# Efficient Training of Probabilistic Neural Networks for Survival Analysis

arXiv: https://arxiv.org/abs/2404.06421 · HTML: https://mlsanity.com/paper/2404.06421/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 9 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
- [Bayesian Learning for Neural Networks: an algorithmic survey](https://mlsanity.com/paper/2211.11865/) (2022)
- [An Effective Meaningful Way to Evaluate Survival Models](https://mlsanity.com/paper/2306.01196/) (2023)
- [BDNNSurv: Bayesian deep neural networks for survival analysis using pseudo values](https://mlsanity.com/paper/2101.03170/) (2021)
- [Uncertainty Estimation in Cancer Survival Prediction](https://mlsanity.com/paper/2003.08573/) (2020)

## Built on by (most cited first, 4 of 4)

- [Position: Stop Chasing the C-index when Evaluating Survival Analysis Models](https://mlsanity.com/paper/2506.02075/) (2025)
- [MENSA: A Multi-Event Network for Survival Analysis with Trajectory-based Likelihood Estimation](https://mlsanity.com/paper/2409.06525/) (2024)
- [Overcoming Dependent Censoring in the Evaluation of Survival Models](https://mlsanity.com/paper/2502.19460/) (2025)
- [SurvUnc: A Meta-Model Based Uncertainty Quantification Framework for Survival Analysis](https://mlsanity.com/paper/2505.14803/) (2025)

## Abstract (arXiv)

Variational Inference (VI) is a commonly used technique for approximate Bayesian inference and uncertainty estimation in deep learning models, yet it comes at a computational cost, as it doubles the number of trainable parameters to represent uncertainty. This rapidly becomes challenging in high-dimensional settings and motivates the use of alternative techniques for inference, such as Monte Carlo Dropout (MCD) or Spectral-normalized Neural Gaussian Process (SNGP). However, such methods have seen little adoption in survival analysis, and VI remains the prevalent approach for training probabilistic neural networks. In this paper, we investigate how to train deep probabilistic survival models in large datasets without introducing additional overhead in model complexity. To achieve this, we adopt three probabilistic approaches, namely VI, MCD, and SNGP, and evaluate them in terms of their prediction performance, calibration performance, and model complexity. In the context of probabilistic survival analysis, we investigate whether non-VI techniques can offer comparable or possibly improved prediction performance and uncertainty calibration compared to VI. In the MIMIC-IV dataset, we find that MCD aligns with VI in terms of the concordance index (0.748 vs. 0.743) and mean absolute error (254.9 vs. 254.7) using hinge loss, while providing C-calibrated uncertainty estimates. Moreover, our SNGP implementation provides D-calibrated survival functions in all datasets compared to VI (4/4 vs. 2/4, respectively). Our work encourages the use of techniques alternative to VI for survival analysis in high-dimensional datasets, where computational efficiency and overhead are of concern.