Machine Learning A Bayesian and Optimization Perspective 2nd Edition by Sergios Theodoridis ISBN 0128188030 978-0128188033

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ISBN 10: 0128188030
ISBN 13: 978-0128188033
Author: Sergios Theodoridis

Machine Learning: A Bayesian and Optimization Perspective, 2nd edition, gives a unified perspective on machine learning by covering both pillars of supervised learning, namely regression and classification. The book starts with the basics, including mean square, least squares and maximum likelihood methods, ridge regression, Bayesian decision theory classification, logistic regression, and decision trees. It then progresses to more recent techniques, covering sparse modelling methods, learning in reproducing kernel Hilbert spaces and support vector machines, Bayesian inference with a focus on the EM algorithm and its approximate inference variational versions, Monte Carlo methods, probabilistic graphical models focusing on Bayesian networks, hidden Markov models and particle filtering. Dimensionality reduction and latent variables modelling are also considered in depth.

This palette of techniques concludes with an extended chapter on neural networks and deep learning architectures. The book also covers the fundamentals of statistical parameter estimation, Wiener and Kalman filtering, convexity and convex optimization, including a chapter on stochastic approximation and the gradient descent family of algorithms, presenting related online learning techniques as well as concepts and algorithmic versions for distributed optimization.

Focusing on the physical reasoning behind the mathematics, without sacrificing rigor, 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. Most of the chapters include typical case studies and computer exercises, both in MATLAB and Python.

The chapters are 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 courses on sparse modeling, deep learning, and probabilistic graphical models.

Machine Learning A Bayesian and Optimization Perspective 2nd Table of contents:

Chapter 1: Introduction

Abstract

1.1. The Historical Context

1.2. Artificial Intelligence and Machine Learning

1.3. Algorithms Can Learn What Is Hidden in the Data

1.4. Typical Applications of Machine Learning

1.5. Machine Learning: Major Directions

1.6. Unsupervised and Semisupervised Learning

1.7. Structure and a Road Map of the Book

References

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

References

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 Loss and Empirical Risk Functions

3.15. Nonparametric Modeling and Estimation

Problems

References

Chapter 4: Mean-Square Error Linear Estimation

Abstract

4.1. Introduction

4.2. Mean-Square Error Linear Estimation: the Normal Equations

4.3. A Geometric Viewpoint: Orthogonality Condition

4.4. Extension to Complex-Valued Variables

4.5. Linear Filtering

4.6. MSE Linear Filtering: a Frequency Domain Point of View

4.7. Some Typical Applications

4.8. Algorithmic Aspects: the Levinson and Lattice-Ladder Algorithms

4.9. Mean-Square Error Estimation of Linear Models

4.10. Time-Varying Statistics: Kalman Filtering

Problems

References

Chapter 5: Online Learning: the Stochastic Gradient Descent Family of Algorithms

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

References

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 the Input Matrix: the SVD Method

6.5. Ridge Regression: a Geometric Point of View

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

References

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

Problems

References

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. Infinitely 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

8.15. Distributed Optimization: Some Highlights

Problems

References

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 Denoising

Problems

References

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

Problems

References

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. Random Fourier Features

11.13. Multiple Kernel Learning

11.14. Nonparametric Sparsity-Aware Learning: Additive Models

11.15. A Case Study: Authorship Identification

Problems

References

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. Latent Variables and the EM Algorithm

12.5. Linear Regression and the EM Algorithm

12.6. Gaussian Mixture Models

12.7. The EM Algorithm: a Lower Bound Maximization View

12.8. Exponential Family of Probability Distributions

12.9. Combining Learning Models: a Probabilistic Point of View

Problems

References

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. Expectation Propagation

13.11. Nonparametric Bayesian Modeling

13.12. Gaussian Processes

13.13. A Case Study: Hyperspectral Image Unmixing

Problems

References

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

References

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

References

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

References

Chapter 17: Particle Filtering

Abstract

17.1. Introduction

17.2. Sequential Importance Sampling

17.3. Kalman and Particle Filtering

17.4. Particle Filtering

Problems

References

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. Selecting a Cost Function

18.6. Vanishing and Exploding Gradients

18.7. Regularizing the Network

18.8. Designing Deep Neural Networks: a Summary

18.9. Universal Approximation Property of Feed-Forward Neural Networks

18.10. Neural Networks: a Bayesian Flavor

18.11. Shallow Versus Deep Architectures

18.12. Convolutional Neural Networks

18.13. Recurrent Neural Networks

18.14. Adversarial Examples

18.15. Deep Generative Models

18.16. Capsule Networks

18.17. Deep Neural Networks: Some Final Remarks

18.18. A Case Study: Neural Machine Translation

18.19. Problems

References

Chapter 19: Dimensionality Reduction and Latent Variable Modeling

Abstract

19.1. Introduction

19.2. Intrinsic Dimensionality

19.3. Principal 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

 
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