Conformal prediction under ambiguous ground truth

TL;DR

This paper addresses the challenge of conformal prediction when labels are ambiguous due to expert disagreement, proposing Monte Carlo methods to better quantify uncertainty by modeling the true label distribution.

Contribution

It introduces Monte Carlo conformal prediction procedures that incorporate expert opinion distributions to improve uncertainty quantification under ambiguous labels.

Findings

Monte Carlo CP achieves better coverage in ambiguous label scenarios.

Applying CP w.r.t. voted labels underestimates true uncertainty.

Case study on skin condition classification demonstrates improved calibration.

Abstract

Conformal Prediction (CP) allows to perform rigorous uncertainty quantification by constructing a prediction set $C(X)$ satisfying $\mathbb{P}(Y \in C(X))\geq 1-\alpha$ for a user-chosen $\alpha \in [0,1]$ by relying on calibration data $(X_1,Y_1),...,(X_n,Y_n)$ from $\mathbb{P}=\mathbb{P}^{X} \otimes \mathbb{P}^{Y|X}$. It is typically implicitly assumed that $\mathbb{P}^{Y|X}$ 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 $\mathbb{P}_{vote}^{Y|X}$. For such ``voted'' labels, CP guarantees are thus w.r.t. $\mathbb{P}_{vote}=\mathbb{P}^X \otimes \mathbb{P}_{vote}^{Y|X}$ rather than the true distribution $\mathbb{P}$. In cases with unambiguous ground truth labels, the distinction between $\mathbb{P}_{vote}$ and $\mathbb{P}$ is irrelevant. However, when experts do not agree because of ambiguous labels, approximating $\mathbb{P}^{Y|X}$ with a one-hot distribution $\mathbb{P}_{vote}^{Y|X}$ ignores this uncertainty. In this paper, we propose to leverage expert opinions to approximate $\mathbb{P}^{Y|X}$ using a non-degenerate distribution $\mathbb{P}_{agg}^{Y|X}$. We develop Monte Carlo CP procedures which provide guarantees w.r.t. $\mathbb{P}_{agg}=\mathbb{P}^X \otimes \mathbb{P}_{agg}^{Y|X}$ by sampling multiple synthetic pseudo-labels from $\mathbb{P}_{agg}^{Y|X}$ 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. $\mathbb{P}_{vote}$ 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.