12693nam 22008533u 450 991056825610332120250628110030.03-030-95860-4(CKB)5680000000039096EBL6986548(OCoLC)1319038749(AU-PeEL)EBL6986548(MiAaPQ)EBC6986548(oapen)https://directory.doabooks.org/handle/20.500.12854/84390(ODN)ODN0010073057(Au-PeEL)EBL6986548(oapen)doab84390(EXLCZ)99568000000003909620250630d2022 uy 0engur|n|---|||||txtrdacontentcrdamediacrrdacarrierRegularized System Identification Learning Dynamic Models from Data1st ed.Cham Springer International Publishing AG20221 online resource (394 p.)Communications and Control Engineering Description based upon print version of record.3-030-95859-0 Intro -- Preface -- Acknowledgements -- Contents -- Abbreviations and Notation -- Notation -- Abbreviations -- 1 Bias -- 1.1 The Stein Effect -- 1.1.1 The James-Stein Estimator -- 1.1.2 Extensions of the James-Stein Estimator -- 1.2 Ridge Regression -- 1.3 Further Topics and Advanced Reading -- 1.4 Appendix: Proof of Theorem 1.1 -- References -- 2 Classical System Identification -- 2.1 The State-of-the-Art Identification Setup -- 2.2 mathcalM: Model Structures -- 2.2.1 Linear Time-Invariant Models -- 2.2.2 Nonlinear Models -- 2.3 mathcalI: Identification Methods-Criteria -- 2.3.1 A Maximum Likelihood (ML) View -- 2.4 Asymptotic Properties of the Estimated Models -- 2.4.1 Bias and Variance -- 2.4.2 Properties of the PEM Estimate as Ntoinfty -- 2.4.3 Trade-Off Between Bias and Variance -- 2.5 X: Experiment Design -- 2.6 mathcalV: Model Validation -- 2.6.1 Falsifying Models: Residual Analysis -- 2.6.2 Comparing Different Models -- 2.6.3 Cross-Validation -- References -- 3 Regularization of Linear Regression Models -- 3.1 Linear Regression -- 3.2 The Least Squares Method -- 3.2.1 Fundamentals of the Least Squares Method -- 3.2.2 Mean Squared Error and Model Order Selection -- 3.3 Ill-Conditioning -- 3.3.1 Ill-Conditioned Least Squares Problems -- 3.3.2 Ill-Conditioning in System Identification -- 3.4 Regularized Least Squares with Quadratic Penalties -- 3.4.1 Making an Ill-Conditioned LS Problem Well Conditioned -- 3.4.2 Equivalent Degrees of Freedom -- 3.5 Regularization Tuning for Quadratic Penalties -- 3.5.1 Mean Squared Error and Expected Validation Error -- 3.5.2 Efficient Sample Reuse -- 3.5.3 Expected In-Sample Validation Error -- 3.6 Regularized Least Squares with Other Types of Regularizers -- 3.6.1 ell1-Norm Regularization -- 3.6.2 Nuclear Norm Regularization -- 3.7 Further Topics and Advanced Reading -- 3.8 Appendix.3.8.1 Fundamentals of Linear Algebra -- 3.8.2 Proof of Lemma 3.1 -- 3.8.3 Derivation of Predicted Residual Error Sum of Squares (PRESS) -- 3.8.4 Proof of Theorem 3.7 -- 3.8.5 A Variant of the Expected In-Sample Validation Error and Its Unbiased Estimator -- References -- 4 Bayesian Interpretation of Regularization -- 4.1 Preliminaries -- 4.2 Incorporating Prior Knowledge via Bayesian Estimation -- 4.2.1 Multivariate Gaussian Variables -- 4.2.2 The Gaussian Case -- 4.2.3 The Linear Gaussian Model -- 4.2.4 Hierarchical Bayes: Hyperparameters -- 4.3 Bayesian Interpretation of the James-Stein Estimator -- 4.4 Full and Empirical Bayes Approaches -- 4.5 Improper Priors and the Bias Space -- 4.6 Maximum Entropy Priors -- 4.7 Model Approximation via Optimal Projection -- 4.8 Equivalent Degrees of Freedom -- 4.9 Bayesian Function Reconstruction -- 4.10 Markov Chain Monte Carlo Estimation -- 4.11 Model Selection Using Bayes Factors -- 4.12 Further Topics and Advanced Reading -- 4.13 Appendix -- 4.13.1 Proof of Theorem 4.1 -- 4.13.2 Proof of Theorem 4.2 -- 4.13.3 Proof of Lemma 4.1 -- 4.13.4 Proof of Theorem 4.3 -- 4.13.5 Proof of Theorem 4.6 -- 4.13.6 Proof of Proposition 4.3 -- 4.13.7 Proof of Theorem 4.8 -- References -- 5 Regularization for Linear System Identification -- 5.1 Preliminaries -- 5.2 MSE and Regularization -- 5.3 Optimal Regularization for FIR Models -- 5.4 Bayesian Formulation and BIBO Stability -- 5.5 Smoothness and Contractivity: Time- and Frequency-Domain Interpretations -- 5.5.1 Maximum Entropy Priors for Smoothness and Stability: From Splines to Dynamical Systems -- 5.6 Regularization and Basis Expansion -- 5.7 Hankel Nuclear Norm Regularization -- 5.8 Historical Overview -- 5.8.1 The Distributed Lag Estimator: Prior Means and Smoothing -- 5.8.2 Frequency-Domain Smoothing and Stability.5.8.3 Exponential Stability and Stochastic Embedding -- 5.9 Further Topics and Advanced Reading -- 5.10 Appendix -- 5.10.1 Optimal Kernel -- 5.10.2 Proof of Lemma 5.1 -- 5.10.3 Proof of Theorem 5.5 -- 5.10.4 Proof of Corollary 5.1 -- 5.10.5 Proof of Lemma 5.2 -- 5.10.6 Proof of Theorem 5.6 -- 5.10.7 Proof of Lemma 5.5 -- 5.10.8 Forward Representations of Stable-Splines Kernels -- References -- 6 Regularization in Reproducing Kernel Hilbert Spaces -- 6.1 Preliminaries -- 6.2 Reproducing Kernel Hilbert Spaces -- 6.2.1 Reproducing Kernel Hilbert Spaces Induced by Operations on Kernels -- 6.3 Spectral Representations of Reproducing Kernel Hilbert Spaces -- 6.3.1 More General Spectral Representation -- 6.4 Kernel-Based Regularized Estimation -- 6.4.1 Regularization in Reproducing Kernel Hilbert Spaces and the Representer Theorem -- 6.4.2 Representer Theorem Using Linear and Bounded Functionals -- 6.5 Regularization Networks and Support Vector Machines -- 6.5.1 Regularization Networks -- 6.5.2 Robust Regression via Huber Loss -- 6.5.3 Support Vector Regression -- 6.5.4 Support Vector Classification -- 6.6 Kernels Examples -- 6.6.1 Linear Kernels, Regularized Linear Regression and System Identification -- 6.6.2 Kernels Given by a Finite Number of Basis Functions -- 6.6.3 Feature Map and Feature Space -- 6.6.4 Polynomial Kernels -- 6.6.5 Translation Invariant and Radial Basis Kernels -- 6.6.6 Spline Kernels -- 6.6.7 The Bias Space and the Spline Estimator -- 6.7 Asymptotic Properties -- 6.7.1 The Regression Function/Optimal Predictor -- 6.7.2 Regularization Networks: Statistical Consistency -- 6.7.3 Connection with Statistical Learning Theory -- 6.8 Further Topics and Advanced Reading -- 6.9 Appendix -- 6.9.1 Fundamentals of Functional Analysis -- 6.9.2 Proof of Theorem 6.1 -- 6.9.3 Proof of Theorem 6.10 -- 6.9.4 Proof of Theorem 6.13.6.9.5 Proofs of Theorems 6.15 and 6.16 -- 6.9.6 Proof of Theorem 6.21 -- References -- 7 Regularization in Reproducing Kernel Hilbert Spaces for Linear System Identification -- 7.1 Regularized Linear System Identification in Reproducing Kernel Hilbert Spaces -- 7.1.1 Discrete-Time Case -- 7.1.2 Continuous-Time Case -- 7.1.3 More General Use of the Representer Theorem for Linear System Identification -- 7.1.4 Connection with Bayesian Estimation of Gaussian Processes -- 7.1.5 A Numerical Example -- 7.2 Kernel Tuning -- 7.2.1 Marginal Likelihood Maximization -- 7.2.2 Stein's Unbiased Risk Estimator -- 7.2.3 Generalized Cross-Validation -- 7.3 Theory of Stable Reproducing Kernel Hilbert Spaces -- 7.3.1 Kernel Stability: Necessary and Sufficient Conditions -- 7.3.2 Inclusions of Reproducing Kernel Hilbert Spaces in More General Lebesque Spaces -- 7.4 Further Insights into Stable Reproducing Kernel Hilbert Spaces -- 7.4.1 Inclusions Between Notable Kernel Classes -- 7.4.2 Spectral Decomposition of Stable Kernels -- 7.4.3 Mercer Representations of Stable Reproducing Kernel Hilbert Spaces and of Regularized Estimators -- 7.4.4 Necessary and Sufficient Stability Condition Using Kernel Eigenvectors and Eigenvalues -- 7.5 Minimax Properties of the Stable Spline Estimator -- 7.5.1 Data Generator and Minimax Optimality -- 7.5.2 Stable Spline Estimator -- 7.5.3 Bounds on the Estimation Error and Minimax Properties -- 7.6 Further Topics and Advanced Reading -- 7.7 Appendix -- 7.7.1 Derivation of the First-Order Stable Spline Norm -- 7.7.2 Proof of Proposition 7.1 -- 7.7.3 Proof of Theorem 7.5 -- 7.7.4 Proof of Theorem 7.7 -- 7.7.5 Proof of Theorem 7.9 -- References -- 8 Regularization for Nonlinear System Identification -- 8.1 Nonlinear System Identification -- 8.2 Kernel-Based Nonlinear System Identification.8.2.1 Connection with Bayesian Estimation of Gaussian Random Fields -- 8.2.2 Kernel Tuning -- 8.3 Kernels for Nonlinear System Identification -- 8.3.1 A Numerical Example -- 8.3.2 Limitations of the Gaussian and Polynomial Kernel -- 8.3.3 Nonlinear Stable Spline Kernel -- 8.3.4 Numerical Example Revisited: Use of the Nonlinear Stable Spline Kernel -- 8.4 Explicit Regularization of Volterra Models -- 8.5 Other Examples of Regularization in Nonlinear System Identification -- 8.5.1 Neural Networks and Deep Learning Models -- 8.5.2 Static Nonlinearities and Gaussian Process (GP) -- 8.5.3 Block-Oriented Models -- 8.5.4 Hybrid Models -- 8.5.5 Sparsity and Variable Selection -- References -- 9 Numerical Experiments and Real World Cases -- 9.1 Identification of Discrete-Time Output Error Models -- 9.1.1 Monte Carlo Studies with a Fixed Output Error Model -- 9.1.2 Monte Carlo Studies with Different Output Error Models -- 9.1.3 Real Data: A Robot Arm -- 9.1.4 Real Data: A Hairdryer -- 9.2 Identification of ARMAX Models -- 9.2.1 Monte Carlo Experiment -- 9.2.2 Real Data: Temperature Prediction -- 9.3 Multi-task Learning and Population Approaches -- 9.3.1 Kernel-Based Multi-task Learning -- 9.3.2 Numerical Example: Real Pharmacokinetic Data -- References -- Appendix Index -- Index.This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authors’ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book.Communications and Control Engineering Machine learningbicsscAutomatic control engineeringbicsscStatistical physicsbicsscBayesian inferencebicsscProbability & statisticsbicsscCybernetics & systems theorybicsscSystem IdentificationMachine LearningLinear Dynamical SystemsNonlinear Dynamical SystemsKernel-based RegularizationBayesian Interpretation of RegularizationGaussian ProcessesReproducing Kernel Hilbert SpacesEstimation TheorySupport Vector MachinesRegularization NetworksMachine learningAutomatic control engineeringStatistical physicsBayesian inferenceProbability & statisticsCybernetics & systems theoryCOM004000MAT029000MAT029010SCI055000SCI064000TEC004000bisacshPillonetto Gianluigi1231715Chen Tianshi1236794Chiuso Alessandro1236795De Nicolao Giuseppe799498Ljung Lennart28309AU-PeELAU-PeELAU-PeELBOOK9910568256103321Regularized System Identification2871538UNINA04916nam 22006735 450 991064589110332120251008133711.09783031228872303122887110.1007/978-3-031-22887-2(PPN)283729066(MiAaPQ)EBC7184746(Au-PeEL)EBL7184746(CKB)26037399200041(MiAaPQ)EBC7184723(DE-He213)978-3-031-22887-2(EXLCZ)992603739920004120230120d2023 u| 0engurcz#---auuuutxtrdacontentcrdamediacrrdacarrierAfrica’s Right to Development in a Climate-Constrained World /by Kennedy Mbeva, Reuben Makomere, Joanes Atela, Victoria Chengo, Charles Tonui1st ed. 2023.Cham :Springer International Publishing :Imprint: Palgrave Macmillan,2023.1 online resource (320 pages)Contemporary African Political Economy,2945-736XPrint version: Mbeva, Kennedy Africa's Right to Development in a Climate-Constrained World Cham : Springer International Publishing AG,c2023 9783031228865 Includes bibliographical references and index.Chapter 1: Introduction -- Chapter 2: The Great Climate Transformation -- Chapter 3: Shift in Global Climate Discourse -- Chapter 4: The Evolving Geopolitics of Climate Change -- Chapter 5: Dynamic Differentiation -- Chapter 6: The Rise of Non-state Actors -- Chapter 7: Emergent Climate-related Policy Issues -- Chapter 8: Governing Complexity -- Chapter 9: Conclusion.“This book, written by promising African scholars, provides important policy lessons on securing a ‘just transition’ towards a low-carbon and climate-resilient society in Africa, and to the realisation of the African Union Agenda 2063” - Dr Ibrahim Assane Mayaki, former Prime Minister of Niger, and former CEO, African Union Development Agency-NEPAD (AUDA-NEPAD) “An important contribution to scholarship on International Relations and African Politics, this book offers a solid and well-grounded treatment of how Africa can best achieve sustainable economic development while also taking ambitious action on climate change” - Professor Chukwumerije Okereke, Director of the Center for Climate Change and Development, Alex Ekwueme Federal University Nigeria “By focusing on the need to balance climate and development goals in Africa, the authors fill a conspicuous knowledge gap on the reality that transition pathways for countries in the Global South will look very different to those in the Global North” - Dr Zainab Usman, Senior Fellow and Director, Africa Program, Carnegie Endowment for International Peace “This book presents a bold new vision for African agency and leadership in a changing climate. It shows how a proactive strategy offers African countries the clearest path to development in a world shaped by climate change” - Prof Thomas Hale, Associate Professor in Public Policy (Global Public Policy), Blavatnik School of Government, University of Oxford “The authors have done a timely and excellent job in articulating a ‘just transition’ from an African perspective” - Dr Bhim Adhikari (PhD), Senior Environmental Economist, Canada's International Development Research Centre (IDRC) This book examines how Africa can secure a ‘just transition’ to low-carbon, climate-resilient economies. Kennedy Mbeva is a Postdoctoral Research Associate at the Blavatnik School of Government, Universityof Oxford Reuben Makomere is a Research Associate at the Africa Research and Impact Network (ARIN) Joanes Atela is the Convenor of the Africa Research and Impact Network (ARIN) Victoria Chengo is a Research Fellow at the Africa Research and Impact Network (ARIN) Charles Tonui is the Policy Convenor at the Africa Research and Impact Network (ARIN).Contemporary African Political Economy,2945-736XAfricaPolitics and governmentPolitical scienceRegionalismEconomic developmentAfrican PoliticsPolitical ScienceRegionalismDevelopment StudiesAfricaPolitics and government.Political science.Regionalism.Economic development.African Politics.Political Science.Regionalism.Development Studies.363.738746338.9607Mbeva Kennedy1275744MiAaPQMiAaPQMiAaPQBOOK9910645891103321Africa's Right to Development in a Climate-Constrained World3006310UNINA