BOOSTED NONPARAMETRIC HAZARDS WITH TIME-DEPENDENT COVARIATES
Autor: | Ningyuan Chen, Hemant Ishwaran, Donald K. K. Lee |
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Rok vydání: | 2021 |
Předmět: |
FOS: Computer and information sciences
Statistics and Probability Hazard (logic) Mathematical optimization Boosting (machine learning) Nonparametric statistics Estimator Machine Learning (stat.ML) Overfitting Regularization (mathematics) Article Statistics - Machine Learning Covariate 62N02 (Primary) 62G05 90B22 (Secondary) Gradient boosting Statistics Probability and Uncertainty Mathematics |
Zdroj: | Ann Stat |
ISSN: | 0090-5364 |
Popis: | Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this, we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent if the model is correctly specified; alternatively, an oracle inequality can be demonstrated for tree-based models. To avoid overfitting, boosting employs several regularization devices. One of them is step-size restriction, but the rationale for this is somewhat mysterious from the viewpoint of consistency. Our work brings some clarity to this issue by revealing that step-size restriction is a mechanism for preventing the curvature of the risk from derailing convergence. |
Databáze: | OpenAIRE |
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