Theoretical guarantees under approximate label-conditional likelihood-ratio estimation

Establish theoretical guarantees for conformal prediction under approximate label-conditional likelihood-ratio estimation under reasonable assumptions on the data distribution, such as bounds on the divergence between the feature distributions conditional on the two labels.

Background

The paper applies weighted Mondrian conformal prediction to gravitational-wave search-pipeline outputs when the calibration and test distributions differ. Exact validity requires the label-conditional likelihood ratios between the test and calibration feature distributions, but these ratios cannot generally be consistently estimated because the test labels are unknown. The authors therefore introduce practical marginal, semi-conditional, and pseudo-label-based approximations.

Because approximation error in the estimated weights can induce bias in the conformal prediction sets, the impact on coverage cannot be bounded without additional assumptions. The paper identifies deriving theoretical guarantees under reasonable distributional assumptions—such as bounds on the divergence between the class-conditional feature distributions—as an unresolved direction for future work.