Machine learning : a Bayesian and optimization perspective - Theodoridis, Sergios, 1951-; ScienceDirect eBooks (London ; San Diego : Elsevier : Academic Press, 2015)
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. 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.
Protein folding prediction as a classification task -- Classification of folding prediction via decision trees -- Problems -- MATLAB Exercises -- References -- Chapter 8: Parameter Learning: A Convex Analytic Path -- 8.1 Introduction -- 8.2 Convex Sets and Functions -- 8.2.1 Convex Sets -- 8.2.2 Convex Functions -- 8.3 Projections onto Convex Sets -- 8.3.1 Properties of Projections -- 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 -- 8.6.1 Regression -- 8.6.2 Classification -- 8.7 Infinite Many Closed Convex Sets: The Online Learning Case -- 8.7.1 Convergence of APSM -- Some practical hints -- 8.8 Constrained Learning -- 8.9 The Distributed APSM -- 8.10 Optimizing Nonsmooth Convex Cost Functions -- 8.10.1 Subgradients and Subdifferentials -- 8.10.2 Minimizing Nonsmooth Continuous Convex Loss Functions: The BatchLearning Case -- The subgradient method -- The generic projected subgradient scheme -- The projected gradient method (PGM) -- Projected subgradient method -- 8.10.3 Online Learning for Convex Optimization -- The PEGASOS algorithm -- 8.11 Regret Analysis -- Regret analysis of the subgradient algorithm -- 8.12 Online Learning and Big Data Applications: A Discussion -- Approximation, estimation and optimization errors -- Batch versus online learning -- 8.13 Proximal Operators -- 8.13.1 Properties of the Proximal Operator -- 8.13.2 Proximal Minimization -- Resolvent of the subdifferential mapping -- 8.14 Proximal Splitting Methods for Optimization -- The proximal forward-backward splitting operator -- Alternating direction method of multipliers (ADMM) -- Mirror descent algorithms -- Problems -- MATLAB Exercises -- 8.15 Appendix to Chapter 8 -- References -- Chapter 9: Sparsity-Aware Learning: Concepts and Theoretical Foundations.
Includes bibliographical references and index.
Print version record.
Elsevier
Safari Books Online
Keywords: Machine learning; Bayesian statistical decision theory; Mathematical optimization; COMPUTERS / General; Bayesian statistical decision theory; Machine learning; Mathematical optimization; Electronic books