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Title: Adaptive concentration and consistency of tree-based survival models Authors:  Yifan Cui - University of North Carolina at Chapel Hill (United States) [presenting]
Ruoqing Zhu - University of Illinois at Urbana-Champaign (United States)
Mai Zhou - University of Kentucky (United States)
Michael Kosorok - University of North Carolina at Chapel Hill (United States)
Abstract: As one of the most popular extensions of random forests, tree-based survival models lack established theoretical results and unified theoretical framework. We investigate the method from the perspective of splitting rules, where the log-rank test statistics is calculated and compared. The splitting rule is essentially treating both resulting child nodes as being identically distributed. However, we demonstrate that this approach is affected by censoring, which may lead to inconsistency of the method. Based on this observation, we develop the adaptive concentration bound result for tree and forest versions of the survival tree models, and establish a general framework for showing the consistency of tree-based survival models. Interestingly, we also show that existing methods based on this biased selection of splitting rule can still lead to consistency as long as the censoring effect is weak.