Classification and Regression Trees

by Breiman; Leo

• ISBN13: 9780412048418
• ISBN10: 0412048418
• eBook ISBN(s): 9781351460484
• Edition: 1st
• Format: Nonspecific Binding
• Copyright: 1984-01-01
• Publisher: Chapman & Hall/
• More Book Details

Summary

The methodology used to construct tree structured rules is the focus of this monograph. Unlike many other statistical procedures, which moved from pencil and paper to calculators, this text's use of trees was unthinkable before computers. Both the practical and theoretical sides have been developed in the authors' study of tree methods. Classification and Regression Trees reflects these two sides, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.

Table of Contents

Preface	viii
Background	1	(17)
Classifiers as Partitions	2	(2)
Use of Data in Constructing Classifiers	4	(2)
The Purposes of Classification Analysis	6	(2)
Estimating Accuracy	8	(5)
The Bayes Rule and Current Classification Procedures	13	(5)
Introduction to Tree Classification	18	(41)
The Ship Classification Problem	18	(2)
Tree Structured Classifiers	20	(3)
Construction of the Tree Classifiers	23	(4)
Initial Tree Growing Methodology	27	(9)
Methodological Development	36	(7)
Two Running Examples	43	(12)
The Advantages of the Tree Structured Approach	55	(4)
Right Sized Trees and Honest Estimates	59	(34)
Introduction	59	(4)
Getting Ready to Prune	63	(3)
Minimal Cost-Complexity Pruning	66	(6)
The Best-Pruned Subtree: An Estimation Problem	72	(9)
Some Examples	81	(12)
Appendix	87	(6)
Splitting Rules	93	(37)
Reducing Misclassification Cost	94	(4)
The Two-Class Problem	98	(5)
The Multiclass Problem: Unit Costs	103	(9)
Priors and Variable Misclassification Costs	112	(3)
Two Examples	115	(6)
Class Probability Trees Via Gini	121	(9)
Appendix	126	(4)
Strengthening and Interpreting	130	(44)
Introduction	130	(1)
Variable Combinations	131	(9)
Surrogate Splits and Their Uses	140	(10)
Estimating Within-Node Cost	150	(5)
Interpretation and Exploration	155	(8)
Computational Efficiency	163	(5)
Comparison of Accuracy with Other Methods	168	(6)
Appendix	171	(3)
Medical Diagnosis and Prognosis	174	(29)
Prognosis After Heart Attack	175	(7)
Diagnosing Heart Attacks	182	(7)
Immunosuppression and the Diagnosis of Cancer	189	(5)
Gait Analysis and the Detection of Outliers	194	(7)
Related Work on Computer-Aided Diagnosis	201	(2)
Mass Spectra Classification	203	(13)
Introduction	203	(2)
Generalized Tree Construction	205	(1)
The Bromine Tree: A Nonstandard Example	205	(11)
Regression Trees	216	(50)
Introduction	216	(1)
An Example	217	(4)
Least Squares Regression	221	(7)
Tree Structured Regression	228	(4)
Pruning and Estimating	232	(5)
A Simulated Example	237	(4)
Two Cross-Validation Issues	241	(6)
Standard Structure Trees	247	(1)
Using Surrogate Splits	248	(3)
Interpretation	251	(4)
Least Absolute Deviation Regression	255	(9)
Overall Conclusions	264	(2)
Bayes Rules and Partitions	266	(13)
Bayes Rule	266	(3)
Bayes Rule for a Partition	269	(3)
Risk Reduction Splitting Rule	272	(2)
Categorical Splits	274	(5)
Optimal Pruning	279	(18)
Tree Terminology	279	(5)
Optimally Pruned Subtrees	284	(9)
An Explicit Optimal Pruning Algorithm	293	(4)
Construction of Trees From a Learning Sample	297	(21)
Estimated Bayes Rule for a Partition	298	(2)
Empirical Risk Reduction Splitting Rule	300	(2)
Optimal Pruning	302	(1)
Test Samples	303	(3)
Cross-Validation	306	(3)
Final Tree Selection	309	(2)
Bootstrap Estimate of Overall Risk	311	(2)
End-Cut Preference	313	(5)
Consistency	318	(24)
Empirical Distributions	319	(2)
Regression	321	(3)
Classification	324	(3)
Proofs for Section 12.1	327	(5)
Proofs for Section 12.2	332	(5)
Proofs for Section 12.3	337	(5)
Bibliography	342	(5)
Notation Index	347	(7)
Subject Index	354