Stochastic Optimization for Large-scale Machine Learning
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Stochastic Optimization for Large-scale Machine Learning
Chauhan, Vinod Kumar
Taylor & Francis Ltd
10/2024
158
Mole
9781032146140
Pré-lançamento - envio 15 a 20 dias após a sua edição
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List of Figures
List of Tables
Preface
Section I BACKGROUND
Introduction
1.1 LARGE-SCALE MACHINE LEARNING
1.2 OPTIMIZATION PROBLEMS
1.3 LINEAR CLASSIFICATION
1.3.1 Support Vector Machine (SVM)
1.3.2 Logistic Regression
1.3.3 First and Second Order Methods
1.3.3.1 First Order Methods
1.3.3.2 Second Order Methods
1.4 STOCHASTIC APPROXIMATION APPROACH
1.5 COORDINATE DESCENT APPROACH
1.6 DATASETS
1.7 ORGANIZATION OF BOOK
Optimisation Problem, Solvers, Challenges and Research Directions
2.1 INTRODUCTION
2.1.1 Contributions
2.2 LITERATURE
2.3 PROBLEM FORMULATIONS
2.3.1 Hard Margin SVM (1992)
2.3.2 Soft Margin SVM (1995)
2.3.3 One-versus-Rest (1998)
2.3.4 One-versus-One (1999)
2.3.5 Least Squares SVM (1999)
2.3.6 v-SVM (2000)
2.3.7 Smooth SVM (2001)
2.3.8 Proximal SVM (2001)
2.3.9 Crammer Singer SVM (2002)
2.3.10 Ev-SVM (2003)
2.3.11 Twin SVM (2007)
2.3.12 Capped lp-norm SVM (2017)
2.4 PROBLEM SOLVERS
2.4.1 Exact Line Search Method
2.4.2 Backtracking Line Search
2.4.3 Constant Step Size
2.4.4 Lipschitz & Strong Convexity Constants
2.4.5 Trust Region Method
2.4.6 Gradient Descent Method
2.4.7 Newton Method
2.4.8 Gauss-Newton Method
2.4.9 Levenberg-Marquardt Method
2.4.10 Quasi-Newton Method
2.4.11 Subgradient Method
2.4.12 Conjugate Gradient Method
2.4.13 Truncated Newton Method
2.4.14 Proximal Gradient Method
2.4.15 Recent Algorithms
2.5 COMPARATIVE STUDY
2.5.1 Results from Literature
2.5.2 Results from Experimental Study
2.5.2.1 Experimental Setup and Implementation Details
2.5.2.2 Results and Discussions
2.6 CURRENT CHALLENGES AND RESEARCH DIRECTIONS
2.6.1 Big Data Challenge
2.6.2 Areas of Improvement
2.6.2.1 Problem Formulations
2.6.2.2 Problem Solvers
2.6.2.3 Problem Solving Strategies/Approaches
2.6.2.4 Platforms/Frameworks
2.6.3 Research Directions
2.6.3.1 Stochastic Approximation Algorithms
2.6.3.2 Coordinate Descent Algorithms
2.6.3.3 Proximal Algorithms
2.6.3.4 Parallel/Distributed Algorithms
2.6.3.5 Hybrid Algorithms
2.7 CONCLUSION
Section II FIRST ORDER METHODS
Mini-batch and Block-coordinate Approach
3.1 INTRODUCTION
3.1.1 Motivation
3.1.2 Batch Block Optimization Framework (BBOF)
3.1.3 Brief Literature Review
3.1.4 Contributions
3.2 STOCHASTIC AVERAGE ADJUSTED GRADIENT (SAAG) METHODS
3.3 ANALYSIS
3.4 NUMERICAL EXPERIMENTS
3.4.1 Experimental setup
3.4.2 Convergence against epochs
3.4.3 Convergence against Time
3.5 CONCLUSION AND FUTURE SCOPE
Variance Reduction Methods
4.1 INTRODUCTION
4.1.1 Optimization Problem
4.1.2 Solution Techniques for Optimization Problem
4.1.3 Contributions
4.2 NOTATIONS AND RELATED WORK
4.2.1 Notations
4.2.2 Related Work
4.3 SAAG-I, II AND PROXIMAL EXTENSIONS
4.4 SAAG-III AND IV ALGORITHMS
4.5 ANALYSIS
4.6 EXPERIMENTAL RESULTS
4.6.1 Experimental Setup
4.6.2 Results with Smooth Problem
4.6.3 Results with non-smooth Problem
4.6.4 Mini-batch Block-coordinate versus mini-batch setting
4.6.5 Results with SVM
4.7 CONCLUSION
Learning and Data Access
5.1 INTRODUCTION
5.1.1 Optimization Problem
5.1.2 Literature Review
5.1.3 Contributions
5.2 SYSTEMATIC SAMPLING
5.2.1 Definitions
5.2.2 Learning using Systematic Sampling
5.3 ANALYSIS
5.4 EXPERIMENTS
5.4.1 Experimental Setup
5.4.2 Implementation Details
5.4.3 Results
5.5 CONCLUSION
Section III SECOND ORDER METHODS
Mini-batch Block-coordinate Newton Method
6.1 INTRODUCTION
6.1.1 Contributions
6.2 MBN
6.3 EXPERIMENTS
6.3.1 Experimental Setup
6.3.2 Comparative Study
6.4 CONCLUSION
Stochastic Trust Region Inexact Newton Method
7.1 INTRODUCTION
7.1.1 Optimization Problem
7.1.2 Solution Techniques
7.1.3 Contributions
7.2 LITERATURE REVIEW
7.3 TRUST REGION INEXACT NEWTON METHOD
7.3.1 Inexact Newton Method
7.3.2 Trust Region Inexact Newton Method
7.4 STRON
7.4.1 Complexity
7.4.2 Analysis
7.5 EXPERIMENTAL RESULTS
7.5.1 Experimental Setup
7.5.2 Comparative Study
7.5.3 Results with SVM
7.6 EXTENSIONS
7.6.1 PCG Subproblem Solver 1
7.6.2 Stochastic Variance Reduced Trust Region Inexact Newton Method
7.7 CONCLUSION
Section IV CONCLUSION
Conclusion and Future Scope
8.1 FUTURE SCOPE 142
Bibliography
Index
List of Tables
Preface
Section I BACKGROUND
Introduction
1.1 LARGE-SCALE MACHINE LEARNING
1.2 OPTIMIZATION PROBLEMS
1.3 LINEAR CLASSIFICATION
1.3.1 Support Vector Machine (SVM)
1.3.2 Logistic Regression
1.3.3 First and Second Order Methods
1.3.3.1 First Order Methods
1.3.3.2 Second Order Methods
1.4 STOCHASTIC APPROXIMATION APPROACH
1.5 COORDINATE DESCENT APPROACH
1.6 DATASETS
1.7 ORGANIZATION OF BOOK
Optimisation Problem, Solvers, Challenges and Research Directions
2.1 INTRODUCTION
2.1.1 Contributions
2.2 LITERATURE
2.3 PROBLEM FORMULATIONS
2.3.1 Hard Margin SVM (1992)
2.3.2 Soft Margin SVM (1995)
2.3.3 One-versus-Rest (1998)
2.3.4 One-versus-One (1999)
2.3.5 Least Squares SVM (1999)
2.3.6 v-SVM (2000)
2.3.7 Smooth SVM (2001)
2.3.8 Proximal SVM (2001)
2.3.9 Crammer Singer SVM (2002)
2.3.10 Ev-SVM (2003)
2.3.11 Twin SVM (2007)
2.3.12 Capped lp-norm SVM (2017)
2.4 PROBLEM SOLVERS
2.4.1 Exact Line Search Method
2.4.2 Backtracking Line Search
2.4.3 Constant Step Size
2.4.4 Lipschitz & Strong Convexity Constants
2.4.5 Trust Region Method
2.4.6 Gradient Descent Method
2.4.7 Newton Method
2.4.8 Gauss-Newton Method
2.4.9 Levenberg-Marquardt Method
2.4.10 Quasi-Newton Method
2.4.11 Subgradient Method
2.4.12 Conjugate Gradient Method
2.4.13 Truncated Newton Method
2.4.14 Proximal Gradient Method
2.4.15 Recent Algorithms
2.5 COMPARATIVE STUDY
2.5.1 Results from Literature
2.5.2 Results from Experimental Study
2.5.2.1 Experimental Setup and Implementation Details
2.5.2.2 Results and Discussions
2.6 CURRENT CHALLENGES AND RESEARCH DIRECTIONS
2.6.1 Big Data Challenge
2.6.2 Areas of Improvement
2.6.2.1 Problem Formulations
2.6.2.2 Problem Solvers
2.6.2.3 Problem Solving Strategies/Approaches
2.6.2.4 Platforms/Frameworks
2.6.3 Research Directions
2.6.3.1 Stochastic Approximation Algorithms
2.6.3.2 Coordinate Descent Algorithms
2.6.3.3 Proximal Algorithms
2.6.3.4 Parallel/Distributed Algorithms
2.6.3.5 Hybrid Algorithms
2.7 CONCLUSION
Section II FIRST ORDER METHODS
Mini-batch and Block-coordinate Approach
3.1 INTRODUCTION
3.1.1 Motivation
3.1.2 Batch Block Optimization Framework (BBOF)
3.1.3 Brief Literature Review
3.1.4 Contributions
3.2 STOCHASTIC AVERAGE ADJUSTED GRADIENT (SAAG) METHODS
3.3 ANALYSIS
3.4 NUMERICAL EXPERIMENTS
3.4.1 Experimental setup
3.4.2 Convergence against epochs
3.4.3 Convergence against Time
3.5 CONCLUSION AND FUTURE SCOPE
Variance Reduction Methods
4.1 INTRODUCTION
4.1.1 Optimization Problem
4.1.2 Solution Techniques for Optimization Problem
4.1.3 Contributions
4.2 NOTATIONS AND RELATED WORK
4.2.1 Notations
4.2.2 Related Work
4.3 SAAG-I, II AND PROXIMAL EXTENSIONS
4.4 SAAG-III AND IV ALGORITHMS
4.5 ANALYSIS
4.6 EXPERIMENTAL RESULTS
4.6.1 Experimental Setup
4.6.2 Results with Smooth Problem
4.6.3 Results with non-smooth Problem
4.6.4 Mini-batch Block-coordinate versus mini-batch setting
4.6.5 Results with SVM
4.7 CONCLUSION
Learning and Data Access
5.1 INTRODUCTION
5.1.1 Optimization Problem
5.1.2 Literature Review
5.1.3 Contributions
5.2 SYSTEMATIC SAMPLING
5.2.1 Definitions
5.2.2 Learning using Systematic Sampling
5.3 ANALYSIS
5.4 EXPERIMENTS
5.4.1 Experimental Setup
5.4.2 Implementation Details
5.4.3 Results
5.5 CONCLUSION
Section III SECOND ORDER METHODS
Mini-batch Block-coordinate Newton Method
6.1 INTRODUCTION
6.1.1 Contributions
6.2 MBN
6.3 EXPERIMENTS
6.3.1 Experimental Setup
6.3.2 Comparative Study
6.4 CONCLUSION
Stochastic Trust Region Inexact Newton Method
7.1 INTRODUCTION
7.1.1 Optimization Problem
7.1.2 Solution Techniques
7.1.3 Contributions
7.2 LITERATURE REVIEW
7.3 TRUST REGION INEXACT NEWTON METHOD
7.3.1 Inexact Newton Method
7.3.2 Trust Region Inexact Newton Method
7.4 STRON
7.4.1 Complexity
7.4.2 Analysis
7.5 EXPERIMENTAL RESULTS
7.5.1 Experimental Setup
7.5.2 Comparative Study
7.5.3 Results with SVM
7.6 EXTENSIONS
7.6.1 PCG Subproblem Solver 1
7.6.2 Stochastic Variance Reduced Trust Region Inexact Newton Method
7.7 CONCLUSION
Section IV CONCLUSION
Conclusion and Future Scope
8.1 FUTURE SCOPE 142
Bibliography
Index
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Trust Region Subproblem;machine learning;Big Data Problems;stochasitc optimization;Backtracking Line Search;Big Data;Cd;algorithms;Stochastic Approximation Approach;TRON Method;Newton Method;Trust Region Radius;Linear SVM;Constant Step Size;Non-linear SVMs;Variance Reduction Techniques;Variance Reduction;Proximal SVM;Inexact Newton Method;Saga;Fuzzy SVM;CS;SVM Problem;Subproblem Solver;Data Access Time;L2 Loss Function;Soft Margin SVM;Hessian Vector Products;Multi-class Data
List of Figures
List of Tables
Preface
Section I BACKGROUND
Introduction
1.1 LARGE-SCALE MACHINE LEARNING
1.2 OPTIMIZATION PROBLEMS
1.3 LINEAR CLASSIFICATION
1.3.1 Support Vector Machine (SVM)
1.3.2 Logistic Regression
1.3.3 First and Second Order Methods
1.3.3.1 First Order Methods
1.3.3.2 Second Order Methods
1.4 STOCHASTIC APPROXIMATION APPROACH
1.5 COORDINATE DESCENT APPROACH
1.6 DATASETS
1.7 ORGANIZATION OF BOOK
Optimisation Problem, Solvers, Challenges and Research Directions
2.1 INTRODUCTION
2.1.1 Contributions
2.2 LITERATURE
2.3 PROBLEM FORMULATIONS
2.3.1 Hard Margin SVM (1992)
2.3.2 Soft Margin SVM (1995)
2.3.3 One-versus-Rest (1998)
2.3.4 One-versus-One (1999)
2.3.5 Least Squares SVM (1999)
2.3.6 v-SVM (2000)
2.3.7 Smooth SVM (2001)
2.3.8 Proximal SVM (2001)
2.3.9 Crammer Singer SVM (2002)
2.3.10 Ev-SVM (2003)
2.3.11 Twin SVM (2007)
2.3.12 Capped lp-norm SVM (2017)
2.4 PROBLEM SOLVERS
2.4.1 Exact Line Search Method
2.4.2 Backtracking Line Search
2.4.3 Constant Step Size
2.4.4 Lipschitz & Strong Convexity Constants
2.4.5 Trust Region Method
2.4.6 Gradient Descent Method
2.4.7 Newton Method
2.4.8 Gauss-Newton Method
2.4.9 Levenberg-Marquardt Method
2.4.10 Quasi-Newton Method
2.4.11 Subgradient Method
2.4.12 Conjugate Gradient Method
2.4.13 Truncated Newton Method
2.4.14 Proximal Gradient Method
2.4.15 Recent Algorithms
2.5 COMPARATIVE STUDY
2.5.1 Results from Literature
2.5.2 Results from Experimental Study
2.5.2.1 Experimental Setup and Implementation Details
2.5.2.2 Results and Discussions
2.6 CURRENT CHALLENGES AND RESEARCH DIRECTIONS
2.6.1 Big Data Challenge
2.6.2 Areas of Improvement
2.6.2.1 Problem Formulations
2.6.2.2 Problem Solvers
2.6.2.3 Problem Solving Strategies/Approaches
2.6.2.4 Platforms/Frameworks
2.6.3 Research Directions
2.6.3.1 Stochastic Approximation Algorithms
2.6.3.2 Coordinate Descent Algorithms
2.6.3.3 Proximal Algorithms
2.6.3.4 Parallel/Distributed Algorithms
2.6.3.5 Hybrid Algorithms
2.7 CONCLUSION
Section II FIRST ORDER METHODS
Mini-batch and Block-coordinate Approach
3.1 INTRODUCTION
3.1.1 Motivation
3.1.2 Batch Block Optimization Framework (BBOF)
3.1.3 Brief Literature Review
3.1.4 Contributions
3.2 STOCHASTIC AVERAGE ADJUSTED GRADIENT (SAAG) METHODS
3.3 ANALYSIS
3.4 NUMERICAL EXPERIMENTS
3.4.1 Experimental setup
3.4.2 Convergence against epochs
3.4.3 Convergence against Time
3.5 CONCLUSION AND FUTURE SCOPE
Variance Reduction Methods
4.1 INTRODUCTION
4.1.1 Optimization Problem
4.1.2 Solution Techniques for Optimization Problem
4.1.3 Contributions
4.2 NOTATIONS AND RELATED WORK
4.2.1 Notations
4.2.2 Related Work
4.3 SAAG-I, II AND PROXIMAL EXTENSIONS
4.4 SAAG-III AND IV ALGORITHMS
4.5 ANALYSIS
4.6 EXPERIMENTAL RESULTS
4.6.1 Experimental Setup
4.6.2 Results with Smooth Problem
4.6.3 Results with non-smooth Problem
4.6.4 Mini-batch Block-coordinate versus mini-batch setting
4.6.5 Results with SVM
4.7 CONCLUSION
Learning and Data Access
5.1 INTRODUCTION
5.1.1 Optimization Problem
5.1.2 Literature Review
5.1.3 Contributions
5.2 SYSTEMATIC SAMPLING
5.2.1 Definitions
5.2.2 Learning using Systematic Sampling
5.3 ANALYSIS
5.4 EXPERIMENTS
5.4.1 Experimental Setup
5.4.2 Implementation Details
5.4.3 Results
5.5 CONCLUSION
Section III SECOND ORDER METHODS
Mini-batch Block-coordinate Newton Method
6.1 INTRODUCTION
6.1.1 Contributions
6.2 MBN
6.3 EXPERIMENTS
6.3.1 Experimental Setup
6.3.2 Comparative Study
6.4 CONCLUSION
Stochastic Trust Region Inexact Newton Method
7.1 INTRODUCTION
7.1.1 Optimization Problem
7.1.2 Solution Techniques
7.1.3 Contributions
7.2 LITERATURE REVIEW
7.3 TRUST REGION INEXACT NEWTON METHOD
7.3.1 Inexact Newton Method
7.3.2 Trust Region Inexact Newton Method
7.4 STRON
7.4.1 Complexity
7.4.2 Analysis
7.5 EXPERIMENTAL RESULTS
7.5.1 Experimental Setup
7.5.2 Comparative Study
7.5.3 Results with SVM
7.6 EXTENSIONS
7.6.1 PCG Subproblem Solver 1
7.6.2 Stochastic Variance Reduced Trust Region Inexact Newton Method
7.7 CONCLUSION
Section IV CONCLUSION
Conclusion and Future Scope
8.1 FUTURE SCOPE 142
Bibliography
Index
List of Tables
Preface
Section I BACKGROUND
Introduction
1.1 LARGE-SCALE MACHINE LEARNING
1.2 OPTIMIZATION PROBLEMS
1.3 LINEAR CLASSIFICATION
1.3.1 Support Vector Machine (SVM)
1.3.2 Logistic Regression
1.3.3 First and Second Order Methods
1.3.3.1 First Order Methods
1.3.3.2 Second Order Methods
1.4 STOCHASTIC APPROXIMATION APPROACH
1.5 COORDINATE DESCENT APPROACH
1.6 DATASETS
1.7 ORGANIZATION OF BOOK
Optimisation Problem, Solvers, Challenges and Research Directions
2.1 INTRODUCTION
2.1.1 Contributions
2.2 LITERATURE
2.3 PROBLEM FORMULATIONS
2.3.1 Hard Margin SVM (1992)
2.3.2 Soft Margin SVM (1995)
2.3.3 One-versus-Rest (1998)
2.3.4 One-versus-One (1999)
2.3.5 Least Squares SVM (1999)
2.3.6 v-SVM (2000)
2.3.7 Smooth SVM (2001)
2.3.8 Proximal SVM (2001)
2.3.9 Crammer Singer SVM (2002)
2.3.10 Ev-SVM (2003)
2.3.11 Twin SVM (2007)
2.3.12 Capped lp-norm SVM (2017)
2.4 PROBLEM SOLVERS
2.4.1 Exact Line Search Method
2.4.2 Backtracking Line Search
2.4.3 Constant Step Size
2.4.4 Lipschitz & Strong Convexity Constants
2.4.5 Trust Region Method
2.4.6 Gradient Descent Method
2.4.7 Newton Method
2.4.8 Gauss-Newton Method
2.4.9 Levenberg-Marquardt Method
2.4.10 Quasi-Newton Method
2.4.11 Subgradient Method
2.4.12 Conjugate Gradient Method
2.4.13 Truncated Newton Method
2.4.14 Proximal Gradient Method
2.4.15 Recent Algorithms
2.5 COMPARATIVE STUDY
2.5.1 Results from Literature
2.5.2 Results from Experimental Study
2.5.2.1 Experimental Setup and Implementation Details
2.5.2.2 Results and Discussions
2.6 CURRENT CHALLENGES AND RESEARCH DIRECTIONS
2.6.1 Big Data Challenge
2.6.2 Areas of Improvement
2.6.2.1 Problem Formulations
2.6.2.2 Problem Solvers
2.6.2.3 Problem Solving Strategies/Approaches
2.6.2.4 Platforms/Frameworks
2.6.3 Research Directions
2.6.3.1 Stochastic Approximation Algorithms
2.6.3.2 Coordinate Descent Algorithms
2.6.3.3 Proximal Algorithms
2.6.3.4 Parallel/Distributed Algorithms
2.6.3.5 Hybrid Algorithms
2.7 CONCLUSION
Section II FIRST ORDER METHODS
Mini-batch and Block-coordinate Approach
3.1 INTRODUCTION
3.1.1 Motivation
3.1.2 Batch Block Optimization Framework (BBOF)
3.1.3 Brief Literature Review
3.1.4 Contributions
3.2 STOCHASTIC AVERAGE ADJUSTED GRADIENT (SAAG) METHODS
3.3 ANALYSIS
3.4 NUMERICAL EXPERIMENTS
3.4.1 Experimental setup
3.4.2 Convergence against epochs
3.4.3 Convergence against Time
3.5 CONCLUSION AND FUTURE SCOPE
Variance Reduction Methods
4.1 INTRODUCTION
4.1.1 Optimization Problem
4.1.2 Solution Techniques for Optimization Problem
4.1.3 Contributions
4.2 NOTATIONS AND RELATED WORK
4.2.1 Notations
4.2.2 Related Work
4.3 SAAG-I, II AND PROXIMAL EXTENSIONS
4.4 SAAG-III AND IV ALGORITHMS
4.5 ANALYSIS
4.6 EXPERIMENTAL RESULTS
4.6.1 Experimental Setup
4.6.2 Results with Smooth Problem
4.6.3 Results with non-smooth Problem
4.6.4 Mini-batch Block-coordinate versus mini-batch setting
4.6.5 Results with SVM
4.7 CONCLUSION
Learning and Data Access
5.1 INTRODUCTION
5.1.1 Optimization Problem
5.1.2 Literature Review
5.1.3 Contributions
5.2 SYSTEMATIC SAMPLING
5.2.1 Definitions
5.2.2 Learning using Systematic Sampling
5.3 ANALYSIS
5.4 EXPERIMENTS
5.4.1 Experimental Setup
5.4.2 Implementation Details
5.4.3 Results
5.5 CONCLUSION
Section III SECOND ORDER METHODS
Mini-batch Block-coordinate Newton Method
6.1 INTRODUCTION
6.1.1 Contributions
6.2 MBN
6.3 EXPERIMENTS
6.3.1 Experimental Setup
6.3.2 Comparative Study
6.4 CONCLUSION
Stochastic Trust Region Inexact Newton Method
7.1 INTRODUCTION
7.1.1 Optimization Problem
7.1.2 Solution Techniques
7.1.3 Contributions
7.2 LITERATURE REVIEW
7.3 TRUST REGION INEXACT NEWTON METHOD
7.3.1 Inexact Newton Method
7.3.2 Trust Region Inexact Newton Method
7.4 STRON
7.4.1 Complexity
7.4.2 Analysis
7.5 EXPERIMENTAL RESULTS
7.5.1 Experimental Setup
7.5.2 Comparative Study
7.5.3 Results with SVM
7.6 EXTENSIONS
7.6.1 PCG Subproblem Solver 1
7.6.2 Stochastic Variance Reduced Trust Region Inexact Newton Method
7.7 CONCLUSION
Section IV CONCLUSION
Conclusion and Future Scope
8.1 FUTURE SCOPE 142
Bibliography
Index
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Trust Region Subproblem;machine learning;Big Data Problems;stochasitc optimization;Backtracking Line Search;Big Data;Cd;algorithms;Stochastic Approximation Approach;TRON Method;Newton Method;Trust Region Radius;Linear SVM;Constant Step Size;Non-linear SVMs;Variance Reduction Techniques;Variance Reduction;Proximal SVM;Inexact Newton Method;Saga;Fuzzy SVM;CS;SVM Problem;Subproblem Solver;Data Access Time;L2 Loss Function;Soft Margin SVM;Hessian Vector Products;Multi-class Data
