# Conditional Distribution Function Estimation Using Neural Networks for Censored and Uncensored Data

arXiv: https://arxiv.org/abs/2207.02384 · HTML: https://mlsanity.com/paper/2207.02384/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 6 Jul 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [A Scalable Discrete-Time Survival Model for Neural Networks](https://mlsanity.com/paper/1805.00917/) (2018)
- [Sparse-Input Neural Networks for High-dimensional Nonparametric Regression and Classification](https://mlsanity.com/paper/1711.07592/) (2017)
- [SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks](https://mlsanity.com/paper/2008.08637/) (2020)
- [Survival Analysis via Ordinary Differential Equations](https://mlsanity.com/paper/2009.03449/) (2020)

## Built on by (most cited first, 7 of 7)

- [Inverting estimating equations for causal inference on quantiles](https://mlsanity.com/paper/2401.00987/) (2024)
- [Conformalized Percentile Interval: Finite Sample Validity and Improved Conditional Performance](https://mlsanity.com/paper/2605.03233/) (2026)
- [Generalized Distribution Prediction for Asset Returns](https://mlsanity.com/paper/2410.23296/) (2024)
- [Flexible Deep Neural Networks for Partially Linear Survival Data: Estimation and Survival Inference](https://mlsanity.com/paper/2512.10570/) (2025)
- [Subgroup Discovery with the Cox Model](https://mlsanity.com/paper/2512.20762/) (2025)
- [Deep Optimal Individualized Treatment Rules for Bivariate Survival Outcomes via Adaptive Prediction-Powered Learning](https://mlsanity.com/paper/2605.29464/) (2026)
- [Random Hazard Forests](https://mlsanity.com/paper/2608.21597/) (2026)

## Abstract (arXiv)

Most work in neural networks focuses on estimating the conditional mean of a continuous response variable given a set of covariates.In this article, we consider estimating the conditional distribution function using neural networks for both censored and uncensored data. The algorithm is built upon the data structure particularly constructed for the Cox regression with time-dependent covariates. Without imposing any model assumption, we consider a loss function that is based on the full likelihood where the conditional hazard function is the only unknown nonparametric parameter, for which unconstraint optimization methods can be applied. Through simulation studies, we show the proposed method possesses desirable performance, whereas the partial likelihood method and the traditional neural networks with L2 loss yield biased estimates when model assumptions are violated. We further illustrate the proposed method with several real-world data sets. The implementation of the proposed methods is made available at https://github.com/bingqing0729/NNCDE.