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Censor Dependent Variational Inference
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Proposes censor-dependent variational inference (CDVI) and the CD-CVAE V-structure VAE, with IS and delta-method variants, for latent variable survival models with theoretical optimality analysis.
Problem
Vanilla variational inference for latent variable survival models uses a censoring-marginal variational distribution, which can be suboptimal (inference gap, latent non-identifiability, posterior collapse) under right censoring.
Approach
Make the variational distribution depend on the censoring indicator (q_{phi1}^delta q_{phi2}^(1-delta)), derive the optimal censor-dependent posterior, and implement it amortized in a V-structure conditional VAE (CD-CVAE) with importance-sampling and delta-method ELBO estimators.
Key results
- On simulated datasets, CD-CVAE with DVI reduces event/censor KL to the true posterior relative to vanilla CVAE (e.g., SD4 E-KL 2.29 vs 3.45 for CVAE).
- CD-CVAE attains the best C-index on WHAS (0.868 vs 0.811 for DSM/RSF-level baselines) and the best time-dependent C-index on NWTCO (0.751).
- Brier-score gains are modest: CD-CVAE best on FLCHAIN (0.110), NWTCO (0.075), and METABRIC (0.203).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use censor-dependent variational inference instead of vanilla CVAE inference | CVAE · Simulated survival datasets SD1–SD5 | E-KL: 1.65 vs 1.65 (SD1); 1.75 -> 1.66 (SD2); 2.79 -> 2.38 (SD3); 3.45 -> 2.88 (SD4); 5.42 -> 4.45 (SD5) | Helped |
| Use censor-dependent variational inference instead of vanilla CVAE inference | CVAE · Simulated survival datasets SD2–SD5 | C-KL: 2.70 -> 1.93 (SD2); 3.18 -> 3.13 (SD3); 4.04 -> 3.89 (SD4); 5.86 -> 5.55 (SD5) | Helped |
| Add importance sampling (IS) (ablation) | CD-CVAE · Simulated datasets SD2–SD5 | E-KL: 1.66 -> 1.64 (SD2); 2.38 -> 2.23 (SD3); 2.88 -> 2.64 (SD4); 4.45 -> 4.11 (SD5) | Helped |
| Add importance sampling (IS) (ablation) | CD-CVAE · Simulated datasets SD2–SD5 | C-KL: 1.93 -> 2.17 (SD2); 3.13 -> 3.21 (SD3); 3.89 -> 4.09 (SD4); 5.55 -> 5.56 (SD5) | Mixed |
| Add the delta method variant (DVI) (ablation) | CD-CVAE · Simulated datasets SD3–SD5 | E-KL: 2.38 -> 2.17 (SD3); 2.88 -> 2.29 (SD4); 4.45 -> 3.89 (SD5) | Helped |
| Add the delta method variant (DVI) (ablation) | CD-CVAE · Simulated datasets SD2–SD5 | C-KL: 1.93 -> 2.55 (SD2); 3.13 -> 3.13 (SD3); 3.89 -> 3.60 (SD4); 5.55 -> 5.51 (SD5) | Mixed |
| Use CD-CVAE instead of the strongest listed baseline | Survival prediction models · FLCHAIN | C-index: 0.801 -> 0.811 | Helped |
| Use CD-CVAE instead of the strongest listed baseline | Survival prediction models · WHAS | C-index: 0.786 -> 0.868 | Helped |
| Use CD-CVAE instead of the strongest listed baseline | Survival prediction models · METABRIC | C-index: 0.689 -> 0.681 | Hurt |
| Use CD-CVAE instead of the strongest listed baseline | Survival prediction models · PBC | C-index: 0.866 -> 0.863 | Hurt |
| Use CD-CVAE instead of the strongest listed baseline | Survival prediction models · FLCHAIN | Brier score: 0.115 -> 0.110 | Helped |
| Use CD-CVAE instead of the strongest listed baseline | Survival prediction models · SUPPORT | Brier score: 0.212 -> 0.218 | Hurt |
Surprising findings
- All-censoring simulated scenarios perform considerably worse than all-event scenarios, and IS/DVI yield little improvement there, suggesting amortization error dominates.
- The authors note that variants of CD-CVAE do not show substantial improvements in time-to-event performance overall, with Cox-PH with l2 regularization competitive on many datasets.
Limitations
- Improvements over state-of-the-art survival baselines are modest and not consistent across datasets and metrics.
- Theoretical guarantees rely on assumptions such as independent censoring and bounded/moment conditions; the sigma update has no closed form.
- Amortization effect may dominate the inference gap, especially for censored observations.
Experimental setup
Datasets: SUPPORT FLCHAIN NWTCO METABRIC WHAS GBSG PBC
Benchmarks: SUPPORT FLCHAIN NWTCO METABRIC WHAS GBSG PBC
Metrics: concordance index time-dependent concordance index Brier score KL divergence to true posterior
Baselines: CoxPH DeepSurv Deep Survival Machine (DSM) Random Survival Forest (RSF) Deep Cox Mixture (DCM) CVAE
Builds on: variational autoencoder importance weighted autoencoder deep survival machine
Closest papers by meaning
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