Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Basic Probability Inequalities for Sums of Independent Random Variables
- 3 Uniform Convergence and Generalization Analysis
- 4 Empirical Covering Number Analysis and Symmetrization
- 5 Covering Number Estimates
- 6 Rademacher Complexity and Concentration Inequalities
- 7 Algorithmic Stability Analysis
- 8 Model Selection
- 9 Analysis of Kernel Methods
- 10 Additive and Sparse Models
- 11 Analysis of Neural Networks
- 12 Lower Bounds and Minimax Analysis
- 13 Probability Inequalities for Sequential Random Variables
- 14 Basic Concepts of Online Learning
- 15 Online Aggregation and Second-Order Algorithms
- 16 Multiarmed Bandits
- 17 Contextual Bandits
- 18 Reinforcement Learning
- Appendix A Basics of Convex Analysis
- Appendix B f-divergence of Probability Measures
- References
- Author Index
- Subject Index
7 - Algorithmic Stability Analysis
Published online by Cambridge University Press: 20 July 2023
Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Basic Probability Inequalities for Sums of Independent Random Variables
- 3 Uniform Convergence and Generalization Analysis
- 4 Empirical Covering Number Analysis and Symmetrization
- 5 Covering Number Estimates
- 6 Rademacher Complexity and Concentration Inequalities
- 7 Algorithmic Stability Analysis
- 8 Model Selection
- 9 Analysis of Kernel Methods
- 10 Additive and Sparse Models
- 11 Analysis of Neural Networks
- 12 Lower Bounds and Minimax Analysis
- 13 Probability Inequalities for Sequential Random Variables
- 14 Basic Concepts of Online Learning
- 15 Online Aggregation and Second-Order Algorithms
- 16 Multiarmed Bandits
- 17 Contextual Bandits
- 18 Reinforcement Learning
- Appendix A Basics of Convex Analysis
- Appendix B f-divergence of Probability Measures
- References
- Author Index
- Subject Index
Summary
In practical applications, we typically solve the empirical risk minimization problem using optimization methods such as stochastic gradient descent (SGD). Such an algorithm searches a model parameter along a path that does not cover the entire model space. Therefore the empirical process analysis may not be optimal to analyze the performance of specific computational procedures. In recent years, another theoretical tool, which we may refer to as stability analysis, has been proposed to analyze such computational procedures.
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- Chapter
- Information
- Mathematical Analysis of Machine Learning Algorithms , pp. 112 - 135Publisher: Cambridge University PressPrint publication year: 2023