIPCC 2019

作者： Guo, Xiaoli Chen, Qing Li, Yin School of Computer and Information Technology Xinyang Normal University Xinyang Henan China

ISBN: (纸本)9781450376334

In this paper, we continue the study of bit-parallel square-based Montgomery multiplier (MM) by Li et al. (Integration 2016, IEEE Access 2018). A square-based MM use an alternative divide and conquer algorithm split a polynomial dueing to the parties of its term degree. Li et al. developed squared-based MM for irreducible trinomials and Type C.1 pentanomials and showed such types of multipliers are at least as efficient as the multipliers using KA. Our contributions consist of two aspects. On one hand, we construct a new MM for a special class of Type C.2 pentanomial, i.e., xm + xm=2 + xk + x2 + 1. By setting a new Montgomery factor, the constructed multiplier can save 1/4 logic gates. On the other hand, our multipliers are motivated by the observation that the optimal Montgomery factors depend on the smallest term degree (non-constant) of the Type C.2 pentanomial. We investigate the main characteristic of square-based MM in the context of Montgomery factor selection. © 2019 Association for Computing Machinery.

关键词： divide and conquer algorithm

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Optimizing Parallelization Strategies for the Big-Means Clustering algorithm 14th

Optimizing Parallelization Strategies for the Big-Means Cl...

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14th International Conference on Optimization and Applications, OPTIMA 2023

作者： Mussabayev, Ravil Mussabayev, Rustam Department of Mathematics University of Washington Padelford Hall C-138 SeattleWA98195-4350 United States Huawei Russian Research Institute Smolenskaya Square 5 Moscow121099 Russia Institute of Information and Computational Technologies Laboratory for Analysis and Modeling of Information Processes Pushkin str. 125 Almaty050010 Kazakhstan

ISBN: (纸本)9783031487507

This study focuses on the optimization of the Big-means algorithm for clustering large-scale datasets, exploring three distinct parallelization strategies. We conducted extensive experiments to assess the computational efficiency, scalability, and clustering performance of each approach, revealing their benefits and limitations. The paper also delves into the trade-offs between computational efficiency and clustering quality, examining the impacts of various factors. Our insights provide practical guidance on selecting the best parallelization strategy based on available resources and dataset characteristics, contributing to a deeper understanding of parallelization techniques for the Big-means algorithm. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Big data Clustering Decomposition divide and conquer algorithm Global optimization K-means K-means++ Minimum sum-of-squares Unsupervised learning

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Aplikace Voroného diagramů v plánování dráhy robotu

Aplikace Voroného diagramů v plánování dráhy robotu

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作者： Chaloupka, Luděk Brno University of Technology

Tato bakalářská práce je zaměřena na tématiku plánování dráhy robotu. Stěžejním problémem je pohyb bezrozměrného (tj. bodového) robotu, bez omezení p... 详细信息

Tato bakalářská práce je zaměřena na tématiku plánování dráhy robotu. Stěžejním problémem je pohyb bezrozměrného (tj. bodového) robotu, bez omezení pohybu a ve scéně s nepohyblivými překážkami (též bodovými). Součástí práce je implementace zmíněných algoritmů pro danou třídu úloh a vymezení vhodné metody.

关键词： Voroného diagram inkrementální algoritmus zametací algoritmus algoritmus rozděl a panuj Dijkstrův algoritmus A* algoritmus Voronoi diagram incremental algorithm plane sweep algorithm divide and conquer algorithm Dijkstra algorithm A* algorithm

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Least Squares Model Averaging for Distributed Data

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JOURNAL OF MACHINE LEARNING RESEARCH 2023年 24卷 1-59页

作者： Zhang, Haili Liu, Zhaobo Zou, Guohua Shenzhen Polytech Univ Inst Appl Math Shenzhen 518055 Peoples R China Shenzhen Univ Inst Adv Study Shenzhen 518060 Peoples R China Capital Normal Univ Sch Math Sci Beijing 100048 Peoples R China

divide and conquer algorithm is a common strategy applied in big data. Model averaging has the natural divide-and-conquer feature, but its theory has not been developed in big data scenarios. The goal of this paper is to fill this gap. We propose two divide-and conquer-type model averaging estimators for linear models with distributed data. Under some regularity conditions, we show that the weights from Mallows model averaging criterion converge in L-2 to the theoretically optimal weights minimizing the risk of the model averaging estimator. We also give the bounds of the in-sample and out-of-sample mean squared errors and prove the asymptotic optimality for the proposed model averaging estimators. Our conclusions hold even when the dimensions and the number of candidate models are divergent. Simulation results and a real airline data analysis illustrate that the proposed model averaging methods perform better than the commonly used model selection and model averaging methods in distributed data cases. Our approaches contribute to model averaging theory in distributed data and parallel computations, and can be applied in big data analysis to save time and reduce the computational burden.

关键词： consistency distributed data divide and conquer algorithm Mallows' criterion model averaging optimality

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How to Use K-means for Big Data Clustering?

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PATTERN RECOGNITION 2023年 137卷

作者： Mussabayev, Rustam Mladenovic, Nenad Jarboui, Bassem Mussabayev, Ravil Inst Informat & Computat Technol Lab Anal & Modeling Informat Proc Pushkin Str 125 Alma Ata 050010 Kazakhstan Univ Washington Dept Math Padelford Hall C-138 Seattle WA 98195 USA Higher Coll Technol Dept Ind Management St 19 Abu Dhabi 25026 U Arab Emirates

K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of data. Therefore, it is crucial to improve K-means by scaling it to big data using as few of the following computational resources as possible: data, time, and algorith-mic ingredients. We propose a new parallel scheme of using K-means and K-means++ algorithms for big data clustering that satisfies the properties of a "true big data" algorithm and outperforms the classical and recent state-of-the-art MSSC approaches in terms of solution quality and runtime. The new approach naturally implements global search by decomposing the MSSC problem without using additional meta -heuristics. This work shows that data decomposition is the basic approach to solve the big data clustering problem. The empirical success of the new algorithm allowed us to challenge the common belief that more data is required to obtain a good clustering solution. Moreover, the present work questions the es-tablished trend that more sophisticated hybrid approaches and algorithms are required to obtain a better clustering solution.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： Big data Clustering Minimum sum -of -squares divide and conquer algorithm Decomposition K -means K -means plus plus Global optimization Unsupervised learning

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Nonlinear Waves in a Two-ring Network with a Transverse Coupling

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Procedia IUTAM 2017年 22卷 244-250页

作者： Dongyuan Yu Nan Ding Jing Zhou Xu Xu College of Mathematics Jilin university No. 2699 Qianjin Street Changchun 130012 P.R. China College of Information Technology Jilin Agricultural University 2888 Xincheng Street Changchun 130012 P. R. China

关键词： Complex network divide and conquer algorithm nonlinear waves Hopf bifurcation spatio-temporal dynamics

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Least squares model averaging for distributed data

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 10235-10293页

作者： Haili Zhang Zhaobo Liu Guohua Zou Institute of Applied Mathematics Shenzhen Polytechnic University Shenzhen China Institute for Advanced Study Shenzhen University Shenzhen China School of Mathematical Sciences Capital Normal University Beijing China

divide and conquer algorithm is a common strategy applied in big data. Model averaging has the natural divide-and-conquer feature, but its theory has not been developed in big data scenarios. The goal of this paper is to fill this gap. We propose two divide-and-conquer-type model averaging estimators for linear models with distributed data. Under some regularity conditions, we show that the weights from Mallows model averaging criterion converge in L2 to the theoretically optimal weights minimizing the risk of the model averaging estimator. We also give the bounds of the in-sample and out-of-sample mean squared errors and prove the asymptotic optimality for the proposed model averaging estimators. Our conclusions hold even when the dimensions and the number of candidate models are divergent. Simulation results and a real airline data analysis illustrate that the proposed model averaging methods perform better than the commonly used model selection and model averaging methods in distributed data cases. Our approaches contribute to model averaging theory in distributed data and parallel computations, and can be applied in big data analysis to save time and reduce the computational burden.

关键词： consistency distributed data divide and conquer algorithm Mallows' criterion model averaging optimality

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Exponential tail bounds for max-recursive sequences

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ELECTRONIC COMMUNICATIONS IN PROBABILITY 2006年 11卷 266-277页

作者： Rueschendorf, Ludger Schopp, Eva-Maria Univ Freiburg Dept Math Stochast D-79104 Freiburg Germany

Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise in the worst case analysis of divide and conquer algorithms, in parallel search algorithms or in the height of random tree models. For the proof we determine asymptotic bounds for the moments or for the Laplace transforms and apply a characterization of exponential tail bounds due to Kasahara (1978).

关键词： recursive algorithm exponential bounds divide and conquer algorithm probabilistic analysis of algorithms

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