Consistency of random survival forests

Hemant Ishwaran, Udaya B. Kogalur

Research output: Contribution to journalArticle

73 Citations (Scopus)

Abstract

We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables-that is, under true implementation of the methodology. Under this setting we show that the forest ensemble survival function converges uniformly to the true population survival function. To prove this result we make one key assumption regarding the feature space: we assume that all variables are factors. Doing so ensures that the feature space has finite cardinality and enables us to exploit counting process theory and the uniform consistency of the Kaplan-Meier survival function.

Original languageEnglish
Pages (from-to)1056-1064
Number of pages9
JournalStatistics and Probability Letters
Volume80
Issue number13-14
DOIs
StatePublished - Jul 1 2010
Externally publishedYes

Fingerprint

Survival Function
Uniform Consistency
Feature Space
Ensemble
Kaplan-Meier
Censored Survival Data
Selection of Variables
Counting Process
Right-censored Data
Bootstrapping
Cardinality
Converge
Methodology

Keywords

  • Consistency
  • Ensemble
  • Factors
  • Kaplan-Meier
  • Random forests

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Consistency of random survival forests. / Ishwaran, Hemant; Kogalur, Udaya B.

In: Statistics and Probability Letters, Vol. 80, No. 13-14, 01.07.2010, p. 1056-1064.

Research output: Contribution to journalArticle

Ishwaran, Hemant ; Kogalur, Udaya B. / Consistency of random survival forests. In: Statistics and Probability Letters. 2010 ; Vol. 80, No. 13-14. pp. 1056-1064.
@article{a25eeae4d87449b586f61641d62432c4,
title = "Consistency of random survival forests",
abstract = "We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables-that is, under true implementation of the methodology. Under this setting we show that the forest ensemble survival function converges uniformly to the true population survival function. To prove this result we make one key assumption regarding the feature space: we assume that all variables are factors. Doing so ensures that the feature space has finite cardinality and enables us to exploit counting process theory and the uniform consistency of the Kaplan-Meier survival function.",
keywords = "Consistency, Ensemble, Factors, Kaplan-Meier, Random forests",
author = "Hemant Ishwaran and Kogalur, {Udaya B.}",
year = "2010",
month = "7",
day = "1",
doi = "10.1016/j.spl.2010.02.020",
language = "English",
volume = "80",
pages = "1056--1064",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",
number = "13-14",

}

TY - JOUR

T1 - Consistency of random survival forests

AU - Ishwaran, Hemant

AU - Kogalur, Udaya B.

PY - 2010/7/1

Y1 - 2010/7/1

N2 - We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables-that is, under true implementation of the methodology. Under this setting we show that the forest ensemble survival function converges uniformly to the true population survival function. To prove this result we make one key assumption regarding the feature space: we assume that all variables are factors. Doing so ensures that the feature space has finite cardinality and enables us to exploit counting process theory and the uniform consistency of the Kaplan-Meier survival function.

AB - We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables-that is, under true implementation of the methodology. Under this setting we show that the forest ensemble survival function converges uniformly to the true population survival function. To prove this result we make one key assumption regarding the feature space: we assume that all variables are factors. Doing so ensures that the feature space has finite cardinality and enables us to exploit counting process theory and the uniform consistency of the Kaplan-Meier survival function.

KW - Consistency

KW - Ensemble

KW - Factors

KW - Kaplan-Meier

KW - Random forests

UR - http://www.scopus.com/inward/record.url?scp=77953020220&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953020220&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2010.02.020

DO - 10.1016/j.spl.2010.02.020

M3 - Article

AN - SCOPUS:77953020220

VL - 80

SP - 1056

EP - 1064

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 13-14

ER -