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Conformalized Interval Arithmetic with Symmetric Calibration

AAAI 2025 · Probabilistic and scientific modeling › Uncertainty and Gaussian processes · approach: Conformal prediction methods · 3 citations (OpenAlex)

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Proposes Conformal Interval Arithmetic (CIA) with symmetric calibration to produce valid prediction intervals for sums/averages of multiple unknown labels, evaluated on group-average and shortest-path cost prediction tasks.

Problem

Conformal prediction gives valid intervals for single labels, but naive interval arithmetic over multiple labels fails to guarantee joint coverage; the sum/average of unknown labels over index sets (e.g., route costs, class averages) lacks valid prediction sets.

Approach

Use absolute residuals of group sums as conformity scores for split conformal prediction, and randomly assign indices to calibration/test with equal probability (symmetric calibration) so calibration group sums and test group sums are exchangeable; extend with stratification, overlap-tolerant bounds, and CQR scores.

Key results

• At alpha=0.1 on Bike, CIA (CQR) Stratified-type variants reach about 0.90 coverage while Bonferroni (Split) reaches 0.96 coverage with much larger intervals (25.84 vs about 4 for CIA).
• CIA variants achieve about 0.89-0.90 coverage at alpha=0.1 on Anaheim and Chicago, while the Group (Split) baseline falls to 0.75 coverage on Chicago.
• Normal (Hetero) baseline under-covers severely on MEPS (about 0.54 coverage at alpha=0.1), whereas CIA attains about 0.90.

Measured effects reported in the paper

Surprising findings

• Bonferroni correction over-covers strongly on most datasets (e.g., 0.99 on Anaheim) with very wide intervals.
• The group-sampling baseline loses validity on the traffic datasets because sampled edge weights are not exchangeable with shortest-path edges.

Limitations

• Validity under overlapping subsets holds only approximately, with a coverage gap that grows with overlap (Anaheim small gap).
• CQR-based sum intervals lose conditional validity since the sum of quantiles is not the quantile of the sum.

Experimental setup

Datasets: Bike Sharing Community Crime Medical Expenditure Panel Survey Anaheim road traffic Chicago road traffic

Benchmarks: Bike Sharing Community Crime MEPS 2019-2021 Anaheim Chicago

Metrics: empirical coverage prediction interval size

Baselines: Group sampling conformal prediction Normal confidence interval Bonferroni correction

Builds on: split conformal prediction conformalized quantile regression Bonferroni correction

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