Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification
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Proposes NeuralSurv, a fully Bayesian deep survival model that combines Pólya-Gamma and marked Poisson process data augmentation with local linearization of a BNN and mean-field CAVI for continuous-time uncertainty-aware survival prediction.
Problem
Deep survival models are frequentist and provide no coherent uncertainty quantification, which limits trust in high-stakes, data-scarce settings; existing Bayesian survival methods (e.g., GPs) scale poorly to high-dimensional covariates.
Approach
A sigmoidal continuous-time hazard with a BNN modulating a Weibull baseline is made conjugate via Pólya-Gamma augmentation of the sigmoid and marked Poisson process augmentation of the integral, combined with first-order local linearization of the BNN around the MAP so mean-field CAVI has closed-form updates linear in the number of weights.
Key results
- On COLON, NeuralSurv reports IPCW IBS 0.218 (best) and C-index 0.671 (best) over the 5-split comparison table.
- On real datasets, NeuralSurv achieves the best IPCW IBS on seven of eight datasets and passes D-calibration consistently.
- NeuralSurv ranks fifth in KM-calibration, a noted weakness; it is best on C-index in four datasets and second best in three.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NeuralSurv instead of the strongest listed deep-survival baseline | Deep survival models · COLON | C-index: 0.584 -> 0.671 | Helped |
| Use NeuralSurv instead of the strongest listed deep-survival baseline | Deep survival models · COLON | IPCW IBS: 0.241 -> 0.218 | Helped |
| Use NeuralSurv instead of the strongest listed deep-survival baseline | Deep survival models · METABRIC | C-index: 0.616 -> 0.584 | Hurt |
| Use NeuralSurv instead of the strongest listed deep-survival baseline | Deep survival models · METABRIC | IPCW IBS: 0.223 -> 0.212 | Helped |
| Use NeuralSurv instead of the strongest listed deep-survival baseline | Deep survival models · GBSG | C-index: 0.655 -> 0.657 | Helped |
| Use NeuralSurv instead of the strongest listed deep-survival baseline | Deep survival models · GBSG | IPCW IBS: 0.229 -> 0.188 | Helped |
Surprising findings
- NeuralSurv ranks fifth on KM-calibration despite strong IBS and D-calibration results.
- The paper reports mild-to-moderate sensitivity of the posterior to the prior on phi.
Limitations
- Assumes a sigmoidal hazard function that may not capture all risk dynamics.
- Mean-field factorization ignores posterior correlations between phi and theta, and linearization around MAP may miss secondary modes.
- Full-dataset coordinate-ascent passes each iteration are a bottleneck for very large cohorts.
Experimental setup
Datasets: COLON METABRIC GBSG NWTCO WHAS SUPPORT VLC Sac 3 simulation study synthetic LogNormal survival data
Benchmarks: COLON METABRIC GBSG NWTCO WHAS SUPPORT VLC Sac 3 synthetic survival data
Metrics: C-index IPCW integrated Brier score D-calibration KM calibration
Baselines: MTLR DeepHit DeepSurv Logistic Hazard CoxTime CoxCC PMF PCHazard BCESurv DySurv Sumo-Net DQS
Builds on: Pólya-Gamma augmentation Delta method variational inference DeepHit Sumo-Net DQS
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