# Individual Survival Curves with Conditional Normalizing Flows

arXiv: https://arxiv.org/abs/2107.12825 · HTML: https://mlsanity.com/paper/2107.12825/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 27 Jul 2021.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016)
- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
- [Graphical Normalizing Flows](https://mlsanity.com/paper/2006.02548/) (2020)
- [Countdown Regression: Sharp and Calibrated Survival Predictions](https://mlsanity.com/paper/1806.08324/) (2018)
- [Gaussian Processes for Survival Analysis](https://mlsanity.com/paper/1611.00817/) (2016)
- [Imitative Planning using Conditional Normalizing Flow](https://mlsanity.com/paper/2007.16162/) (2020)
- [A General Framework for Survival Analysis and Multi-State Modelling](https://mlsanity.com/paper/2006.04893/) (2020)

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

- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression](https://mlsanity.com/paper/2405.05429/) (2024)
- [Machine Learning in Epidemiology](https://mlsanity.com/paper/2602.16352/) (2026)
- [Proper Scoring Rules for Right-Censored Survival Data](https://mlsanity.com/paper/2606.06393/) (2026)

## Abstract (arXiv)

Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point of view of machine learning have been concerned with precise per-individual predictions instead of population studies, driven by the rise of individualized medicine. We introduce here a conditional normalizing flow based estimate of the time-to-event density as a way to model highly flexible and individualized conditional survival distributions. We use a novel hierarchical formulation of normalizing flows to enable efficient fitting of flexible conditional distributions without overfitting and show how the normalizing flow formulation can be efficiently adapted to the censored setting. We experimentally validate the proposed approach on a synthetic dataset as well as four open medical datasets and an example of a common financial problem.