Enhancing Conformal E-value Thresholds

E-values provide a convenient framework for hypothesis testing and aggregating evidence, but their standard rejection rule relies on Markov's inequality and uses a generic threshold, which can be conservative. We work in a conformal prediction framework, where we exploit the known finite-sample distribution of conformal p-values to derive smaller deterministic thresholds for the average of arbitrary dependent e-values constructed with any p-to-e calibrator, while preserving the finite-sample coverage guarantee. The main idea is to combine a refined Markov inequality with tailored deterministic bounds, leading to an optimization problem whose solution yields a rejection threshold smaller than the classical threshold. We apply the method to e-cross-conformal prediction, where experiments show that our methodology often yields shorter and more stable prediction sets than randomized thresholding. Unlike the latter, our method is deterministic and reproducible.