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Robust Conditional Conformal Prediction via Branched Normalizing Flow

NeurIPS 2026 · Learning theory and algorithms › Prediction and decision losses · approach: Conformal prediction sets · 0 citations (OpenAlex)

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Bounds conditional coverage gap under distribution shift by Wasserstein distance between calibration and test joint distributions, and proposes Branched Normalizing Flow (augmented, with CQR) to normalize test inputs and map prediction sets back to the test distribution.

Problem

Split conformal prediction loses conditional coverage under distribution shift (especially multi-source domain generalization), since existing methods only align marginal conformal score distributions.

Approach

Bound the integrated conditional coverage gap by the joint Wasserstein distance between calibration and test distributions, then learn a two-branch invertible flow (input branch independent of label, label branch with Gaussian noise augmentation) that pushes the test distribution onto the calibration distribution; CQR is applied in normalized space and the set is mapped back via the inverse label

Key results

• Augmented BNF + CQR achieves the lowest WSCG among compared methods with marginal coverage and WSC close to 0.9 across datasets (box plots, 10 trials, 100 test mixtures each).
• Augmented BNF + CQR under distribution shift approaches i.i.d. CQR performance, though CQR itself shows nonzero WSCG even under i.i.d. data.
• Augment-Conditioned BNF significantly reduces prediction set size under MSDG while preserving coverage robustness.

Surprising findings

• Even under i.i.d. data, CQR exhibits nonzero WSCG due to its own approximation error.

Limitations

• Empirical optimization of Wasserstein objective means transformed test data may not perfectly match calibration distribution, so WSCG is not fully eliminated.
• Requires a mild structural assumption (factorized architecture) relating P and Q labeling processes.
• Source-agnostic noise makes Augmented BNF prediction sets larger under MSDG.

Experimental setup

Datasets: PTS Bike Rental Seattle-Loop PEMSD4 PEMSD8 MIMIC-IV eICU U.S. ILI collaborating hospital data

Benchmarks: PTS Bike Rental Seattle-Loop PEMSD4 PEMSD8 MIMIC-IV eICU U.S. ILI

Metrics: marginal coverage worst-slice coverage (WSC) worst-slice coverage gap (WSCG) prediction set size

Baselines: Split CP Importance-Weighted CP Worst-Case CP Wasserstein-Regularized CP CQR

Builds on: conformalized quantile regression Real NVP normflows Wasserstein-regularized conformal prediction worst-slice coverage

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