دانلود کتاب Statistical Machine Learning: A Unified Framework (Chapman & Hall/CRC Texts in Statistical Science)

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Title Page
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Contents
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Preface
Part I: Inference and Learning Machines
1. A Statistical Machine Learning Framework
1.1 Statistical Machine Learning: A Brief Overview
1.2 Machine Learning Environments
1.2.1 Feature Vectors
1.2.1.1 Feature Vector Representations
1.2.1.2 The Curse of Feature Vector Dimensionality
1.2.1.3 Feature Vector Engineering Methods
1.2.2 Stationary Statistical Environments
1.2.3 Strategies for Teaching Machine Learning Algorithms
1.2.4 Prior Knowledge
1.2.4.1 Feature Maps Specify Relevant Statistical Regularities
1.2.4.2 Similar Inputs Predict Similar Responses
1.2.4.3 Only a Small Number of Model Parameters Are Relevant
1.2.4.4 Different Feature Detectors Share Parameters
1.3 Empirical Risk Minimization Framework
1.3.1 ANN Graphical Notation
1.3.2 Risk Functions
1.3.3 Regularization Terms
1.3.4 Optimization Methods
1.3.4.1 Batch Gradient Descent Learning
1.3.4.2 Adaptive Gradient Descent Learning
1.4 Theory-Based System Analysis and Design
1.4.1 Stage 1: System Specification
1.4.2 Stage 2: Theoretical Analyses
1.4.3 Stage 3: Physical Implementation
1.4.4 Stage 4: System Behavior Evaluation
1.5 Supervised Learning Machines
1.5.1 Discrepancy Functions
1.5.2 Basis Functions and Hidden Units
1.5.3 Recurrent Neural Networks (RNNs)
1.6 Unsupervised Learning Machines
1.7 Reinforcement Learning Machines
1.7.1 Reinforcement Learning Overview
1.7.2 Value Function Reinforcement Passive Learning
1.7.3 Policy Gradient Reinforcement Reactive Learning
1.8 Further Readings
2. Set Theory for Concept Modeling
2.1 Set Theory and Logic
2.2 Relations
2.2.1 Types of Relations
2.2.2 Directed Graphs
2.2.3 Undirected Graphs
2.3 Functions
2.4 Metric Spaces
2.5 Further Readings
3. Formal Machine Learning Algorithms
3.1 Environment Models
3.1.1 Time Models
3.1.2 Event Environments
3.2 Machine Models
3.2.1 Dynamical Systems
3.2.2 Iterated Maps
3.2.3 Vector Fields
3.3 Intelligent Machine Models
3.4 Further Readings
Part II: Deterministic Learning Machines
4. Linear Algebra for Machine Learning
4.1 Matrix Notation and Operators
4.2 Linear Subspace Projection Theorems
4.3 Linear System Solution Theorems
4.4 Further Readings
5. Matrix Calculus for Machine Learning
5.1 Convergence and Continuity
5.1.1 Deterministic Convergence
5.1.2 Continuous Functions
5.2 Vector Derivatives
5.2.1 Vector Derivative Definitions
5.2.2 Theorems for Computing Matrix Derivatives
5.2.3 Useful Derivative Calculations for Deep Learning
5.2.4 Gradient Backpropagation for Deep Learning
5.3 Objective Function Analysis
5.3.1 Taylor Series Expansions
5.3.2 Gradient Descent Type Algorithms
5.3.3 Critical Point Classification
5.3.3.1 Identifying Critical Points
5.3.3.2 Identifying Flat Regions
5.3.3.3 Identifying Local Minimizers
5.3.3.4 Identifying Saddlepoints
5.3.3.5 Identifying Global Minimizers
5.3.4 Lagrange Multipliers
5.4 Further Readings
6. Convergence of Time-Invariant Dynamical Systems
6.1 Dynamical System Existence Theorems
6.2 Invariant Sets
6.3 Lyapunov Convergence Theorems
6.3.1 Lyapunov Functions
6.3.2 Invariant Set Theorems
6.3.2.1 Finite State Space Convergence Analyses
6.3.2.2 Continuous State Space Convergence Analyses
6.4 Further Readings
7. Batch Learning Algorithm Convergence
7.1 Search Direction and Stepsize Choices
7.1.1 Search Direction Selection
7.1.2 Stepsize Selection
7.2 Descent Algorithm Convergence Analysis
7.3 Descent Strategies
7.3.1 Gradient and Steepest Descent
7.3.2 Newton-Type Descent
7.3.2.1 Newton-Raphson Algorithm
7.3.2.2 Levenberg-Marquardt Algorithm
7.3.3 L-BFGS and Conjugate Gradient Descent Methods
7.4 Further Readings
Part III: Stochastic Learning Machines
8. Random Vectors and Random Functions
8.1 Probability Spaces
8.1.1 Sigma-Fields
8.1.2 Measures
8.2 Random Vectors
8.2.1 Measurable Functions
8.2.2 Discrete, Continuous, and Mixed Random Vectors
8.3 Existence of the Radon-Nikodým Density (Optional Reading)
8.3.1 Lebesgue Integral
8.3.2 The Radon-Nikod ym Probability Density Function
8.3.3 Vector Support Specification Measures
8.4 Expectation Operations
8.4.1 Random Functions
8.4.2 Expectations of Random Functions
8.4.3 Conditional Expectation and Independence
8.5 Concentration Inequalities
8.6 Further Readings
9. Stochastic Sequences
9.1 Types of Stochastic Sequences
9.2 Partially Observable Stochastic Sequences
9.3 Stochastic Convergence
9.3.1 Convergence with Probability One
9.3.2 Convergence in Mean Square
9.3.3 Convergence in Probability
9.3.4 Convergence in Distribution
9.3.5 Stochastic Convergence Relationships
9.4 Combining and Transforming Stochastic Sequences
9.5 Further Readings
10. Probability Models of Data Generation
10.1 Learnability of Probability Models
10.1.1 Correctly Specified and Misspecified Models
10.1.2 Smooth Parametric Probability Models
10.1.3 Local Probability Models
10.1.4 Missing-Data Probability Models
10.2 Gibbs Probability Models
10.3 Bayesian Networks
10.3.1 Factoring a Chain
10.3.2 Bayesian Network Factorization
10.4 Markov Random Fields
10.4.1 The Markov Random Field Concept
10.4.2 MRF Interpretation of Gibbs Distributions
10.5 Further Readings
11. Monte Carlo Markov Chain Algorithm Convergence
11.1 Monte Carlo Markov Chain (MCMC) Algorithms
11.1.1 Countably Infinite First-Order Chains on Finite State Spaces
11.1.2 Convergence Analysis of Monte Carlo Markov Chains
11.1.3 Hybrid MCMC Algorithms
11.1.4 Finding Global Minimizers and Computing Expectations
11.1.5 Assessing and Improving MCMC Convergence Performance
11.1.5.1 Assessing Convergence for Expectation Approximation
11.1.5.2 MCMC Convergence Challenges and Heuristics
11.2 MCMC Metropolis-Hastings (MH) Algorithms
11.2.1 Metropolis-Hastings Algorithm Definition
11.2.2 Convergence Analysis of Metropolis-Hastings Algorithms
11.2.3 Important Special Cases of the Metropolis-Hastings Algorithm
11.2.4 Metropolis-Hastings Machine Learning Applications
11.3 Further Readings
12. Adaptive Learning Algorithm Convergence
12.1 Stochastic Approximation (SA) Theory
12.1.1 Passive versus Reactive Statistical Environments
12.1.1.1 Passive Learning Environments
12.1.1.2 Reactive Learning Environments
12.1.2 Average Downward Descent
12.1.3 Annealing Schedule
12.1.4 The Main Stochastic Approximation Theorem
12.1.5 Assessing Stochastic Approximation Algorithm Convergence
12.2 Learning in Passive Statistical Environments Using SA
12.2.1 Implementing Different Optimization Strategies
12.2.2 Improving Generalization Performance
12.3 Learning in Reactive Statistical Environments Using SA
12.3.1 Policy Gradient Reinforcement Learning
12.3.2 Stochastic Approximation Expectation Maximization
12.3.3 Markov Random Field Learning (Contrastive Divergence)
12.3.4 Generative Adversarial Network (GAN) Learning
12.4 Further Readings
Part IV: Generalization Performance
13. Statistical Learning Objective Function Design
13.1 Empirical Risk Function
13.2 Maximum Likelihood (ML) Estimation Methods
13.2.1 ML Estimation: Probability Theory Interpretation
13.2.2 ML Estimation: Information Theory Interpretation
13.2.2.1 Entropy
13.2.2.2 Cross-Entropy Minimization: ML Estimation
13.2.3 Properties of Cross-Entropy Global Minimizers
13.2.4 Pseudolikelihood Empirical Risk Function
13.2.5 Missing-Data Likelihood Empirical Risk Function
13.3 Maximum a Posteriori (MAP) Estimation Methods
13.3.1 Parameter Priors and Hyperparameters
13.3.2 Maximum a Posteriori (MAP) Risk Function
13.3.3 Bayes Risk Interpretation of MAP Estimation
13.4 Further Readings
14. Simulation Methods for Evaluating Generalization
14.1 Sampling Distribution Concepts
14.1.1 K-Fold Cross-Validation
14.1.2 Sampling Distribution Estimation with Unlimited Data
14.2 Bootstrap Methods for Sampling Distribution Simulation
14.2.1 Bootstrap Approximation of Sampling Distribution
14.2.2 Monte Carlo Bootstrap Sampling Distribution Estimation
14.3 Further Readings
15. Analytic Formulas for Evaluating Generalization
15.1 Assumptions for Asymptotic Analysis
15.2 Theoretical Sampling Distribution Analysis
15.3 Con dence Regions
15.4 Hypothesis Testing for Model Comparison Decisions
15.4.1 Classical Hypothesis Testing
15.4.2 Bayesian Hypothesis Testing
15.5 Further Readings
16. Model Selection and Evaluation
16.1 Cross-Validation Risk Model Selection Criteria
16.2 Bayesian Model Selection Criteria
16.2.1 Bayesian Model Selection Problem
16.2.2 Laplace Approximation for Multidimensional Integration
16.2.3 Bayesian Information Criteria
16.3 Model Misspecification Detection Model Selection Criteria
16.3.1 Nested Models Method for Assessing Model Misspecification
16.3.2 Information Matrix Discrepancy Model Selection Criteria
16.4 Further Readings
References
Algorithm Index
Subject Index