TriBet: Relative E-values for Online Machine-generated Text Detection

To ensure a formal guarantee that fully human-written text streams are *not falsely accused* as machine-generated text (MGT), the online betting framework (e-values) has been successfully applied on various existing detectors. However, current two-sample e-value methods fail in two real-world application scenarios: the false positive rate (FPR) is often out of control and the test power drops drastically when (1) the reference domain is similar but not exactly same as test domain (cross-domain), or (2) proxy model of detector is outdated compared to the modern source model. We identify the root cause as an online calibration dilemma: two-sample optimization and betting relies on a null-calibrating offset that is unidentifiable from unlabeled test streams under shift. We resolve this with a triple-sample betting framework (TriBet) that conduct online MGT detection as relative testing against both human and machine references using a witness score, and introduces a conformal test-inclusive domain-shift betting strategy to achieve FPR control without fragile online calibration. We show that TriBet is a level-$\alpha$ sequential test with asymptotic power one, and characterize its expected stopping time. Empirically, we evaluate on 15 source LLMs, 8 proxy models and mixed-document streams, TriBet consistently delivers faster and more powerful detection than both oracle and online betting baselines while keeping FPR strictly controlled.