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Convergence of the recursive identification algorithms for multivariate pseudo-linear regressive systems

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2016年第6期30卷 824-842页

作者： Wang, Xuehai Ding, Feng Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China Henan Univ Urban Construct Sch Math & Phys Pingdingshan 467036 Peoples R China

The performance analysis of the recursive algorithms for the multivariate systems with an autoregressive moving average noise process is still open. This paper analyzes the convergence of two recursive identification algorithms, the multivariate recursive generalized extended least squares algorithm and the multivariate generalized extended stochastic gradient algorithm, for pseudo-linear multivariate systems and proves that the parameter estimation errors consistently converge to zero under persistent excitation conditions. The simulation results show that the proposed algorithms work well. Copyright (C) 2015 JohnWiley & Sons, Ltd.

关键词： parameter estimation least squares algorithm stochastic gradient algorithm pseudo-linear regressive model martingale convergence theorem

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PROJECTED stochastic gradientS FOR CONVEX CONSTRAINED PROBLEMS IN HILBERT SPACES

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SIAM JOURNAL ON OPTIMIZATION 2019年第3期29卷 2079-2099页

作者： Geiersbach, Caroline Pflug, Georg Ch Univ Vienna Dept Stat & Operat Res A-1030 Vienna Austria IIASA Schlosspl 1 A-2361 Laxenburg Austria

Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates u(n) converges weakly to a point in the set of minimizers with probability one. In the strongly convex case, the sequence converges strongly to the unique optimum with probability one. An application to a class of PDE constrained problems with a convex objective, convex constraint, and random elliptic PDE constraints is shown. Theoretical results are demonstrated numerically.

关键词： stochastic approximation stochastic gradient algorithm random elliptic PDEs as constraints PDE constrained optimization under uncertainty optimization in Hilbert spaces

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Generalized predictive control of a class of MIMO models via a projection neural network

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NEUROCOMPUTING 2017年 234卷 192-197页

作者： Ye, Qian Lou, Xuyang Sheng, Li Wuxi Inst Technol Wuxi 214121 Peoples R China Jiangnan Univ Inst Syst Engn Wuxi 214122 Peoples R China China Univ Petr East China Coll Informat & Control Engn Qingdao 266580 Peoples R China

The system identification and generalized predictive control of a class of multiple input multiple output models are studied. The generalized predictive control problem with unknown parameters is first addressed by finding a control sequence for control performance as a goal. Then, the unknown parameters of the models are estimated by a new stochastic gradient algorithm providing high estimation accuracy. Third, the generalized predictive control problem is formulated to a quadratic programming problem with linear inequality constraints. Finally, the constrained quadratic programming problem is solved through a generalized projection neural network with simple structure and small number of neurons, while previous projection neural networks have complex structure and require more neurons. Numerical simulations are provided to reinforce our theoretical results.

关键词： Generalized predictive control Projection neural network System identification stochastic gradient algorithm MIMO model

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The Cost of Privacy in Asynchronous Differentially-Private Machine Learning

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2021年 16卷 2118-2129页

作者： Farokhi, Farhad Wu, Nan Smith, David Kaafar, Mohamed Ali Univ Melbourne Dept Elect & Elect Engn Melbourne Vic 3010 Australia Macquarie Univ Dept Comp Sydney NSW 2109 Australia CSIROs Data61 Eveleigh NSW 2015 Australia Australian Natl Univ Coll Engn & Comp Sci CECS Canberra ACT 2600 Australia

We consider training machine learning models using data located on multiple private and geographically-scattered servers with different privacy settings. Due to the distributed nature of the data, communicating with all collaborating private data owners simultaneously may prove challenging or altogether impossible. We consider differentially-private asynchronous algorithms for collaboratively training machine-learning models on multiple private datasets. The asynchronous nature of the algorithms implies that a central learner interacts with the private data owners one-on-one whenever they are available for communication without needing to aggregate query responses to construct gradients of the entire fitness function. Therefore, the algorithm efficiently scales to many data owners. We define the cost of privacy as the difference between the fitness of a privacy-preserving machine-learning model and the fitness of trained machine-learning model in the absence of privacy concerns. We demonstrate that the cost of privacy has an upper bound that is inversely proportional to the combined size of the training datasets squared and the sum of the privacy budgets squared. We validate the theoretical results with experiments on financial and medical datasets. The experiments illustrate that collaboration among more than 10 data owners with at least 10,000 records with privacy budgets greater than or equal to 1 results in a superior machine-learning model in comparison to a model trained in isolation on only one of the datasets, illustrating the value of collaboration and the cost of the privacy. The number of the collaborating datasets can be lowered if the privacy budget is higher.

关键词： Training Data models Distributed databases Biological system modeling Degradation Privacy Machine learning Machine learning differential privacy stochastic gradient algorithm asynchronous

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Identification of nonlinear dynamic systems using convex combinations of multiple adaptive radius basis function networks

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MEASUREMENT 2013年第1期46卷 628-638页

作者： Zeng, Xiangping Zhao, Haiquan Jin, Weidong He, Zhengyou Li, Tianrui SW Jiaotong Univ Sch Informat Sci & Technol Chengdu 610031 Peoples R China SW Jiaotong Univ Sch Elect Engn Chengdu 610031 Peoples R China

To improve performance of nonlinear adaptive filter based on radius basis function (RBF) networks, a generalized combination scheme is proposed for nonlinear dynamic system identification in this paper. The nonlinear filter proposed is constructed by the convex combination of multiple RBF networks (MCRBF). Its adaptive algorithm with different step sizes is derived by the gradient descent rule, and can overcome the contradiction between convergence speed and precision of the stochastic gradient (SG) algorithm for RBF networks, which is imposed by the selection of a fixed value for the adaption step. Computer simulations demonstrate that the performance of the nonlinear filter proposed is superior to the RBF for nonlinear dynamic system identification in terms of convergence speed, steady state error and tracking capability. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.

关键词： Nonlinear dynamic system identification Radial basis function Convex combination stochastic gradient algorithm Nonlinear adaptive filter

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Adaptive power allocation strategies for distributed space-time coding in cooperative MIMO networks

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IET COMMUNICATIONS 2014年第7期8卷 1141-1150页

作者： Peng, Tong de Lamare, Rodrigo C. Schmeink, Anke Univ York Dept Elect Commun Res Grp York YO10 5DD N Yorkshire England Rhein Westfal TH Aachen Inst Theoret Informat Technol D-52056 Aachen Germany

Adaptive power allocation (PA) algorithms with different criteria for a cooperative multiple-input multiple-output network equipped with distributed space-time coding are proposed and evaluated. Joint constrained optimisation algorithms to determine the PA parameters and the receive filter are proposed for each transmitted symbol in each link, as well as the channel coefficients matrix. Linear receive filter and maximum-likelihood detection are considered with amplify-and-forward and decode-and-forward cooperation strategies. In these proposed algorithms, the elements in the PA matrices are optimised at the destination node and then transmitted back to the relay nodes via a feedback channel. The effects of the feedback errors are considered. Linear minimum mean square error expressions and the PA matrices depend on each other and are updated iteratively. stochastic gradient algorithms are developed with reduced computational complexity. Simulation results show that the proposed algorithms obtain significant performance gains as compared with existing PA schemes.

关键词： channel allocation space-time codes cooperative communication MIMO communication channel coding filtering theory matrix algebra maximum likelihood detection amplify and forward communication decode and forward communication optimisation error statistics feedback stochastic processes gradient methods least mean squares methods adaptive power allocation strategy distributed space-time coding cooperative multiple input multiple output network joint constrained optimisation algorithm PA parameter determination symbol transmission channel coefflcients matrix linear receive filter maximum likelihood detection amplify and forward cooperation strategy decode and forward cooperation strategy destination node PA matrix optimisation relay nodes feedback channel feedback error linear minimum mean square error iterative method stochastic gradient algorithm computational complexity reduction

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A Unified Convergence Analysis for Shuffling-Type gradient Methods

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JOURNAL OF MACHINE LEARNING RESEARCH 2021年第1期22卷 1-44页

作者： Nguyen, Lam M. Quoc Tran-Dinh Phan, Dzung T. Phuong Ha Nguyen van Dijk, Marten IBM Res Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA Univ N Carolina Dept Stat & Operat Res Chapel Hill NC 27599 USA eBay Inc San Jose CA 95125 USA Ctr Wiskunde & Informat Amsterdam Netherlands

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many known variants such as randomized reshuffling, deterministic or randomized single permutation, and cyclic and incremental gradient schemes. We focus on two different settings: strongly convex and nonconvex problems, but also discuss the non-strongly convex case. Our main contribu-tion consists of new non-asymptotic and asymptotic convergence rates for a wide class of shuffling-type gradient methods in both nonconvex and convex settings. We also study uni-formly randomized shuffling variants with different learning rates and model assumptions. While our rate in the nonconvex case is new and significantly improved over existing works under standard assumptions, the rate on the strongly convex one matches the existing best-known rates prior to this paper up to a constant factor without imposing a bounded gradient condition. Finally, we empirically illustrate our theoretical results via two nu-merical examples: nonconvex logistic regression and neural network training examples. As byproducts, our results suggest some appropriate choices for diminishing learning rates in certain shuffling variants.

关键词： stochastic gradient algorithm shuffling-type gradient scheme sampling with-out replacement non-convex finite-sum minimization strongly convex minimization

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An efficient MDS-based topographic mapping algorithm

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NEUROCOMPUTING 2005年第3期64卷 285-299页

作者： Matsuda, Y Yamaguchi, K Univ Tokyo Grad Sch Arts & Sci Dept Gen Syst Studies Kazunori Yamaguchi LabMeguro Ku Tokyo 1538902 Japan

Here, an multidimensional scaling-based (MDS-based) topographic mapping algorithm is proposed, named the stochastic MDS network. Because this network utilizes not local but global information over all the units, it can find more optimal results than previous models. In addition, by using a stochastic gradient algorithm, the mapping formation in this network is carried out as efficiently as in SOM-like models based on only the local information. Some simple numerical experiments verified the validity and efficiency of this network. It was also applied to the formation of large-scale topographic mappings, and could form various interesting mappings. (c) 2004 Elsevier B.V. All rights reserved.

关键词： multidimensional scaling stochastic gradient algorithm topographic mapping the self-organizing map

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Adaptive minimum error-rate filtering design: A review

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SIGNAL PROCESSING 2008年第7期88卷 1671-1697页

作者： Chen, Sheng Tan, Shuang Xu, Lei Hanzo, Lajos Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England

Adaptive filtering has been an enabling technology and has found ever-increasing applications in various state-of-the-art communication systems. Traditionally, adaptive filtering has been developed based on the Wiener or minimum mean square error (MMSE) approach, and the famous least mean square algorithm with its low computational complexity readily meets the fast real-time computational constraint of modern high-speed communication systems. For a communication system, however, it is the system's bit error rate (BER), not the mean square error (MSE), that really matters. It has been recognised that minimising the MSE criterion does not necessarily produce the minimum BER (MBER) performance. The introduction of the novel MBER design has opened up a whole new chapter in the optimisation of communication systems, and its design trade-offs have to be documented in contrast to those of the classic but actually still unexhausted MMSE and other often-used optimisation criteria. This contribution continues this theme, and we provide a generic framework for adaptive minimum error-probability filter design suitable for the employment in a variety of communication systems. Advantages and disadvantages of the adaptive minimum error-probability filter design are analysed extensively, in comparison with the classic Wiener filter design. (c) 2008 Elsevier B.V. All rights reserved.

关键词： adaptive filter Wiener solution minimum mean square error minimum bit error rate stochastic gradient algorithm least mean square algorithm least bit error rate algorithm

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M-DCSK-Based Chaotic Communications in MIMO Multipath Channels With No Channel State Information

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2010年第12期57卷 1001-1005页

作者： Wang, Shilian Wang, Xiaodong Natl Univ Def Technol Sch Elect Sci & Engn Changsha 410073 Hunan Peoples R China Columbia Univ Dept Elect Engn New York NY 10027 USA

We consider chaotic digital communications in multiple-input-multiple-output (MIMO) wireless multipath fading channels. In particular, we focus on systems that employ M-ary differential chaos shift keying (M-DCSK). We consider two transceiver schemes, both of which require no channel state information at either the transmitter or the receiver. The first one employs a distinct chaotic sequence at each transmit antenna to spread the same data symbol and transmits omnidirectionally. At each receive antenna, the corresponding differential detection statistic is formed, and these statistics are then combined with equal gain for symbol detection. The second scheme employs a single chaotic spreading sequence and makes use of adaptive transmit and receive beamforming. The beamformers are updated by using a simple stochastic gradient method that is based on the received signal power and a finite-rate feedback strategy. Simulation results show that both schemes can effectively exploit the spatial diversity of the underlying MIMO system, and the adaptive beamforming scheme significantly outperforms the omnidirectional transmission.

关键词： Adaptive beamforming chaotic communications equal gain combining multiple-input-multiple-output (MIMO) M-ary differential chaos shift keying (DCSK) stochastic gradient algorithm

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