# SSH-Net: A Deep Neural Network for Predicting Failure Time Distribution Functions under Competing Risks with Application to GPU Data

arXiv: https://arxiv.org/abs/2606.20451 · HTML: https://mlsanity.com/paper/2606.20451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 18 Jun 2026.

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

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Continuous and Discrete-Time Survival Prediction with Neural Networks](https://mlsanity.com/paper/1910.06724/) (2019)
- [Deep Recurrent Survival Analysis](https://mlsanity.com/paper/1809.02403/) (2018)
- [Neural Fine-Gray: Monotonic neural networks for competing risks](https://mlsanity.com/paper/2305.06703/) (2023)
- [A Spatially Correlated Competing Risks Time-to-Event Model for Supercomputer GPU Failure Data](https://mlsanity.com/paper/2303.16369/) (2023)
- [The Use of Variational Inference for Lifetime Data with Spatial Correlations](https://mlsanity.com/paper/2507.09559/) (2025)

## Abstract (arXiv)

Competing risks are commonly observed in engineering fields and can bring challenges to time-to-event data modeling when the application scenarios are complicated. Recently, deep neural networks have received great attention for prediction with competing risks, due to their flexibility and high learning capability. However, the complexity of neural network structure brings extra difficulty in hyperparameter tuning based on different data inputs. Additionally, when an engineered system has complex physical structures with multiple hierarchical levels, treating all structural levels as a single group of inputs may fail to capture critical information. To address the issues, we propose a Structured Segmented Hazard Deep Neural Network (SSH-Net) for failure time prediction under cause-specific competing risks framework. Our approach associates neural network structure with data structures, and allows different covariate groups to impact the failure prediction through separate sub-networks. The neural network is constructed based on a cause-specific competing risks model. The SSH-Net outputs cause-specific hazard functions, and utilizes the penalized log-likelihood as the loss function. The prediction accuracy of SSH-Net is validated through simulation studies by evaluating the Brier score, the area under receiver operating characteristic curves (AUC), and the root mean square error (RMSE) of the predicted cause-specific cumulative incident function. We further demonstrate the model's ability to predict failure time distribution functions using the Titan GPU failure time data.