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Multi-Source Conformal Inference Under Distribution Shift
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Derives efficient influence functions for target-site conformal quantiles under multi-source missing outcomes and proposes a data-adaptive federated weighting of source sites to get valid, efficient prediction intervals under distribution shift.
Problem
Constructing distribution-free prediction intervals for missing outcomes in a target site when multiple heterogeneous source sites have covariate shift and possibly different conditional outcome distributions, with privacy constraints on data sharing.
Approach
Uses semiparametric efficient influence functions for the conformal-score quantile under common conditional outcome distribution (CCOD), plus a per-source influence function under a working partial CCOD assumption, and aggregates site-specific quantiles with penalized data-adaptive federated weights that downweight sites whose quantiles differ from the target. Cross-fitting with SuperLearner nuisa
Key results
- Federated method achieves nominal marginal coverage with shorter intervals than the target-only method, with widths close to the oracle width (~3.29) in simulations with n=3000 under strong heterogeneity and CCOD violation.
- Pooled sample method under ASR is overly conservative, with interval widths about five times longer than the federated method.
- In the Norwood LOS application, the federated method yields tighter intervals than target-only; e.g., for a South-region patient with local ASR at 80% the interval is over 30 days shorter.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use federated weighting instead of target-only estimation | MuSCI prediction intervals · synthetic simulations, strong covariate and concept shift | marginal coverage | Helped |
| use federated weighting instead of target-only estimation | MuSCI prediction intervals · synthetic simulations, strong covariate and concept shift | prediction interval width | Helped |
| assume CCOD and pool the samples rather than use federated weighting | pooled sample method · synthetic simulations, ASR score, strong covariate and concept shift | prediction interval width | Hurt |
| assume CCOD and pool the samples rather than use federated weighting | pooled sample method · synthetic simulations, ASR score, strong covariate and concept shift | marginal coverage | Hurt |
| use pooled samples rather than federated weighting | pooled sample method · synthetic simulations, local ASR score, strong covariate and concept shift | marginal coverage | Hurt |
| use local ASR rather than ASR | conformal score selection · synthetic simulations with small sample sizes | robustness to heteroscedasticity | Helped |
| use CQR rather than local ASR | conformal score selection · synthetic simulations with larger sample sizes | marginal coverage | Helped |
| use CQR rather than local ASR | conformal score selection · synthetic simulations with small sample sizes | sample size needed to attain nominal coverage | Hurt |
| use federated weighting instead of target-only estimation | MuSCI prediction intervals · STS-CHSD Norwood surgery LOS application | prediction interval width | Helped |
| use federated weighting rather than full pooling | MuSCI prediction intervals · STS-CHSD Norwood surgery LOS application | prediction interval width | No clear effect |
Surprising findings
- The pooled sample (CCOD) method performs poorly under ASR, being overly conservative, and ASR itself is not robust in conditional coverage.
Limitations
- Efficient influence function derivation under CCOD requires the assumption that conditional outcome distributions are shared; data-adaptive weighting only addresses partial violations.
- MAR assumption is untestable and is assumed in the application.
- Covariate-adaptive ensemble weights are left to future work.
Experimental setup
Datasets: simulated multi-site data (5 sites) STS Congenital Heart Surgery Database (Norwood procedures, 2016-2022)
Benchmarks: simulated multi-site DGPs (162 scenarios) STS-CHSD Norwood length-of-stay data
Metrics: marginal coverage prediction interval width conditional coverage federated weights vs discrepancy
Baselines: target-only nonparametric conformal method pooled sample (CCOD) method
Builds on: conformal prediction under covariate shift robust prediction intervals under covariate shift (Lei and Candès / Yang et al.) trans-Lasso adaptive Lasso SuperLearner
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