Conformal prediction under ambiguous ground truth

Conformal Prediction (CP) allows to perform rigorous uncertainty quantification by constructing a prediction set C(X) satisfying mathbbP(Y ∈ C(X))≥ 1-α for a user-chosen α ∈ [0,1] by relying on calibration data (X1,Y1),...,(Xn,Yn) from mathbbP=mathbbPX otimes mathbbPY|X. It is typically implicitly assumed that mathbbPY|X is the "true" posterior label distribution. However, in many real-world scenarios, the labels Y1,...,Yn are obtained by aggregating expert opinions using a voting procedure, resulting in a one-hot distribution mathbbPvoteY|X. For such ``voted'' labels, CP guarantees are thus w.r.t. mathbbPvote=mathbbPX otimes mathbbPvoteY|X rather than the true distribution mathbbP. In cases with unambiguous ground truth labels, the distinction between mathbbPvote and mathbbP is irrelevant. However, when experts do not agree because of ambiguous labels, approximating mathbbPY|X with a one-hot distribution mathbbPvoteY|X ignores this uncertainty. In this paper, we propose to leverage expert opinions to approximate mathbbPY|X using a non-degenerate distribution mathbbPaggY|X. We develop Monte Carlo CP procedures which provide guarantees w.r.t. mathbbPagg=mathbbPX otimes mathbbPaggY|X by sampling multiple synthetic pseudo-labels from mathbbPaggY|X for each calibration example X1,...,Xn. In a case study of skin condition classification with significant disagreement among expert annotators, we show that applying CP w.r.t. mathbbPvote under-covers expert annotations: calibrated for 72% coverage, it falls short by on average 10%; our Monte Carlo CP closes this gap both empirically and theoretically.