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A nonlinear Gauss-Seidel algorithm for inference about GLMM

COMPUTATIONAL STATISTICS 2000年第2期15卷 229-241页

作者： Jiang, JM Case Western Reserve Univ Dept Stat Cleveland OH 44106 USA

A nonlinear Gauss-Seidel type algorithm is proposed for computing the maximum posterior estimates of the random effects in a generalized linear mixed model. We show that the algorithm converges in virtually all typical situations of generalized linear mixed models. A numerical example shows the superiority of the proposed algorithm over the standard Newton-Raphson procedure when the number of random effects is large.

关键词： maximum posterior generalized linear mixed models recursive algorithm convergence

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Spline representation and redundancies of one-dimensional ReLU neural network models

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ANALYSIS AND APPLICATIONS 2023年第1期21卷 127-163页

作者： Plonka, Gerlind Riebe, Yannick Kolomoitsev, Yurii Gottingen Univ Inst Numer & Appl Math Lotzestr 16-18 Gottingen Germany

We analyze the structure of a one-dimensional deep ReLU neural network (ReLU DNN) in comparison to the model of continuous piecewise linear (CPL) spline functions with arbitrary knots. In particular, we give a recursive algorithm to transfer the parameter set determining the ReLU DNN into the parameter set of a CPL spline function. Using this representation, we show that after removing the well-known parameter redundancies of the ReLU DNN, which are caused by the positive scaling property, all remaining parameters are independent. Moreover, we show that the ReLU DNN with one, two or three hidden layers can represent CPL spline functions with K arbitrarily prescribed knots (breakpoints), where K is the number of real parameters determining the normalized ReLU DNN (up to the output layer parameters). Our findings are useful to fix a priori conditions on the ReLU DNN to achieve an output with prescribed breakpoints and function values.

关键词： ReLU deep neural network free knot spline functions recursive algorithm parameter redundancies

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Design of state and parametric estimation algorithms for nonlinear systems with hysteresis-saturation nonlinearities

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2017年第2期27卷 146-153页

作者： Salhi, Houda Kamoun, Samira Univ Sfax Natl Engn Sch Sfax ENIS Lab Sci & Tech Automat Control & Comp Engn Lab SA Sfax Tunisia

The paper deals with the parameter estimation problem of Wiener state-space models with hysteresis-saturation nonlinearities. A recursive parametric and state estimation algorithm is presented for the Wiener system by combining the adjustable model idea, the least squares technique and the Kalman filter principle. The basic idea is to decompose the hysteresis-saturation nonlinearity into two asymmetric saturation nonlinearities and to estimate jointly the state variables, the parameters and the internal variable of the considered Wiener model using the available input-output data. The proposed recursive algorithm can be extended to nonlinear systems with other hard nonlinearities.

关键词： recursive algorithm parameter estimation state estimation wiener model hysteresis-saturation nonlinearity adjustable model least squares Kalman filter

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Distributed recursive Gaussian Processes for RSS Map Applied to Target Tracking

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2017年第3期11卷 492-503页

作者： Yin, Feng Gunnarsson, Fredrik Chinese Univ Hong Kong Shenzhen & Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China Ericsson Res SE-58330 Linkoping Sweden

We propose a distributed recursive Gaussian process (drGP) regression framework for building received-signal-strength (RSS) map. The proposed framework adopts independent mobile devices in prescribed local areas to construct local RSS maps through recursive computation of the posterior distribution of the RSS on a fixed set of grids as training data gradually become available. The training input positions can be either precise or subject to errors of known distribution. All the local RSS maps are then fused to give a global map in the second step. The proposed framework is of significantly reduced computational complexity and scalable to big data generated from large-scale sensor networks. We further demonstrate its use in both static fingerprinting and mobile target tracking. The experimental results show that with our distributed framework satisfactory positioning accuracy can be achieved with much less complexity and storage than the standard framework.

关键词： Distributed algorithm Gaussian processes particle filtering recursive algorithm RSS fingerprinting

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A novel recursive subspace identification approach of closed-loop systems

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MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS 2013年第6期19卷 526-539页

作者： Wang, Jia Wang, Hong-Wei Gu, Hong Dalian Univ Technol Sch Control Sci & Engn Dalian Peoples R China Dalian Univ Technol Sch Control Sci & Engn Dalian Peoples R China

In this paper, a subspace model identification method under closed-loop experimental condition is presented which can be implemented to recursively identify and update the system model. The projected matrices play an important role in this identification scheme which can be obtained by the projection of the input and output data onto the space of exogenous inputs and recursively updated through sliding window technique. The propagator type method in array signal processing is then applied to calculate the subspace spanned by the column vectors of the extended observability matrix without singular value decomposition. The speed of convergence of the proposed method is mainly dependent on the number of block Hankel matrix rows and the initialization accuracy of the projected data matrices. The proposed method is feasible for the closed-loop system contaminated with coloured noises. Two numerical examples show the effectiveness of the proposed algorithm.

关键词： subspace identification method recursive algorithm closed-loop system LQ decomposition

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Gradient-Based recursive Parameter Estimation Methods for a Class of Time-Varying Systems from Noisy Observations

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2024年第11期43卷 7089-7116页

作者： Xu, Ning Liu, Qinyao Ding, Feng Jiangnan Univ Minist Educ Sch Internet Things Engn Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Xian Jiaotong Liverpool Univ Sch Adv Technol Dept Mechatron & Robot Suzhou 215123 Peoples R China Hubei Univ Technol Sch Elect & Elect Engn Wuhan 430068 Peoples R China

It is essential for meeting the stringent real-time demands encountered in actual production scenarios. Employing the low computational complexity of recursive algorithms, some new schemes are developed for the parameter estimation of a class of time-varying systems. The temporal evolution of parameters is characterized through the autoregressive process, facilitating the construction of the identification model with regard to the autoregressive coefficients. Based on the computational efficiency of the gradient search, a parametric autoregression-based stochastic gradient algorithm is derived with an appropriate step size, achieving a compromise between the steepest descent and convergence rate. In order to address the limitation of the low estimation accuracy in gradient algorithms, a parametric autoregression-based multi-innovation stochastic gradient algorithm is explored by making use of the favorable information for corrections. The simulation results are given to demonstrate the effectiveness of the proposed algorithms. Therefore, for a class of time-varying systems whose parameters become the further insight through the autoregressive process, the proposed gradient methods can obtain the parameter estimates faster and more accurately while ensuring the real-time performance of time-varying systems.

关键词： Parameter estimation recursive algorithm Gradient search Multi-innovation identification Time-varying system

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Parallel Communication-Avoiding algorithm for Triangular Matrix Inversion on Homogeneous and Heterogeneous Platforms

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INTERNATIONAL JOURNAL OF PARALLEL PROGRAMMING 2015年第4期43卷 631-655页

作者： Mahfoudhi, Ryma Mahjoub, Zaher Nasri, Wahid Univ Tunis El Manar Fac Sci Tunis Tunis 2092 Tunisia Higher Sch Sci & Tech Tunis Tunis 1008 Tunisia

We address in this paper the parallelization of a recursive algorithm for large scale triangular matrix inversion based on the 'Divide and Conquer' (D&C) paradigm. A set of different versions of an original sequential algorithm are first presented. A theoretical performance study permits to establish an accurate comparison between the designed algorithms. Afterwards, we develop in the second part of the paper, an optimal parallel avoiding-communication algorithm for a given number of available homogeneous and heterogeneous processors. To reach this target, we use a so called 'non equitable and incomplete' version of the D&C paradigm consisting in recursively decomposing the original problem into two sub-problems of non equal sizes, then decomposing only one sub-problem in the same previous manner. The theoretical study is validated by a series of experiments achieved on three target platforms, namely an 8-core shared memory machine, a distributed memory cluster and a heterogeneous CPU-GPU cluster. The obtained results permit to illustrate the interest of the contribution.

关键词： Communication-avoiding Cost optimality Distributed memory machine Divide and Conquer GPU Homogeneous platform Heterogeneous platform Load balancing Parallel algorithm recursive algorithm Scheduling Shared memory machine Triangular matrix inversion

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A new power system digital harmonic analyzer

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IEEE TRANSACTIONS ON POWER DELIVERY 2007年第2期22卷 772-780页

作者： Tomic, Josif J. Kusljevic, Miodrag D. Vujicic, Vladimir V. Univ Novi Sad Novi Sad 21000 Serbia Termoelektro Enel AD Belgrade 11060 Serbia

In this paper, new digital instruments measuring power-quality indicators and harmonic analyzers are developed. A new technique for simultaneous local system frequency and amplitudes of the fundamental and higher harmonies estimation from either a voltage or current signal is presented. The structure consists of threedecoupled modules: the first one for an adaptive filter of input signal, the second one for frequency estimation, and the third one for harmonic amplitude estimation. A very suitable algorithm for frequency and harmonic amplitude estimation is obtained. This technique provides accurate frequency estimates with error in the range of 0.002 Hz and amplitude estimates with error in the range of 0.03% for SNR = 60 dB in about 25 ms. The theoretical basis and practical implementation of the technique are described. To demonstrate the performance of the developed algorithm, computer simulated data records are processed. Data of the distribution power system voltage signals are also collected in the laboratory environment and are processed in a newly developed digital PC-based harmonic analyzer. It has been found that the proposed method really meets the need of offline applications. Even more, by using the parallel computation algorithms, this method should meet the need of online applications and should be more practical.

关键词： adaptive filtering amplitude estimation computer relaying digital filters finite-impulse-response (FIR) filter frequency estimation frequency measurement harmonic analysis harmonic analyzer harmonics power quality (PQ) recursive algorithm

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Scalable Distributed Filtering for a Class of Discrete-Time Complex Networks Over Time-Varying Topology

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2020年第8期31卷 2930-2941页

作者： Liu, Yang Wang, Zidong Zhou, Donghua Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China Brunel Univ London Dept Comp Sci Uxbridge UB8 3PH Middx England Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

This article is concerned with the distributed filtering problem for a class of discrete complex networks over time-varying topology described by a sequence of variables. In the developed scalable filtering algorithm, only the local information and the information from the neighboring nodes are used. As such, the proposed filter can be implemented in a truly distributed manner at each node, and it is no longer necessary to have a certain center node collecting information from all the nodes. The aim of the addressed filtering problem is to design a time-varying filter for each node such that an upper bound of the filtering error covariance is ensured and the desired filter gain is then calculated by minimizing the obtained upper bound. The filter is established by solving two sets of recursive matrix equations, and thus, the algorithm is suitable for online application. Sufficient conditions are provided under which the filtering error is exponentially bounded in mean square. The monotonicity of the filtering error with respect to the coupling strength is discussed as well. Finally, an illustrative example is presented to demonstrate the feasibility and effectiveness of our distributed filtering strategy.

关键词： Complex networks Topology Couplings Covariance matrices Heuristic algorithms Scalability Complex networks distributed filtering error boundedness monotonicity recursive algorithm time-varying topology

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ON INVERSE MAPPINGS OF RESIDUE CLASS REPRESENTING SUM-DISTINCT SETS OBTAINED FROM HADAMARD-MATRICES

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1993年第3-4期49卷 163-169页

作者： JEVTIC, DB Computer Engineering Department Santa Clara University Santa Clara CA 95053 United States

Inverse mappings arc algorithms which return the subset of a given sum. The O(n log n) inverse mapping described here is related to recursively defined residue class representing sum-distinct sets from {0, 1}n. The se... 详细信息

关键词： RESIDUAL VECTORS HERMITE EQUIVALENT FORM recursive algorithm

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