Consistency of Random Survival Forests

By Hemant Ishwaran, Udaya B. Kogalur. 2008

246 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Generalized random forests (2016, background): “…Devroye and Lugosi, 2008; Biau and Scornet, 2016; Bühlmann and Yu, 2002; Denil, Matheson and De Freitas, 2014; Geurts, Ernst and Wehenkel, 2006; Ishwaran and Kogalur, 2010; Lin and Jeon, 2006; Meinshausen, 2006; Mentch and Hooker, 2016; Scornet, Biau and Vert, 2015; Sexton and Laake, 2009;…”
A review of survival trees (2011, methodology): “Uniform consistency of RSF, under the assumption of a discrete feature space, is established in Ishwaran and Kogalur (2010a).”
Narrowing the Gap: Random Forests In Theory and In Practice (2013, background): “In particular, Meinshausen (2006) has shown that a model of random forests for quantile regression is consistent and Ishwaran & Kogalur (2010) have shown the consistency of their survival forests model.”
Understanding Random Forests: From Theory to Practice (2014, methodology): “Finally, let us complete this review by mentioning consistency results in the case of domain-specific adaptations of random forests, including quantile regression [Meinshausen, 2006], survival analysis [Ishwaran and Kogalur, 2010] and online forest construction [Denil et al., 2013b].”
Consistency of Online Random Forests (2013, methodology): “A model of random forests for survival analysis was shown to be consistent in Ishwaran & Kogalur (2010).”