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stochastic gradient algorithm under (h,φ)-entropy criterion

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2007年第6期26卷 941-960页

作者： Chen, B. Hu, J. Pu, L. Sun, Z. Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China

Motivated by the work of Erdogmus and Principe, we use the error (h, phi)-entropy as the supervised adaptation criterion. Several properties of the (h, phi)-entropy criterion and the connections with traditional error criteria are investigated. By a kernel estimate approach, we obtain the nonparametric estimator of the instantaneous (h, phi)-entropy. Then, we develop the general stochastic information gradient algorithm, and derive the approximate upper bound for the step size in the adaptive linear neuron training. Moreover, the (h, phi) pair are optimized to improve the performance of the proposed algorithm. For the finite impulse response identification with white Gaussian input and noise, the exact optimum phi function is derived. Finally, simulation experiments verify the results and demonstrate the noticeable performance improvement that may be achieved by the optimum (h, phi)-entropy criterion.

关键词： (h, phi)-entropy stochastic gradient algorithm adaptive filtering kernel methods

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stochastic gradient algorithm for state space system with d-step delay

Stochastic gradient algorithm for state space system with <i...

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26th Chinese Control and Decision Conference (CCDC)

作者： Gu, Ya Ding, Rui Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China

ISBN: (纸本)9781479937066

This paper researches parameter and state estimation problems for linear systems with d-step delay. Combining the linear transformation and the property of the shift operator, the canonical state space model with d-step delay is transformed into an identification model. The stochastic gradient algorithm is raised to identify the parameter vectors. Finally, an example is presented to validate the given algorithms.

关键词： stochastic gradient algorithm State space models Time-delay

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Further results on almost sure convergence of the stochastic gradient algorithm

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 1999年第3期13卷 161-181页

作者： Radenkovic, MS Univ Colorado Dept Elect Engn Denver CO 80217 USA

In this paper, we consider the rate of convergence of the parameter estimation error and the cost function for the stochastic gradient-type algorithm. The problem is solved in the case of the minimum-variance stochastic adaptive control. It is proven that the cost function has the rate of convergence, comparable with the one established for the least-squares algorithm. Comparison of the two algorithms is made under the same conditions related to the process noise and the structure of the system model. In addition it is shown, that the convergence rate for the parameter estimation error, is of the same order as in the case of extended least-squares algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： stochastic adaptive control stochastic gradient algorithm almost sure convergence rate of convergence

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Improved Redundant Rule-Based stochastic gradient algorithm for Time-Delayed Models Using Lasso Regression

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IEEE ACCESS 2022年 10卷 3336-3342页

作者： Zhao, Hangtao Lv, Lixin Ji, Yuejiang Wuxi Vocat Coll Sci & Technol Wuxi 214122 Jiangsu Peoples R China

This paper proposes an improved redundant rule based lasso regression stochastic gradient (RR-LR-SG) algorithm for time-delayed models. The improved SG algorithm can update the parameter elements with different step-sizes and directions, thus it is more adaptive;while the lasso regression method can pick out the small weights from the redundant parameter vector, it therefore can obtain the time-delay easily. To show the effectiveness of the proposed algorithm, the convergence analysis is also given. The simulated numerical results are consistent with the analytically derived results of the proposed algorithm.

关键词： Convergence Licenses Iterative methods Cost function Mathematical models Lead Costs Parameter estimation time-delayed model lasso regression redundant rule stochastic gradient algorithm

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Bias compensated stochastic gradient algorithm for identification of an ARX-type nonlinear rational model and its application in modeling of the dynamic of the cellular toxicity

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2022年第9期32卷 5268-5280页

作者： Jing, Shaoxue Kiely, Janice Luxton, Richard Huaiyin Normal Univ Sch Phys & Elect Elect Engn 111 Changjiang West Rd Huaian 223300 Jiangsu Peoples R China Univ West England Dept Engn Design & Math Bristol Avon England

Nonlinear rational model (NRM) is a generalized nonlinear model, the NARMAX model and Volterra model can be regarded as its special cases. In this article, the parameter identification of a class of nonlinear rational models is studied. Due to the coupling of the model output and the information vector, the parameter identification of the NRM is very challenging. To reduce the complexity of the identification, the stochastic gradient algorithm is used. However, the estimate given by traditional stochastic gradient algorithm is biased. To obtain unbiased estimation, the bias is calculated by using the observations and the previous estimate and then compensated to the biased estimate. A variable factor considering the estimation error is introduced to speed up the algorithm. Theoretical analysis shows that the proposed algorithm can obtain an unbiased estimate and has the complexity of O(n). The proposed algorithm is validated by a numerical example and is applied in modeling the dynamics of the cellular toxicity using the tetra-ethyl ammonium chloride. Results show that the proposed algorithm can obtain an accurate estimate for the nonlinear rational model with less computation.

关键词： adaptive modeling bias compensation nonlinear rational model parameter estimation stochastic gradient algorithm

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Cost function adaptation: a stochastic gradient algorithm for data echo cancellation

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IEE PROCEEDINGS-VISION IMAGE AND SIGNAL PROCESSING 2000年第6期147卷 516-526页

作者： Rusu, C Cowan, CFN Tampere Univ Technol Digital Media Inst Signal Proc Lab FIN-33101 Tampere Finland Tech Univ Cluj Napoca Dept Elect & Telecommun Cluj Napoca Romania Queens Univ Belfast Dept Elect & Elect Engn Belfast BT9 5AH Antrim North Ireland

A family of stochastic gradient algorithms and their behaviour in the data echo cancellation work platform are presented. The cost function adaptation algorithms use an error exponent update strategy based on an absolute error mapping, which is updated at every iteration. The quadratic and nonquadratic cost functions are special cases of the new family. Several possible realisations are introduced using these approaches. The noisy error problem is discussed and the digital recursive filter estimator is proposed. The simulation outcomes confirm the effectiveness of the proposed family of algorithms.

关键词： telephone lines function evaluation adaptive signal processing echo suppression Digital signal processing parameter estimation stochastic processes stochastic gradient algorithm data echo cancellation LMS recursive filters data communication absolute error mapping gradient methods noisy error problem error exponent update error analysis Filtering methods in signal processing iteration Interpolation and function approximation (numerical analysis) digital recursive filter estimator simulation Other topics in statistics filtering theory quadratic cost functions nonquadratic cost functions cost function adaptation

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Law of the iterated logarithm for a constant-gain linear stochastic gradient algorithm

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2000年第2期39卷 533-570页

作者： Joslin, JA Heunis, AJ Siemens Canada Kanata ON K2K 2M5 Canada Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

We study almost-sure limiting properties, taken as epsilon SE arrow 0, of the finite horizon sequence of random estimates {theta(0)(epsilon), theta(1)(epsilon), theta(2)(epsilon),..., theta([T/epsilon])(epsilon)} for the linear stochastic gradient algorithm theta(n+1)(epsilon) = theta(n)(epsilon)+epsilon [a(n+1) - (theta(n)(epsilon))' Xn+1]Xn+1, theta(o)(epsilon) (Delta)(=)theta* nonrandom, where T is an element of (0,infinity) is an arbitrary constant, epsilon is an element of (0, 1] is a (small) adaptation gain, and {a(n)} and {X-n} are data sequences which drive the algorithm. These limiting properties are expressed in the form of a functional law of the iterated logarithm.

关键词： stochastic gradient algorithm L-mixing processes functional law of the iterated logarithm

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Aitken-Based stochastic gradient algorithm for ARX Models with Time Delay

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2019年第6期38卷 2863-2876页

作者： Wang, Cheng Li, Kaicheng Jiangnan Univ Sch Internet Things Engn Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Beijing Jiaotong Univ Natl Engn Res Ctr Rail Transportat Operat & Contr Beijing 100044 Peoples R China

This paper proposes an Aitken-based stochastic gradient algorithm for ARX models with time delay. By using the redundant rule, the ARX model can be transformed into an augmented model. Based on the Aitken method, the parameters of the augmented model can be estimated, and then, the unknown parameters of the ARX model and the time delay can be computed. The performance of the Aitken-based stochastic gradient algorithm is then analyzed. Furthermore, a numerical example and a real system example are provided to show the effectiveness of the proposed algorithm. Compared with the traditional stochastic gradient algorithm, the Aitken-based stochastic gradient algorithm achieves better convergence performance that the parameter estimation errors converge below 3% in both examples after 400 steps.

关键词： Parameter estimation ARX model Time delay Aitken method stochastic gradient algorithm

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Prediction of the performance and exhaust emissions of a compression ignition engine using a wavelet neural network with a stochastic gradient algorithm

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ENERGY 2018年 142卷 1128-1138页

作者： Molkdaragh, R. Rahimi Jafarmadar, S. Khalilaria, Sh Saraee, H. Soukht Urmia Univ Mech Engn Dept Orumiyeh *** West Azerbaijan Iran

The purpose of this research is to use a wavelet neural network (WNN) and stochastic gradient algorithm (SGA) to predict the performance and exhaust emissions of a compression ignition engine with nanoparticles-diesel fuel. The percentage of the additive of nanoparticles to the fuel ranges between 20 and 80 ppm. A model of WNN has been applied in order to predict the relationship between the power, fuel consumption (FC), specific fuel consumption (SFC), CO, NOx, and HC with the amount of nano particles at different speeds. The input variables are of two parameters (the percentage of nanoparticles and engine speed), while the output variables are of six parameters (power, FC, SFC, CO, NOx, and HC). In this work, considering the characteristics of the utilized wavelet function and application of the SGA method, satisfactory results were obtained in prediction of exhaust emissions and performance of the target engine. In addition, two common artificial neural networks (ANNs) (back propagation (BP) and non-linear autoregressive with exogenous input (NARX)) were used in predicting the performance of internal combustion engines compared with WNN results. Therefore, evaluation results of these three networks showed that the WNN with the SGA are very accurate and useful method to perform the prediction and model nonlinear phenomena of internal combustion engines. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： WNN BPNN NARXNN stochastic gradient algorithm Compression ignition engine Performance Emissions

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A novel maximum likelihood-based stochastic gradient algorithm for Hammerstein nonlinear systems with coloured noise

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2019年第1期32卷 23-29页

作者： Pu, Yan Chen, Jing Jiangnan Univ Sch Sci Sch Internet Things Engn Wuxi 214122 Jiangsu Peoples R China

This paper proposes a novel maximum likelihood based stochastic gradient algorithm for Hammerstein nonlinear systems with coloured noise. The unknown noises in the information vector are replaced by their estimates, and then the parameters can be obtained by using the proposed algorithm through the noise estimates. Compared with the maximum likelihood-based recursive least squares algorithm, the proposed algorithm has less computation burden. Furthermore, the performance of the proposed algorithm is analysed and compared using a simulation example.

关键词： system identification stochastic gradient algorithm recursive least squares algorithm maximum likelihood Hammerstein system

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