Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates

George Chen
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1001-1010, 2019.

Abstract

We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-chen19a, title = {Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates}, author = {Chen, George}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {1001--1010}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/chen19a/chen19a.pdf}, url = {https://proceedings.mlr.press/v97/chen19a.html}, abstract = {We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.} }
Endnote
%0 Conference Paper %T Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates %A George Chen %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-chen19a %I PMLR %P 1001--1010 %U https://proceedings.mlr.press/v97/chen19a.html %V 97 %X We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.
APA
Chen, G.. (2019). Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:1001-1010 Available from https://proceedings.mlr.press/v97/chen19a.html.

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