فهرست مطالب

• Cover
• Information Science and Statistics
• Pattern Recognition and Machine Learning
• ©
• Preface
• Mathematical notation
• Contents
• Chapter 1: Introduction
• 1.1 Example: Polynomial Curve Fitting
• 1.2 Probability Theory
• 1.3 Model Selection
• 1.4 The Curse of Dimensionality
• 1.5 Decision Theory
• 1.6 Information Theory
• Exercises
• Chapter 2: Probability Distributions
• 2.1 Binary Variables
• 2.2 Multinomial Variables
• 2.3 The Gaussian Distribution
• 2.4 The Exponential Family
• 2.5 Nonparametric Methods
• Exercises
• Chapter 3: Linear Models for Regression
• 3.1 Linear Basis Function Models
• 3.2 The Bias-Variance Decomposition
• 3.3 Bayesian Linear Regression
• 3.4 Bayesian Model Comparison
• 3.5 The Evidence Approximation
• 3.6 Limitations of Fixed Basis Functions
• Exercises
• Chapter 4: Linear Models for Classification
• 4.1 Discriminant Functions
• 4.2 Probabilistic Generative Models
• 4.3 Probabilistic Discriminative Models
• 4.4 The Laplace Approximation
• 4.5 Bayesian Logistic Regression
• Exercises
• Chapter 5: Neural Networks
• 5.1 Feed-forward Network Functions
• 5.2 Network Training
• 5.3 Error Backpropagation
• 5.4 The Hessian Matrix
• 5.5 Regularization in Neural Networks
• 5.6 Mixture Density Networks
• 5.7 Bayesian Neural Networks
• Exercises
• Chapter 6: Kernel Methods
• 6.1 Dual Representations
• 6.2 Constructing Kernels
• 6.3 Radial Basis Function Networks
• 6.4 Gaussian Processes
• Exercises
• Chapter 7: Sparse Kernel Machines
• 7.1 Maximum Margin Classifiers
• 7.2 Relevance Vector Machines
• Exercises
• Chapter 8: Graphical Models
• 8.1 Bayesian Networks
• 8.2 Conditional Independence
• 8.3 Markov Random Fields
• 8.4 Inference in Graphical Models
• Exercises
• Chapter 9: Mixture Models and EM
• 9.1 K-means Clustering
• 9.2 Mixtures of Gaussians
• 9.3 An Alternative View of EM
• 9.4 The EM Algorithm in General
• Exercises
• Chapter 10: Approximate Inference
• 10.1 Variational Inference
• 10.2 Illustration: Variational Mixture of Gaussians
• 10.3 Variational Linear Regression
• 10.4 Exponential Family Distributions
• 10.5 Local Variational Methods
• 10.6 Variational Logistic Regression
• 10.7 Expectation Propagation
• Exercises
• Chapter 11: Sampling Methods
• 11.1 Basic Sampling Algorithms
• 11.2 Markov Chain Monte Carlo
• 11.3 Gibbs Sampling
• 11.4 Slice Sampling
• 11.5 The Hybrid Monte Carlo Algorithm
• 11.6 Estimating the Partition Function
• Exercises
• Chapter 12: Continuous Latent Variables
• 12.1 Principal Component Analysis
• 12.2 Probabilistic PCA
• 12.3 Kernel PCA
• 12.4 Nonlinear Latent Variable Models
• Exercises
• Chapter 13: Sequential Data
• 13.1 Markov Models
• 13.2 Hidden Markov Models
• 13.3 Linear Dynamical Systems
• Exercises
• Chapter 14: Combining Models
• 14.1 Bayesian Model Averaging
• 14.2 Committees
• 14.3 Boosting
• 14.4 Tree-based Models
• 14.5 Conditional Mixture Models
• Exercises
• Appendix A. Data Sets
• Appendix B. Probability Distributions
• Appendix C. Properties of Matrices
• Appendix D. Calculus of Variations
• Appendix E. Lagrange Multipliers
• References
• Index