Papers › Conformal prediction under ambiguous ground truth

Conformal prediction under ambiguous ground truth

18 Jul 2023arXiv:2307.09302archive 2025-07-28

David Stutz, Abhijit Guha Roy, Tatiana Matejovicova, Patricia Strachan, Ali Taylan Cemgil, Arnaud Doucet

Conformal Prediction (CP) allows to perform rigorous uncertainty quantification by constructing a prediction set C(X) satisfying ℙ(Y ∈C(X))≥1-α for a user-chosen α∈[0,1] by relying on calibration data (X₁,Y₁),...,(Xₙ,Yₙ) 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 Y₁,...,Yₙ are obtained by aggregating expert opinions using a voting procedure, resulting in a one-hot distribution ℙᵥₒₜₑ^(Y|X). For such ``voted'' labels, CP guarantees are thus w.r.t. ℙᵥₒₜₑ=ℙ^X ⊗ℙᵥₒₜₑ^(Y|X) rather than the true distribution ℙ. In cases with unambiguous ground truth labels, the distinction between ℙᵥₒₜₑ and ℙ is irrelevant. However, when experts do not agree because of ambiguous labels, approximating ℙ^(Y|X) with a one-hot distribution ℙᵥₒₜₑ^(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 X₁,...,Xₙ. In a case study of skin condition classification with significant disagreement among expert annotators, we show that applying CP w.r.t. ℙᵥₒₜₑ 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.

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