Survival Mixture Density Networks

Xintian Han, Mark Goldstein, Rajesh Ranganath
Proceedings of the 7th Machine Learning for Healthcare Conference, PMLR 182:224-248, 2022.

Abstract

Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v182-han22a, title = {Survival Mixture Density Networks}, author = {Han, Xintian and Goldstein, Mark and Ranganath, Rajesh}, booktitle = {Proceedings of the 7th Machine Learning for Healthcare Conference}, pages = {224--248}, year = {2022}, editor = {Lipton, Zachary and Ranganath, Rajesh and Sendak, Mark and Sjoding, Michael and Yeung, Serena}, volume = {182}, series = {Proceedings of Machine Learning Research}, month = {05--06 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v182/han22a/han22a.pdf}, url = {https://proceedings.mlr.press/v182/han22a.html}, abstract = {Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.} }
Endnote
%0 Conference Paper %T Survival Mixture Density Networks %A Xintian Han %A Mark Goldstein %A Rajesh Ranganath %B Proceedings of the 7th Machine Learning for Healthcare Conference %C Proceedings of Machine Learning Research %D 2022 %E Zachary Lipton %E Rajesh Ranganath %E Mark Sendak %E Michael Sjoding %E Serena Yeung %F pmlr-v182-han22a %I PMLR %P 224--248 %U https://proceedings.mlr.press/v182/han22a.html %V 182 %X Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.
APA
Han, X., Goldstein, M. & Ranganath, R.. (2022). Survival Mixture Density Networks. Proceedings of the 7th Machine Learning for Healthcare Conference, in Proceedings of Machine Learning Research 182:224-248 Available from https://proceedings.mlr.press/v182/han22a.html.

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