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When Does Trimming Help Conformal Prediction? A Retained-Law Diagnostic under Calibration Contamination

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

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Analyses fixed-threshold trimming of contaminated calibration data as conditioning that induces a retained law, giving an exact finite-sample coverage identity, a componentwise diagnostic (clean covariance cost plus retained-contamination cost), and certificate templates.

Problem

Clean-target coverage of split conformal prediction when calibration data are contaminated and the practitioner trims suspicious calibration points with a fixed anomaly-score threshold; when does trimming help?

Approach

Treat trimming as conditioning the contaminated calibration law on a retention event, yielding a retained law R; clean coverage then reduces to a one-dimensional score-CDF transfer gap between R and P, which decomposes into a clean-side covariance cost and a retained-contamination cost governed by the dirty-to-clean retention ratio.

Key results

• Ordinary split conformal clean coverage 0.8709 under epsilon=0.2; Stein trimming at q=0.990 raises coverage to 0.8950 (clean oracle 0.8984).
• Without retention-probability separation (p_d about p_c), retained mixture coefficient equals epsilon (0.200) and trimming gives coverage 0.8754, not helping.
• With m=10,000, coverage stays at about 0.8888 for Stein q=0.950, limited by retained-to-clean score-law transfer rather than sample size.

Surprising findings

• Increasing calibration size to 10,000 does not raise coverage above the population-level mixture bound; the limit is the score-law transfer, not finite-sample slack.
• Covariate-only trimming provides no benefit when contamination is label-only, and ordinary split conformal over-covers in that case.

Limitations

• Guarantees are marginal in the clean test point, not conditional or subgroup-conditional, and not adversarial-contamination valid.
• Sharpness holds only within the scalar-discrepancy information class.
• Experiments are a single synthetic setting; population diagnostics use known simulation laws and conservative certificates are loose.

Experimental setup

Datasets: synthetic heteroscedastic regression

Benchmarks: synthetic heteroscedastic regression with covariate contamination

Metrics: clean coverage interval width population diagnostics (p_c, p_d, mixture coefficient, trimm conservative lower bound

Baselines: ordinary split conformal clean oracle calibration worst-case robust quantile correction

Builds on: split conformal prediction Huber epsilon-contamination model conformalised quantile regression

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