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Analysis of the Least Mean Square algorithm with processing delays in the adaptive arm for Gaussian inputs for system identification

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SIGNAL PROCESSING 2024年 217卷

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92697 USA Univ Fed Santa Catarina Dept Elect & Elect Engn Florianopolis SC Brazil

This paper analyzes the effect of a processing delay on the Least Mean Squares (LMS) algorithm for a system identification problem when the processing delay is in the adaptive arm of the filter. Thus the sensing of the input signal is delayed. The input is assumed to be a zero mean stationary Gaussian process. The theoretical mean and mean square behavior of the adaptive weight vector is analyzed. The weight vector is shown to be biased and significantly affects the mean square deviation (MSD). Monte Carlo simulations are presented in support of the assumptions used to derive the theoretical model as a function of the delay, bandwidth and step-size for the LMS algorithm. The results suggest bias problems with other more complicated adaptive filtering algorithms such as Normalized LMS and Recursive Least Squares.

关键词： Adaptive filters Analysis LMS algorithm stochastic algorithms

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Block-wise primal-dual algorithms for large-scale doubly penalized ANOVA modeling

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2024年 194卷

作者： Fu, Penghui Tan, Zhiqiang Rutgers State Univ Dept Stat Piscataway NJ 08854 USA Chinese Univ Hong Kong Shenzhen Sch Data Sci Shenzhen 518172 Guangdong Peoples R China

For multivariate nonparametric regression, doubly penalized ANOVA modeling (DPAM) has recently been proposed, using hierarchical total variations (HTVs) and empirical norms as penalties on the component functions such as main effects and multi -way interactions in a functional ANOVA decomposition of the underlying regression function. The two penalties play complementary roles: the HTV penalty promotes sparsity in the selection of basis functions within each component function, whereas the empirical -norm penalty promotes sparsity in the selection of component functions. To facilitate large-scale training of DPAM using backfitting or block minimization, two suitable primal -dual algorithms are developed, including both batch and stochastic versions, for updating each component function in single -block optimization. Existing applications of primal -dual algorithms are intractable for DPAM with both HTV and empirical -norm penalties. The validity and advantage of the stochastic primal -dual algorithms are demonstrated through extensive numerical experiments, compared with their batch versions and a previous active -set algorithm, in large-scale scenarios.

关键词： ANOVA modeling Nonparametric regression Penalized estimation Primal-dual algorithms stochastic algorithms stochastic gradient methods Total variation

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Inhomogeneous functionals and approximations of invariant distributions of ergodic diffusions: Central limit theorem and moderate deviation asymptotics

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stochastic PROCESSES AND THEIR APPLICATIONS 2021年 133卷 74-110页

作者： Ganguly, Arnab Sundar, P. Louisiana State Univ Dept Math Baton Rouge LA 70803 USA

The paper studies asymptotics of inhomogeneous integral functionals of an ergodic diffusion process under the effect of discretization. Convergence to the corresponding functionals of the invariant distribution is shown for suitably chosen discretization steps, and the fluctuations are analyzed through central limit theorem and moderate deviation principle. The results will be particularly useful for understanding accuracy of an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. This is an infinite-time horizon problem, and the accuracy of numerical schemes in this context are comparatively much less studied than the ones used for generating approximate trajectories of diffusions over finite time intervals. The potential applications of these results also extend to other areas including mathematical physics, parameter inference of ergodic diffusions and analysis of multiscale dynamical systems with averaging. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Estimation of invariant distributions Ergodic diffusions Euler approximation Central limit theorem Large and moderate deviations stochastic algorithms

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stochastic Analysis of the Recursive Least Squares Algorithm for Cyclostationary Colored Inputs

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年第0期68卷 676-686页

作者： Eweda, Eweda Bershad, Neil J. Bermudez, Jose C. M. C4 Adv Solut Abu Dhabi U Arab Emirates Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA Univ Fed Santa Catarina Dept Elect Engn Florianopolis SC Brazil Catholic Univ Pelotas UCPel Pelotas Grad Program Elect Engn & Comp Pelotas RS Brazil

This paper studies the stochastic behavior of the recursive least squares (RLS) algorithm in a system identification framework for a cyclostationary colored input. The input cyclostationary signal is modeled by a colored random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the adaptive weights as a function of the input cyclostationarity. The MSD behaviors of the RLS and LMS algorithms are compared for cyclostationary colored input. Monte Carlo simulations provide strong support for the theory. A separate analysis for white Gaussian and non-Gaussian inputs is presented in support of the assumptions made for the mathematical model above.

关键词： Adaptive Filters Analysis RLS Algorithm stochastic algorithms

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A correctness result for synthesizing plans with loops in stochastic domains

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2020年 119卷 92-107页

作者： Treszkai, Laszlo Belle, Vaishak Univ Edinburgh Sch Informat Edinburgh Midlothian Scotland Alan Turing Inst London England

Finite-state controllers (FSCs), such as plans with loops, are powerful and compact representations of action selection widely used in robotics, video games and logistics. There has been steady progress on synthesizing FSCs in deterministic environments, but the algorithmic machinery needed for lifting such techniques to stochastic environments is not yet fully understood. While the derivation of FSCs has received some attention in the context of discounted expected reward measures, they are often solved approximately and/or without correctness guarantees. In essence, that makes it difficult to analyze fundamental concerns such as: do all paths terminate, and do the majority of paths reach a goal state? In this paper, we present new theoretical results on a generic technique for synthesizing FSCs in stochastic environments, allowing for highly granular specifications on termination and goal satisfaction. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Plan and program synthesis stochastic domains Loops in plans and programs stochastic algorithms Planning in robotics

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Statistical Metamorphic Testing of Neural Network Based Intrusion Detection Systems

Statistical Metamorphic Testing of Neural Network Based Intr...

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IEEE International Conference on Cyber Security and Resilience (IEEE CSR)

作者： Reitman, Faqeer Ur Izurieta, Clemente Montana State Univ Gianforte Sch Comp Bozeman MT 59717 USA Montana State Univ Gianforte Sch Comp Idaho Natl Labs Bozeman MT USA

ISBN: (纸本)9781665402859

Testing computationally complex neural network-based applications (i.e. network intrusion detection systems) is a challenging task due to the absence of a test oracle. Metamorphic testing is a method to potentially solve the oracle problem when the correctness of individual output is difficult to determine. However, due to the stochastic nature of these applications, multiple runs with the same input can produce slightly different results;thus rendering traditional metamorphic testing technique inadequate. To address this problem, this paper proposes a statistical metamorphic testing technique to test neural network based Network Intrusion Detection Systems (N-IDSs) in a non-deterministic environment. We also performed mutation analysis to show the effectiveness of the proposed approach. The results show that the proposed method has a strong defect detection capability and is able to kill 100% implementation bugs in two neural network-based N-IDSs, and 66.66% in a neural network-based cancer prediction system.

关键词： Metamorphic testing oracle problem statistical hypothesis testing intrusion detection system neural networks stochastic algorithms

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Identification of Mechanical Parameters in Flexible Drive Systems Using Hybrid Particle Swarm Optimization Based on the Quasi-Newton Method

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algorithms 2023年第8期16卷 371-371页

作者： Hafez, Ishaq Dhaouadi, Rached Amer Univ Sharjah Coll Engn Mechatron Grad Program Sharjah 26666 U Arab Emirates Amer Univ Sharjah Coll Engn Dept Elect Engn Sharjah 26666 U Arab Emirates

This study presents hybrid particle swarm optimization with quasi-Newton (HPSO-QN), a hybrid optimization method for accurately identifying mechanical parameters in two-mass model (2MM) systems. These systems are commonly used to model and control high-performance electric drive systems with elastic joints, which are prevalent in modern industrial production. The proposed method combines the global exploration capabilities of particle swarm optimization (PSO) with the local exploitation abilities of the quasi-Newton (QN) method to precisely estimate the motor and load inertias, shaft stiffness, and friction coefficients of the 2MM system. By integrating these two optimization techniques, the HPSO-QN method exhibits superior accuracy and performance compared to standard PSO algorithms. Experimental validation using a 2MM system demonstrates the effectiveness of the proposed method in accurately identifying and improving the mechanical parameters of these complex systems. The HPSO-QN method offers significant implications for enhancing the modeling, performance, and stability of 2MM systems and can be extended to other systems with flexible shafts and couplings. This study contributes to the development of accurate and effective parameter identification methods for complex systems, emphasizing the crucial role of precise parameter estimation in achieving optimal control performance and stability.

关键词： parameter identification two-mass model electric drive systems particle swarm optimization quasi-Newton method hybrid optimization stochastic algorithms mechanical parameters optimal control performance elastic joints

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stochastic Analysis of the LMS and NLMS algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第18期66卷 4753-4765页

作者： Eweda, Eweda Bershad, Neil J. Bermudez, Jose Carlos M. C4 Adv Solut Abu Dhabi 128627 U Arab Emirates Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory.

关键词： Adaptive filters analysis LMS algorithm NLMS algorithm stochastic algorithms non-Gaussian processes

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GLOBAL LINEAR CONVERGENCE OF EVOLUTION STRATEGIES ON MORE THAN SMOOTH STRONGLY CONVEX FUNCTIONS

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SIAM JOURNAL ON OPTIMIZATION 2022年第2期32卷 1402-1429页

作者： Akimoto, Youhei Auger, Anne Glasmachers, Tobias Morinaga, Daiki Univ Tsukuba Fac Engn Informat & Syst Tsukuba Ibaraki 3058571 Japan RIKEN AIP Tsukuba Ibaraki 3058571 Japan Ecole Polytech IP Paris INRIA F-91128 Paris France Ecole Polytech IP Paris CMAP F-91128 Paris France Ruhr Univ Bochum Inst Neural Computat D-44801 Bochum Germany Univ Tsukuba Dept Comp Sci Tsukuba Ibaraki 3058571 Japan

Evolution strategies (ESs) are zeroth-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMAES is nowadays recognized as one of the state-of-the-art zeroth-order optimizers for difficult problems. Despite ample empirical evidence that ESs with a step-size control mechanism converge linearly, theoretical guarantees of linear convergence of ESs have been established only on limited classes of functions. In particular, theoretical results on convex functions are missing, where zeroth-order and also first-order optimization methods are often analyzed. In this paper, we establish almost sure linear convergence and a bound on the expected hitting time of an ES family, namely, the (1+ 1)(kappa)-ES, which includes the (1+1)-ES with (generalized) one-fifth success rule and an abstract covariance matrix adaptation with bounded condition number, on a broad class of functions. The analysis holds for monotonic transformations of positively homogeneous functions and of quadratically bounded functions, the latter of which particularly includes monotonic transformation of strongly convex functions with Lipschitz continuous gradient. As far as the authors know, this is the first work that proves linear convergence of ES on such a broad class of functions.

关键词： evolution strategies randomized derivative free optimization black-box optimization linear convergence stochastic algorithms

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stochastic Methods for Solving High-Dimensional Partial Differential Equations 13th

Stochastic Methods for Solving High-Dimensional Partial Diff...

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13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC)

作者： Billaud-Friess, Marie Macherey, Arthur Nouy, Anthony Prieur, Clementine Cent Nantes LMJL UMR CNRS 6629 1 Rue Noe F-44321 Nantes France Univ Grenoble Alpes INRIA CNRS Grenoble INP Inst EngnLJK F-38000 Grenoble France

ISBN: (纸本)9783030434656;9783030434649

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms.

关键词： stochastic algorithms High dimensional PDEs Adaptive sparse interpolation

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