Machine Learning

A Bayesian and Optimization Perspective

1st Edition - March 27, 2015

Author: Sergios Theodoridis

Hardback ISBN:

9 7 8 - 0 - 1 2 - 8 0 1 5 2 2 - 3

eBook ISBN:

9 7 8 - 0 - 1 2 - 8 0 1 7 2 2 - 7

This tutorial text gives a unifying perspective on machine learning by covering both probabilistic and deterministic approaches -which are based on optimization techniques –… Read more

Purchase options

LIMITED OFFER

Save 50% on book bundles

Immediately download your ebook while waiting for your print delivery. No promo code is needed.

This tutorial text gives a unifying perspective on machine learning by covering both probabilistic and deterministic approaches -which are based on optimization techniques – together with the Bayesian inference approach, whose essence lies in the use of a hierarchy of probabilistic models.The book presents the major machine learning methods as they have been developed in different disciplines, such as statistics, statistical and adaptive signal processing and computer science. Focusing on the physical reasoning behind the mathematics, all the various methods and techniques are explained in depth, supported by examples and problems, giving an invaluable resource to the student and researcher for understanding and applying machine learning concepts.

The book builds carefully from the basic classical methods to the most recent trends, with chapters written to be as self-contained as possible, making the text suitable for different courses: pattern recognition, statistical/adaptive signal processing, statistical/Bayesian learning, as well as short courses on sparse modeling, deep learning, and probabilistic graphical models.

Preface
Acknowledgments
Notation
Dedication
Chapter 1: Introduction
- Abstract
- 1.1 What Machine Learning is About
- 1.2 Structure and a Road Map of the Book
Chapter 2: Probability and Stochastic Processes
- Abstract
- 2.1 Introduction
- 2.2 Probability and Random Variables
- 2.3 Examples of Distributions
- 2.4 Stochastic Processes
- 2.5 Information Theory
- 2.6 Stochastic Convergence
- Problems
Chapter 3: Learning in Parametric Modeling: Basic Concepts and Directions
- Abstract
- 3.1 Introduction
- 3.2 Parameter Estimation: The Deterministic Point of View
- 3.3 Linear Regression
- 3.4 Classification
- 3.5 Biased Versus Unbiased Estimation
- 3.6 The Cramér-Rao Lower Bound
- 3.7 Sufficient Statistic
- 3.8 Regularization
- 3.9 The Bias-Variance Dilemma
- 3.10 Maximum Likelihood Method
- 3.11 Bayesian Inference
- 3.12 Curse of Dimensionality
- 3.13 Validation
- 3.14 Expected and Empirical Loss Functions
- 3.15 Nonparametric Modeling and Estimation
- Problems
Chapter 4: Mean-Square Error Linear Estimation
- Abstract
- 4.1 Introduction
- 4.2 Mean-Square Error Linear Estimation: The Normal Equations
Chapter 5: Stochastic Gradient Descent: The LMS Algorithm and its Family
- Abstract
- 5.1 Introduction
- 5.2 The Steepest Descent Method
- 5.3 Application to the Mean-Square Error Cost Function
- 5.4 Stochastic Approximation
- 5.5 The Least-Mean-Squares Adaptive Algorithm
- 5.6 The Affine Projection Algorithm
- 5.7 The Complex-Valued Case
- 5.8 Relatives of the LMS
- 5.9 Simulation Examples
- 5.10 Adaptive Decision Feedback Equalization
- 5.11 The Linearly Constrained LMS
- 5.12 Tracking Performance of the LMS in Nonstationary Environments
- 5.13 Distributed Learning: The Distributed LMS
- 5.14 A Case Study: Target Localization
- 5.15 Some Concluding Remarks: Consensus Matrix
- Problems
- MATLAB Exercises
Chapter 6: The Least-Squares Family
- Abstract
- 6.1 Introduction
- 6.2 Least-Squares Linear Regression: A Geometric Perspective
- 6.3 Statistical Properties of the LS Estimator
- 6.4 Orthogonalizing the Column Space of X: The SVD Method
- 6.5 Ridge Regression
- 6.6 The Recursive Least-Squares Algorithm
- 6.7 Newton’s Iterative Minimization Method
- 6.8 Steady-State Performance of the RLS
- 6.9 Complex-Valued Data: The Widely Linear RLS
- 6.10 Computational Aspects of the LS Solution
- 6.11 The Coordinate and Cyclic Coordinate Descent Methods
- 6.12 Simulation Examples
- 6.13 Total-Least-Squares
- Problems
Chapter 7: Classification: A Tour of the Classics
- Abstract
- 7.1 Introduction
- 7.2 Bayesian Classification
- 7.3 Decision (Hyper)Surfaces
- 7.4 The Naive Bayes Classifier
- 7.5 The Nearest Neighbor Rule
- 7.6 Logistic Regression
- 7.7 Fisher’s Linear Discriminant
- 7.8 Classification Trees
- 7.9 Combining Classifiers
- 7.10 The Boosting Approach
- 7.11 Boosting Trees
- 7.12 A Case Study: Protein Folding Prediction
- Problems
Chapter 8: Parameter Learning: A Convex Analytic Path
- Abstract
- 8.1 Introduction
- 8.2 Convex Sets and Functions
- 8.3 Projections onto Convex Sets
- 8.4 Fundamental Theorem of Projections onto Convex Sets
- 8.5 A Parallel Version of POCS
- 8.6 From Convex Sets to Parameter Estimation and Machine Learning
- 8.7 Infinite Many Closed Convex Sets: The Online Learning Case
- 8.8 Constrained Learning
- 8.9 The Distributed APSM
- 8.10 Optimizing Nonsmooth Convex Cost Functions
- 8.11 Regret Analysis
- 8.12 Online Learning and Big Data Applications: A Discussion
- 8.13 Proximal Operators
- 8.14 Proximal Splitting Methods for Optimization
- Problems
- MATLAB Exercises
- 8.15 Appendix to Chapter 8
Chapter 9: Sparsity-Aware Learning: Concepts and Theoretical Foundations
- Abstract
- 9.1 Introduction
- 9.2 Searching for a Norm
- 9.3 The Least Absolute Shrinkage and Selection Operator (LASSO)
- 9.4 Sparse Signal Representation
- 9.5 In Search of the Sparsest Solution
- 9.6 Uniqueness of the ℓ₀ Minimizer
- 9.7 Equivalence of ℓ₀ and ℓ₁ Minimizers: Sufficiency Conditions
- 9.8 Robust Sparse Signal Recovery from Noisy Measurements
- 9.9 Compressed Sensing: The Glory of Randomness
- 9.10 A Case Study: Image De-Noising
- Problems
Chapter 10: Sparsity-Aware Learning: Algorithms and Applications
- Abstract
- 10.1 Introduction
- 10.2 Sparsity-Promoting Algorithms
- 10.3 Variations on the Sparsity-Aware Theme
- 10.4 Online Sparsity-Promoting Algorithms
- 10.5 Learning Sparse Analysis Models
- 10.6 A Case Study: Time-Frequency Analysis
- 10.7 Appendix to Chapter 10: Some Hints from the Theory of Frames
- Problems
Chapter 11: Learning in Reproducing Kernel Hilbert Spaces
- Abstract
- 11.1 Introduction
- 11.2 Generalized Linear Models
- 11.3 Volterra, Wiener, and Hammerstein Models
- 11.4 Cover’s Theorem: Capacity of a Space in Linear Dichotomies
- 11.5 Reproducing Kernel Hilbert Spaces
- 11.6 Representer Theorem
- 11.7 Kernel Ridge Regression
- 11.8 Support Vector Regression
- 11.9 Kernel Ridge Regression Revisited
- 11.10 Optimal Margin Classification: Support Vector Machines
- 11.11 Computational Considerations
- 11.12 Online Learning in RKHS
- 11.13 Multiple Kernel Learning
- 11.14 Nonparametric Sparsity-Aware Learning: Additive Models
- 11.15 A Case Study: Authorship Identification
- Problems
Chapter 12: Bayesian Learning: Inference and the EM Algorithm
- Abstract
- 12.1 Introduction
- 12.2 Regression: A Bayesian Perspective
- 12.3 The Evidence Function and Occam’s Razor Rule
- 12.4 Exponential Family of Probability Distributions
- 12.5 Latent Variables and the EM Algorithm
- 12.6 Linear Regression and the EM Algorithm
- 12.7 Gaussian Mixture Models
- 12.8 Combining Learning Models: A Probabilistic Point of View
- Problems
- MATLAB Exercises
- 12.9 Appendix to Chapter 12
Chapter 13: Bayesian Learning: Approximate Inference and Nonparametric Models
- Abstract
- 13.1 Introduction
- 13.2 Variational Approximation in Bayesian Learning
- 13.3 A Variational Bayesian Approach to Linear Regression
- 13.4 A Variational Bayesian Approach to Gaussian Mixture Modeling
- 13.5 When Bayesian Inference Meets Sparsity
- 13.6 Sparse Bayesian Learning (SBL)
- 13.7 The Relevance Vector Machine Framework
- 13.8 Convex Duality and Variational Bounds
- 13.9 Sparsity-Aware Regression: A Variational Bound Bayesian Path
- 13.10 Sparsity-Aware Learning: Some Concluding Remarks
- 13.11 Expectation Propagation
- 13.12 Nonparametric Bayesian Modeling
- 13.13 Gaussian Processes
- 13.14 A Case Study: Hyperspectral Image Unmixing
- Problems
Chapter 14: Monte Carlo Methods
- Abstract
- 14.1 Introduction
- 14.2 Monte Carlo Methods: The Main Concept
- 14.3 Random Sampling Based on Function Transformation
- 14.4 Rejection Sampling
- 14.5 Importance Sampling
- 14.6 Monte Carlo Methods and the EM Algorithm
- 14.7 Markov Chain Monte Carlo Methods
- 14.8 The Metropolis Method
- 14.9 Gibbs Sampling
- 14.10 In Search of More Efficient Methods: A Discussion
- 14.11 A Case Study: Change-Point Detection
- Problems
Chapter 15: Probabilistic Graphical Models: Part I
- Abstract
- 15.1 Introduction
- 15.2 The Need for Graphical Models
- 15.3 Bayesian Networks and the Markov Condition
- 15.4 Undirected Graphical Models
- 15.5 Factor Graphs
- 15.6 Moralization of Directed Graphs
- 15.7 Exact Inference Methods: Message-Passing Algorithms
- Problems
Chapter 16: Probabilistic Graphical Models: Part II
- Abstract
- 16.1 Introduction
- 16.2 Triangulated Graphs and Junction Trees
- 16.3 Approximate Inference Methods
- 16.4 Dynamic Graphical Models
- 16.5 Hidden Markov Models
- 16.6 Beyond HMMs: A Discussion
- 16.7 Learning Graphical Models
- Problems
Chapter 17: Particle Filtering
- Abstract
- 17.1 Introduction
- 17.2 Sequential Importance Sampling
- 17.3 Kalman and Particle Filtering
- 17.4 Particle Filtering
- Problems
Chapter 18: Neural Networks and Deep Learning
- Abstract
- 18.1 Introduction
- 18.2 The Perceptron
- 18.3 Feed-Forward Multilayer Neural Networks
- 18.4 The Backpropagation Algorithm
- 18.5 Pruning the Network
- 18.6 Universal Approximation Property of Feed-Forward Neural Networks
- 18.7 Neural Networks: A Bayesian Flavor
- 18.8 Learning Deep Networks
- 18.9 Deep Belief Networks
- 18.10 Variations on the Deep Learning Theme
- 18.11 Case Study: A Deep Network for Optical Character Recognition
- 18.12 CASE Study: A Deep Autoencoder
- 18.13 Example: Generating Data via a DBN
- Problems
- MATLAB Exercises
Chapter 19: Dimensionality Reduction and Latent Variables Modeling
- Abstract
- 19.1 Introduction
- 19.2 Intrinsic Dimensionality
- 19.3 Principle Component Analysis
- 19.4 Canonical Correlation Analysis
- 19.5 Independent Component Analysis
- 19.6 Dictionary Learning: The k-SVD Algorithm
- 19.7 Nonnegative Matrix Factorization
- 19.8 Learning Low-Dimensional Models: A Probabilistic Perspective
- 19.9 Nonlinear Dimensionality Reduction
- 19.10 Low-Rank Matrix Factorization: A Sparse Modeling Path
- 19.11 A Case Study: fMRI Data Analysis
- Problems
Appendix A: Linear Algebra
- A.1 Properties of Matrices
- A.2 Positive Definite and Symmetric Matrices
- A.3 Wirtinger Calculus
Appendix B: Probability Theory and Statistics
- B.1 Cramér-Rao Bound
- B.2 Characteristic Functions
- B.3 Moments and Cumulants
- B.4 Edgeworth Expansion of a pdf
Appendix C: Hints on Constrained Optimization
- C.1 Equality Constraints
- C.2 Inequality Constrains
Index