Understanding Machine Learning: From Theory to Algorithms

Download Understanding Machine Learning tutorial, a complete eBook created by Shai Shalev-Shwartz and Shai Ben-David.

Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides an extensive theoretical account of the fundamental ideas underlying machine learning and the mathematical derivations that transform these principles into practical algorithms.

Following a presentation of the basics of the field, the book covers a wide array of central topics that have not been addressed by previous textbooks.

Table of contents

  • Introduction
  • What Is Learning?
  • When Do We Need Machine Learning?
  • Types of Learning
  • Relations to Other Fields
  • How to Read This Book
  • Possible Course Plans Based on This Book
  • Notation
  • Part I Foundations
  • A Formal Learning Model
  • PAC Learning
  • A More General Learning Model
  • Releasing the Realizability Assumption – Agnostic PAC
  • Learning
  • The Scope of Learning Problems Modeled
  • Summary
  • Bibliographic Remarks
  • Exercises
  • Learning via Uniform Convergence
  • Uniform Convergence Is Sufficient for Learnability
  • Examples
  • Threshold Functions
  • Intervals
  • Axis Aligned Rectangles
  • Finite Classes
  • VC-Dimension and the Number of Parameters
  • The Fundamental Theorem of PAC learning
  • Proof of Theorem
  • Characterizing Nonuniform Learnability
  • Structural Risk Minimization
  • Minimum Description Length and Occam’s Razor
  • Occam’s Razor
  • Other Notions of Learnability – Consistency
  • Discussing the Different Notions of Learnability
  • The No-Free-Lunch Theorem Revisited
  • Summary
  • Bibliographic Remarks
  • Exercises
  • The Runtime of Learning
  • Learning -Term DNF
  • Efficiently Learnable, but Not by a Proper ERM
  • Hardness of Learning*
  • Bibliographic Remarks
  • Exercises
  • Part II From Theory to Algorithms
  • Linear Regression
  • Least Squares
  • Linear Regression for Polynomial Regression Tasks
  • Logistic Regression
  • Bibliographic Remarks
  • Exercises
  • The VC-Dimension of L(B, T)
  • AdaBoost for Face Recognition
  • Bibliographic Re
  • xii Contents
  • k-Fold Cross Validation
  • Train-Validation-Test Split
  • What to Do If Learning Fails
  • Bibliographic Remarks
  • Exercises
  • Controlling the Fitting-Stability Tradeoff
  • Bibliographic Remarks
  • Exercises
  • Stochastic Gradient Descent
  • Gradient Descent
  • Analysis of GD for Convex-Lipschitz Functions
  • Stochastic Gradient Descent (SGD)
  • Analysis of SGD for Convex-Lipschitz-Bounded Functions
  • Learning with SGD
  • SGD for Risk Minimization
  • Analyzing SGD for Convex-Smooth Learning Problems
  • SGD for Regularized Loss Minimization
  • Bibliographic Remarks
  • Exercises
  • Support Vector Machines
  • Margin and Hard-SVM
  • Bibliographic Remarks
  • Exercises
  • Kernel Methods
  • Embeddings into Feature Spaces
  • The Kernel Trick
  • Kernels as a Way to Express Prior Knowledge
  • Characterizing Kernel Functions*
  • Implementing Soft-SVM with Kernels
  • Summary
  • Bibliographic Remarks
  • Exercises
  • Multiclass, Ranking, and Complex Prediction Problems
  • One-versus-All and All-Pairs
  • Linear Predictors for Ranking
  • Bipartite Ranking and Multivariate Performance Measures
  • Linear Predictors for Bipartite Ranking
  • Bibliographic Remarks
  • Exercises
  • Nearest Neighbor
  • Analysis
  • A Generalization Bound for the -NN Rule
  • Feedforward Neural Networks
  • Learning Neural Networks
  • The Expressive Power of Neural Networks
  • Geometric Intuition
  • The Sample Complexity of Neural Networks
  • The Runtime of Learning Neural Networks
  • SGD and Backpropagation
  • Contents xv
  • Online Learnability
  • Online Classification in the Unrealizable Case
  • Weighted-Majority
  • Online Convex Optimization
  • The Online Perceptron Algorithm
  • Summary
  • Bibliographic Remarks
  • The k-Means Algorithm
  • Spectral Clustering
  • Graph Cut
  • Graph Laplacian and Relaxed Graph Cuts
  • Unnormalized Spectral Clustering
  • Information Bottleneck*
  • Maximum Likelihood Estimation for Continuous Random Variables
  • Maximum Likelihood and Empirical Risk Minimization
  • Linear Discriminant Analysis
  • Latent Variables and the EM Algorithm


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Understanding Machine Learning: From Theory to Algorithms

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