T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP

Jiaye Teng, Zeren Tan, Yang Yuan
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:10203-10213, 2021.

Abstract

It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence interval of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP \citep{katzman2018deepsurv,kvamme2019time}), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first algorithm \emph{WCCI}, we revisit weighted conformal inference and introduce a new non-conformity score based on partial likelihood. We then propose a two-stage algorithm \emph{T-SCI}, where we run WCCI in the first stage and apply quantile conformal inference to calibrate the results in the second stage. Theoretical analysis shows that T-SCI returns guaranteed coverage under milder assumptions than WCCI. We conduct extensive experiments on synthetic data and real data using different methods, which validate our analysis.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-teng21a, title = {T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP}, author = {Teng, Jiaye and Tan, Zeren and Yuan, Yang}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {10203--10213}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/teng21a/teng21a.pdf}, url = {https://proceedings.mlr.press/v139/teng21a.html}, abstract = {It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence interval of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP \citep{katzman2018deepsurv,kvamme2019time}), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first algorithm \emph{WCCI}, we revisit weighted conformal inference and introduce a new non-conformity score based on partial likelihood. We then propose a two-stage algorithm \emph{T-SCI}, where we run WCCI in the first stage and apply quantile conformal inference to calibrate the results in the second stage. Theoretical analysis shows that T-SCI returns guaranteed coverage under milder assumptions than WCCI. We conduct extensive experiments on synthetic data and real data using different methods, which validate our analysis.} }
Endnote
%0 Conference Paper %T T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP %A Jiaye Teng %A Zeren Tan %A Yang Yuan %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-teng21a %I PMLR %P 10203--10213 %U https://proceedings.mlr.press/v139/teng21a.html %V 139 %X It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence interval of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP \citep{katzman2018deepsurv,kvamme2019time}), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first algorithm \emph{WCCI}, we revisit weighted conformal inference and introduce a new non-conformity score based on partial likelihood. We then propose a two-stage algorithm \emph{T-SCI}, where we run WCCI in the first stage and apply quantile conformal inference to calibrate the results in the second stage. Theoretical analysis shows that T-SCI returns guaranteed coverage under milder assumptions than WCCI. We conduct extensive experiments on synthetic data and real data using different methods, which validate our analysis.
APA
Teng, J., Tan, Z. & Yuan, Y.. (2021). T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:10203-10213 Available from https://proceedings.mlr.press/v139/teng21a.html.

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