Foundations of Machine Learning

ISBN-10: 026201825X
ISBN-13: 9780262018258
Edition: 2012
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Description: This graduate-level textbook introduces fundamental concepts and methods in machine learning. It describes several important modern algorithms, provides the theoretical underpinnings of these algorithms, and illustrates key aspects for their  More...

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Book details

Copyright year: 2012
Publisher: MIT Press
Publication date: 8/17/2012
Binding: Hardcover
Pages: 432
Size: 7.75" wide x 9.50" long x 1.25" tall
Weight: 1.826
Language: English

This graduate-level textbook introduces fundamental concepts and methods in machine learning. It describes several important modern algorithms, provides the theoretical underpinnings of these algorithms, and illustrates key aspects for their application. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning fills the need for a general textbook that also offers theoretical details and an emphasis on proofs. Certain topics that are often treated with insufficient attention are discussed in more detail here; for example, entire chapters are devoted to regression, multi-class classification, and ranking. The first three chapters lay the theoretical foundation for what follows, but each remaining chapter is mostly self-contained. The appendix offers a concise probability review, a short introduction to convex optimization, tools for concentration bounds, and several basic properties of matrices and norms used in the book.The book is intended for graduate students and researchers in machine learning, statistics, and related areas; it can be used either as a textbook or as a reference text for a research seminar.

Preface
Introduction
Applications and problems
Definitions and terminology
Cross-validation
Learning scenarios
Outline
The PAC Learning Framework
The PAC learning model
Guarantees for finite hypothesis sets - consistent case
Guarantees for finite hypothesis sets - inconsistent case
Generalities
Deterministic versus stochastic scenarios
Bayes error and noise
Estimation and approximation errors
Model selection
Chapter notes
Exercises
Rademacher Complexity and VC-Dimension
Rademacher complexity
Growth function
VC-dimension
Lower bounds
Chapter notes
Exercises
Support Vector Machines
Linear classification
SVMs - separable case
Primal optimization problem
Support vectors
Dual optimization problem
Leave-one-out analysis
SVMs - non-separable case
Primal optimization problem
Support vectors
Dual optimization problem
Margin theory
Chapter notes
Exercises
Kernel Methods
Introduction
Positive definite symmetric kernels
Definitions
Reproducing kernel Hilbert space
Properties
Kernel-based algorithms
SVMs with PDS kernels
Representer theorem
Learning guarantees
Negative definite symmetric kernels
Sequence kernels
Weighted transducers
Rational kernels
Chapter notes
Exercises
Boosting
Introduction
AdaBoost
Bound on the empirical error
Relationship with coordinate descent
Relationship with logistic regression
Standard use in practice
Theoretical results
VC-dimension-based analysis
Margin-based analysis
Margin maximization
Game-theoretic interpretation
Discussion
Chapter notes
Exercises
On-Line Learning
Introduction
Prediction with expert advice
Mistake bounds and Halving algorithm
Weighted majority algorithm
Randomized weighted majority algorithm
Exponential weighted average algorithm
Linear classification
Perceptron algorithm
Winnow algorithm
On-line to batch conversion
Game-theoretic connection
Chapter notes
Exercises
Multi-Class Classification
Multi-class classification problem
Generalization bounds
Uncombined multi-class algorithms
Multi-class SVMs
Multi-class boosting algorithms
Decision trees
Aggregated multi-class algorithms
One-versus-all
One-versus-one
Error-correction codes
Structured prediction algorithms
Chapter notes
Exercises
Ranking
The problem of ranking
Generalization bound
Ranking with SVMs
RankBoost
Bound on the empirical error
Relationship with coordinate descent
Margin bound for ensemble methods in ranking
Bipartite ranking
Boosting in bipartite ranking
Area under the ROC curve
Preference-based setting
Second-stage ranking problem
Deterministic algorithm
Randomized algorithm
Extension to other loss functions
Discussion
Chapter notes
Exercises
Regression
The problem of regression
Generalization bounds
Finite hypothesis sets
Rademacher complexity bounds
Pseudo-dimension bounds
Regression algorithms
Linear regression
Kernel ridge regression
Support vector regression
Lasso
Group norm regression algorithms
On-line regression algorithms
Chapter notes
Exercises
Algorithmic Stability
Definitions
Stability-based generalization guarantee
Stability of kernel-based regularization algorithms
Application to regression algorithms: SVR and KRR
Application to classification algorithms: SVMs
Discussion
Chapter notes
Exercises
Dimensionality Reduction
Principal Component Analysis
Kernel Principal Component Analysis (KPCA)
KPCA and manifold learning
Isomap
Laplacian eigenmaps
Locally linear embedding (LLE)
Johnson-Lindenstrauss lemma
Chapter notes
Exercises
Learning Automata and Languages
Introduction
Finite automata
Efficient exact learning
Passive learning
Learning with queries
Learning automata with queries
Identification in the limit
Learning reversible automata
Chapter notes
Exercises
Reinforcement Learning
Learning scenario
Markov decision process model
Policy
Definition
Policy value
Policy evaluation
Optimal policy
Planning algorithms
Value iteration
Policy iteration
Linear programming
Learning algorithms
Stochastic approximation
TD(0) algorithm
Q-learning algorithm
SARSA
TD(�) algorithm
Large state space
Chapter notes
Conclusion
Linear Algebra Review
Vectors and norms
Norms
Dual norms
Matrices
Matrix norms
Singular value decomposition
Symmetric positive semidefinite (SPSD) matrices
Convex Optimization
Differentiation and unconstrained optimization
Convexity
Constrained optimization
Chapter notes
Probability Review
Probability
Random variables
Conditional probability and independence
Expectation, Markov's inequality, and moment-generating function
Variance and Chebyshev's inequality
Concentration inequalities
Hoeffding's inequality
McDiarmid's inequality
Other inequalities
Binomial distribution: Slud's inequality
Normal distribution: tail bound
Khintchine-Kahane inequality
Chapter notes
Exercises
Notation
References
Index

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