Conformal prediction under ambiguous ground truth

Code

• github.com/google-deepmind/uncertain_ground_truth
  Officialjax★ 678
• github.com/alaalab/webcp
  pytorch★ 7

Abstract

Conformal Prediction (CP) allows to perform rigorous uncertainty quantification by constructing a prediction set C(X) satisfying P(Y C(X)) 1- for a user-chosen [0,1] by relying on calibration data (X_1,Y_1),...,(X_n,Y_n) from P=P^X P^Y|X. It is typically implicitly assumed that P^Y|X is the "true" posterior label distribution. However, in many real-world scenarios, the labels Y_1,...,Y_n are obtained by aggregating expert opinions using a voting procedure, resulting in a one-hot distribution P_vote^Y|X. For such ``voted'' labels, CP guarantees are thus w.r.t. P_vote=P^X P_vote^Y|X rather than the true distribution P. In cases with unambiguous ground truth labels, the distinction between P_vote and P is irrelevant. However, when experts do not agree because of ambiguous labels, approximating P^Y|X with a one-hot distribution P_vote^Y|X ignores this uncertainty. In this paper, we propose to leverage expert opinions to approximate P^Y|X using a non-degenerate distribution P_agg^Y|X. We develop Monte Carlo CP procedures which provide guarantees w.r.t. P_agg=P^X P_agg^Y|X by sampling multiple synthetic pseudo-labels from P_agg^Y|X for each calibration example X_1,...,X_n. In a case study of skin condition classification with significant disagreement among expert annotators, we show that applying CP w.r.t. P_vote 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.

Tasks

Reproductions