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Online Differentially Private Conformal Prediction for Uncertainty Quantification
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Proposes an online differentially private conformal prediction framework (ODPCP) that privatizes a coin-betting quantile tracker of non-conformity scores, extended to conformal quantile regression (ODPCQR), with long-run coverage guarantees.
Problem
Conformal prediction on streaming data with distribution shifts is hard to combine with differential privacy, since existing private CP methods are offline and need full dataset access.
Approach
Estimate the (1-alpha)-quantile of non-conformity scores online via a parameter-free coin-betting (KT estimator) update on noisy pinball-loss subgradients, so each one-pass update satisfies DP; extend to CQR for heteroscedastic intervals.
Key results
- On synthetic Setting 2 with µ=2 GDP, ODPCP long-run coverage is 0.886 vs 0.888 for the non-private Original (target 0.9), with width 5.23 vs 5.18 in Case 1.
- With µ=0.5 GDP, coverage drops to about 0.85 for CP in Case 1 (0.850) while width grows to 7.69 vs 5.18 for Original.
- ODPCQR keeps coverage near 0.895 across µ values in Setting 2 and gives shorter intervals than ODPCP under strong privacy, per the authors.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add µ-GDP noise to ODPCP (reduce µ from 2 to 0.5) | ODPCP · Setting 2, Cases 1–6 | long-run coverage: 0.886 -> 0.850 (Case 1); 0.886 -> 0.841 (Case 2) | Hurt |
| add µ-GDP noise to ODPCP (reduce µ from 2 to 0.5) | ODPCP · Setting 2, Cases 1–6 | long-run width: 5.23 -> 7.69 (Case 1); 6.56 -> 9.68 (Case 2) | Hurt |
| use conformal quantile regression instead of conformal prediction | ODPCP · Setting 2, Cases 1–6 with strong privacy | long-run coverage: 0.850 -> 0.895 (Case 1); 0.841 -> 0.896 (Case 2), µ=0.5 | Helped |
| use conformal quantile regression instead of conformal prediction | ODPCP · Setting 2, Cases 1–6 with strong privacy | long-run width: 7.69 -> 5.90 (Case 1); 9.68 -> 7.24 (Case 2), µ=0.5 | Helped |
| use a privately trained LDPSGD base model instead of SGD | ODPCP · Setting 1, Cases 1–2 | long-run width: 3.23 -> 5.05 (Case 1, Original); 3.26 -> 5.16 (Case 1, µ=2) | Hurt |
| use a privately trained LDPSGD base model instead of SGD | ODPCP · Setting 1, Cases 1–2 | long-run coverage: 0.887 -> 0.888 (Case 1, µ=2) | No clear effect |
| vary the truncation constant c (ablation) | ODPCP · Setting 2 dataset | coverage | Mixed |
| vary the initialization parameters (λ1, W0) (ablation) | ODPCP · simulations | coverage | No clear effect |
Surprising findings
- Privacy noise in the quantile update can slightly raise coverage in ODPCQR at strong privacy, which the authors attribute to wider intervals compensating for noise.
Limitations
- Long-run coverage guarantee only (asymptotic), not finite-sample per-step coverage
- Privacy-induced noise widens prediction intervals and increases volatility at strong privacy levels
- Assumes bounded non-conformity scores in the theory
Experimental setup
Datasets: synthetic regression data (Settings 1 and 2) ELEC2 PAMAP2
Benchmarks: synthetic Settings 1 and 2 ELEC2 NSWdemand PAMAP2 heart rate subject 102
Metrics: long-run coverage long-run interval width rolling coverage
Baselines: Original (Podkopaev et al., 2024 non-private online CP) DPCP (Angelopoulos et al., 2022)
Builds on: conformal prediction coin-betting parameter-free online convex optimization conformal quantile regression Gaussian differential privacy DPCP
Closest papers by meaning
- Certification for Differentially Private Prediction in Gradient-Based Training (ICML 2025 · similarity 0.87)
- Robust Conformal Prediction Using Privileged Information (NeurIPS 2024 · similarity 0.86)
- Rectifying Conformity Scores for Better Conditional Coverage (ICML 2025 · similarity 0.86)
- Instance-Specific Asymmetric Sensitivity in Differential Privacy (NeurIPS 2024 · similarity 0.86)
- Exploring the Noise Robustness of Online Conformal Prediction (NeurIPS 2025 · similarity 0.86)
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