# Survival Analysis as Imprecise Classification with Trainable Kernels

arXiv: https://arxiv.org/abs/2506.10140 · HTML: https://mlsanity.com/paper/2506.10140/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 73 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [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)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [High-Dimensional Survival Analysis: Methods and Applications](https://mlsanity.com/paper/2205.02948/) (2022)
- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [DNNSurv: Deep Neural Networks for Survival Analysis Using Pseudo Values](https://mlsanity.com/paper/1908.02337/) (2019)
- [MHAttnSurv: Multi-Head Attention for Survival Prediction Using Whole-Slide Pathology Images](https://mlsanity.com/paper/2110.11558/) (2021)
- [A General Machine Learning Framework for Survival Analysis](https://mlsanity.com/paper/2006.15442/) (2020)
- [Deep Kernel Survival Analysis and Subject-Specific Survival Time Prediction Intervals](https://mlsanity.com/paper/2007.12975/) (2020)
- [Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee](https://mlsanity.com/paper/2206.10477/) (2022)
- [Hierarchical Transformer for Survival Prediction Using Multimodality Whole Slide Images and Genomics](https://mlsanity.com/paper/2211.16632/) (2022)
- [Survival analysis as a classification problem](https://mlsanity.com/paper/1909.11171/) (2019)
- [Adaptive Transformer Modelling of Density Function for Nonparametric Survival Analysis](https://mlsanity.com/paper/2409.06209/) (2024)
- [Kernel Cox partially linear regression: building predictive models for cancer patients' survival](https://mlsanity.com/paper/2310.07187/) (2023)

## Built on by (most cited first, 2 of 2)

- [Attention-Based Estimation of the Individual Treatment Benefit Probability under Dose Variation](https://mlsanity.com/paper/2606.13821/) (2026)
- [Surv-IPTB: An Attention-Based Model for Estimating Individual Probability of Treatment Benefit with Survival Data](https://mlsanity.com/paper/2608.06288/) (2026)

## Abstract (arXiv)

Survival analysis is a fundamental tool for modeling time-to-event data in healthcare, engineering, and finance, where censored observations pose significant challenges. While traditional methods like the Beran estimator offer nonparametric solutions, they often struggle with the complex data structures and heavy censoring. This paper introduces three novel survival models, iSurvM (the imprecise Survival model based on Mean likelihood functions), iSurvQ (the imprecise Survival model based on the Quantiles of likelihood functions), and iSurvJ (the imprecise Survival model based on the Joint learning), that combine imprecise probability theory with attention mechanisms to handle censored data without parametric assumptions. The first idea behind the models is to represent censored observations by interval-valued probability distributions for each instance over time intervals between events moments. The second idea is to employ the kernel-based Nadaraya-Watson regression with trainable attention weights for computing the imprecise probability distribution over time intervals for the entire dataset. The third idea is to consider three decision strategies for training, which correspond to the proposed three models. Experiments on synthetic and real datasets demonstrate that the proposed models, especially iSurvJ, consistently outperform the Beran estimator from the accuracy and computational complexity points of view. Codes implementing the proposed models are publicly available.