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| "The optimal collaborative prediction set C*(x) has a two-threshold form: it augments the human-proposed set H(x) with labels whose score exceeds threshold a*, and prunes labels within H(x) whose score exceeds threshold b* (Theorem 2.1, Section 2).", | |
| "The counterfactual harm principle requires P(Y not in C(X) | Y in H(X)) < epsilon, i.e., the AI must not remove correct labels the human already proposed (Section 1).", | |
| "The complementarity principle requires P(Y in C(X) | Y not in H(X)) >= 1-delta, i.e., the AI must recover correct labels the human missed (Section 1).", | |
| "The offline calibration procedure gives distribution-free finite-sample coverage guarantees whose bounds depend on the sizes of the calibration sets used to fit a* and b* (Proposition 4.1, Section 4.1).", | |
| "The CUP-Online algorithm updates thresholds a_t and b_t via stochastic approximation steps (a_{t+1}=a_t+eta(1{s(x_t,y_t)>a_t}-delta), and analogously for b_t) to track target error rates under arbitrary distribution shift, including shifts caused by humans adapting their behavior to the AI (Section 4.2, Proposition 4.2)." | |
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