
Machine Learning
A Bayesian and Optimization Perspective
Description
Key Features
- All major classical techniques: Mean/Least-Squares regression and filtering, Kalman filtering, stochastic approximation and online learning, Bayesian classification, decision trees, logistic regression and boosting methods.
- The latest trends: Sparsity, convex analysis and optimization, online distributed algorithms, learning in RKH spaces, Bayesian inference, graphical and hidden Markov models, particle filtering, deep learning, dictionary learning and latent variables modeling.
- Case studies - protein folding prediction, optical character recognition, text authorship identification, fMRI data analysis, change point detection, hyperspectral image unmixing, target localization, channel equalization and echo cancellation, show how the theory can be applied.
- MATLAB code for all the main algorithms are available on an accompanying website, enabling the reader to experiment with the code.
Readership
University Researchers, R&D engineers, graduate students taking a machine learning course.
Table of Contents
- 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
Product details
- No. of pages: 1062
- Language: English
- Copyright: © Academic Press 2015
- Published: March 27, 2015
- Imprint: Academic Press
- eBook ISBN: 9780128017227
About the Author
Sergios Theodoridis

Affiliations and Expertise
Ratings and Reviews
Latest reviews
(Total rating for all reviews)
Yanet R. Sun Jan 06 2019
machine learning a bayesian and optimization perspective
This book explains to the reader an impresive variety of Machine Learning related topics. Most these topics are treated with electrical engineering flavor and some of them from the Bayesian perspective. Furthermore, some topics like sparse representations are not commonly included in ML books .This book includes two chapters on that topic, which is a very interesting thing. This combination of topics makes this book a singular one, worthy to purchase for me. Deep Learning is a very extensie ML topic, which in my opinion is not worthy to compress within a chapter. Probably talking about neural networks and the theory behind their aplications in learning representations is a much better approach. I feel this is much more desirable for the reader of this kind of book to take advantage of the deep knowledge an author like S. Theodoridis posses.
Akram A. Tue Jun 26 2018
Machine Learning.
Amazingly insightful!!!
Andrews S. Mon May 14 2018
Great book!
This is a great book. Very comprehensive, very detailed and well written!
h f. Thu Apr 12 2018
sample and solution
This is an excellent book for ML. But, where can I find the solution manual of the book ?
Andrews S. Fri Dec 29 2017
Great book!
I loved this book. It shows a complete overview of the machine learning domain. It's suitable for anybody that's interested on AI.