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Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach
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Proposes detect-then-impute conformal prediction (PDI-CP and JDI-CP) that handles cellwise outliers in test features by applying the same detection and imputation to calibration features, with JDI-CP giving a distribution-free 1-2α coverage guarantee.
Problem
Predictive intervals via conformal prediction lose exchangeability when some cells of the test feature are contaminated by cellwise outliers.
Approach
Wrap any detection and imputation procedure around conformal prediction: apply the same detect-then-impute to calibration features using the test-time mask, so calibration and processed test features become exchangeable (approximately for PDI-CP, pairwise via Jackknife+ for JDI-CP).
Key results
- On simulations with nominal 90% coverage, PDI-CP and JDI-CP maintain coverage near the target with interval lengths close to the oracle Baseline, while SCP and WCP fail to reach the target (WCP yields infinite-width intervals at epsilon=0.2).
- Theorem: JDI-CP achieves finite-sample coverage of at least 1-2α for arbitrary imputation rules under the sure detection assumption.
- Under DDC with varying thresholds (Table), PDI and JDI coverage stays around 0.895-0.909 for a 90% target across p from 0.99 to 0.5.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use detect-then-impute conformal prediction instead of SCP or WCP on contaminated test features | Conformal prediction with cellwise outliers · Synthetic data, Settings A–C | coverage | Helped |
| Use detect-then-impute conformal prediction instead of SCP or WCP on contaminated test features | Conformal prediction with cellwise outliers · Synthetic data, Settings A–C | prediction interval length | No clear effect |
| Use detect-then-impute conformal prediction instead of SCP or WCP | Airfoil · Airfoil | coverage | Helped |
| Use detect-then-impute conformal prediction instead of SCP or WCP | Wind direction prediction · Wind direction data | coverage | Helped |
| Use detect-then-impute conformal prediction instead of WCP | Riboflavin prediction · Riboflavin | coverage | Helped |
| Replace Mean Imputation with kNN or MICE (ablation) | PDI-CP and JDI-CP · Simulation | coverage | No clear effect |
| Use one-class SVM or cellMCD instead of DDC for detection (ablation) | PDI-CP and JDI-CP · Simulation, ε=0.1 | coverage | No clear effect |
| Lower the DDC threshold from p=0.99 to p=0.5 (ablation) | PDI-CP and JDI-CP · Setting A, ε=0.1 | coverage: PDI-CP: 0.902 -> 0.909; JDI-CP: 0.895 -> 0.904 | No clear effect |
| Lower the DDC threshold from p=0.99 to p=0.5 (ablation) | DDC · Setting A, ε=0.1 | FDR: 0.035 -> 0.793 | Hurt |
| Lower the DDC threshold from p=0.99 to p=0.5 (ablation) | DDC · Setting A, ε=0.1 | TPR: 0.987 -> 1 | Helped |
| Use the naive DI-plus-SCP construction without calibration-feature masks (ablation) | Naive-DI · Setting A, ε ∈ {0.1, 0.15, 0.2} | coverage | Hurt |
| Use conservative joint masking across calibration and test features (ablation) | C-JDI · Simulation | prediction interval length | Hurt |
Surprising findings
- Naive combination of DI with split conformal prediction fails to achieve 1-α coverage in several cases.
- WCP can output infinite-width prediction intervals when contamination probability is high.
Limitations
- PDI-CP coverage gap depends on false discoveries of the detector and mean imputation error; only 1-α guaranteed when detection has no false discoveries.
- JDI-CP only guarantees 1-2α coverage due to Jackknife+ limits.
- Coverage guarantees rely on the sure detection assumption and isolated detection; coverage beyond isolated detection is only characterized via gap terms.
Experimental setup
Datasets: airfoil self-noise (UCI) wind direction data (INMET station, Brazil) riboflavin gene expression (DSM)
Benchmarks: simulated Settings A, B, C airfoil wind direction riboflavin
Metrics: empirical marginal coverage average prediction interval length TPR FDR
Baselines: Baseline (oracle masking SCP) SCP WCP Naive-DI C-JDI
Builds on: split conformal prediction Jackknife+ DDC (detect deviating cells) weighted conformal prediction CP-MDA-Nested
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