Random Forests

By: Yu. L. Pavlov

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Hardcover | 1 March 2000

At a Glance

Hardcover
128 Pages

Age
22+

Dimensions(cm)
24.77 x 17.15 x 0.64

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This monograph deals with random forests and aims to show that, despite the outward simplicity of the forest graph design, the problems emerging in relation to the phenomenon are challenging, and their solution often requires subtle mathematical methods. The book focuses on forests formed by simply generated trees. While the notion of the simply generated family of trees covers many known tree classes, this approach to the study of random forests gives a chance to obtain results for various forest types in a uniform way. The main objective of the book is to provide the full description of the limit behaviour of the random forest's most important characteristics: maximum tree size and number of trees of a given size and height. The main probability methods used in the book are the generalized allocation scheme and methods of the branching process theory. This monograph should be of value and interest to researchers in probabilistic methods and discrete mathematics.

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Preface	p. 3
Probabilistic methods in studying trees and forests	p. 7
Trees and forests	p. 7
Random forests and generalized allocation scheme	p. 13
Random forests and branching processes	p. 17
Simply generated forests	p. 33
Additions and references	p. 37
The maximum size of a tree in a random forest	p. 39
Problem statement and summary of results	p. 39
Asymptotics of NP[subscript r]	p. 41
The limit behaviour of the total progeny of the branching process	p. 46
The convergence of the sum of auxiliary random variables to the normal law	p. 54
The asymptotics of the sum of auxiliary random variables in the critical case	p. 60
Proofs of the main results	p. 71
Additions and references	p. 74
Limit distributions of the number of trees of a given size	p. 76
Problem statement and summary of results	p. 76
The convergence of the sum of auxiliary random variables to the normal law	p. 78
The limit behaviour of the sum of auxiliary random variables in the critical case	p. 87
Proofs of the main results	p. 94
Additions and references	p. 95
Limit distributions of the height of a random forest	p. 98
Problem statement and summary of results	p. 98
The limit behaviour of auxiliary probabilities in the subcritical case	p. 100
The limit behaviour of auxiliary probabilities in the critical case	p. 105
Proofs of the main results	p. 112
Additions and references	p. 113
Bibliography	p. 118
Table of Contents provided by Blackwell. All Rights Reserved.

Random Forests

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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