Intro
Contents
Preface to the Second Edition
Preface to the First Edition
Notation and Abbreviations
Sets, Bags, and Sequences
Stochastics
Machine Learning
Programming
Confidence Prediction
Other Notations
Abbreviations
1 Introduction
1.1 Machine Learning
1.1.1 Learning Under Randomness
1.1.2 Learning Under Unconstrained Randomness
1.2 A Shortcoming of Statistical Learning Theory
1.2.1 The Hold-Out Estimate of Confidence
1.2.2 The Contribution of This Book
1.3 The Online Framework
1.3.1 Online Learning

1.3.2 Online/Offline Compromises
1.3.3 One-Off and Offline Learning
1.3.4 Induction, Transduction, and the Online Framework
1.4 Conformal Prediction
1.4.1 Nested Prediction Sets
1.4.2 Validity
1.4.3 Efficiency
1.4.4 Conditionality
1.4.5 Flexibility of Conformal Predictors
1.5 Probabilistic Prediction Under Unconstrained Randomness
1.5.1 Universally Consistent Probabilistic Predictor
1.5.2 Probabilistic Prediction Using a Finite Dataset
1.5.3 Venn Prediction
1.5.4 Conformal Predictive Distributions
1.6 Beyond Randomness
1.6.1 Testing Randomness

1.6.2 Online Compression Models
1.7 Context
Part I Set Prediction
2 Conformal Prediction: General Case and Regression
2.1 Confidence Predictors
2.1.1 Assumptions
2.1.2 Simple Predictors and Confidence Predictors
2.1.3 Validity
2.1.4 Randomized Confidence Predictors
2.1.5 Confidence Predictors Over a Finite Horizon
2.1.6 One-Off and Offline Confidence Predictors
2.2 Conformal Predictors
2.2.1 Bags
2.2.2 Nonconformity and Conformity
2.2.3 p-Values
2.2.4 Definition of Conformal Predictors
2.2.5 Validity
2.2.6 Smoothed Conformal Predictors

2.2.7 Finite-Horizon Conformal Prediction
2.2.8 One-Off and Offline Conformal Predictors
2.2.9 General Schemes for Defining Nonconformity
Conformity to a Bag
Conformity to a Property
2.2.10 Deleted Conformity Measures
2.3 Conformalized Ridge Regression
2.3.1 Least Squares and Ridge Regression
2.3.2 Basic CRR
2.3.3 Two Modifications
2.3.4 Dual Form Ridge Regression
2.4 Conformalized Nearest Neighbours Regression
2.5 Efficiency of Conformalized Ridge Regression
2.5.1 Hard and Soft Models
2.5.2 Bayesian Ridge Regression
2.5.3 Efficiency of CRR

2.6 Are There Other Ways to Achieve Validity?
2.7 Conformal Transducers
2.7.1 Definitions and Properties of Validity
2.7.2 Normalized Confidence Predictors and Confidence Transducers
2.8 Proofs
2.8.1 Proof of Theorem 2.2
2.8.2 Proof of Theorem 2.7
Regularizing the Rays in Upper CRR
Proof Proper
2.8.3 Proof of Theorem 2.10
2.9 Context
2.9.1 Exchangeability vs Randomness
2.9.2 Conformal Prediction
2.9.3 Two Equivalent Definitions of Nonconformity Measures
2.9.4 The Two Meanings of Conformity in Conformal Prediction