Table of Contents

Cover image

Title page

Copyright

About the Authors

Preface

Symbols and Abbreviations

1. Introduction

1.1 Elements of System Identification

1.2 Traditional Identification Criteria

1.3 Information Theoretic Criteria

1.4 Organization of This Book

Appendix A Unifying Framework of ITL

2. Information Measures

2.1 Entropy

2.2 Mutual Information

2.3 Information Divergence

2.4 Fisher Information

2.5 Information Rate

Appendix B -Stable Distribution

Appendix C Proof of (2.17)

Appendix D Proof of Cramer–Rao Inequality

3. Information Theoretic Parameter Estimation

3.1 Traditional Methods for Parameter Estimation

3.2 Information Theoretic Approaches to Classical Estimation

3.3 Information Theoretic Approaches to Bayes Estimation

3.4 Information Criteria for Model Selection

Appendix E: EM Algorithm

Appendix F: Minimum MSE Estimation

Appendix G: Derivation of AIC Criterion

4. System Identification Under Minimum Error Entropy Criteria

4.1 Brief Sketch of System Parameter Identification

4.2 MEE Identification Criterion

4.3 Identification Algorithms Under MEE Criterion

4.4 Convergence Analysis

4.5 Optimization of -Entropy Criterion

4.6 Survival Information Potential Criterion

4.7 Δ-Entropy Criterion

4.8 System Identification with MCC

Appendix H Vector Gradient and Matrix Gradient

5. System Identification Under Information Divergence Criteria

5.1 Parameter Identifiability Under KLID Criterion

5.2 Minimum Information Divergence Identification with Reference PDF

6. System Identification Based on Mutual Information Criteria

6.1 System Identification Under the MinMI Criterion

6.2 System Identification Under the MaxMI Criterion

Appendix I MinMI Rate Criterion

References

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