Conformal prediction under ambiguous ground truth (2307.09302v2)

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.

• The paper introduces Monte Carlo conformal prediction to address limitations of classical CP by effectively handling ambiguous label distributions.
• It empirically validates the approach in skin condition classification, achieving improved coverage guarantees that align closely with expected uncertainty levels.
• The method extends to multi-label and augmented data scenarios, providing adaptable and robust solutions for real-world applications with high uncertainty.

Conformal Prediction under Ambiguous Ground Truth: A Detailed Overview

The paper presents a significant advancement in the domain of Conformal Prediction (CP) by addressing the challenges posed by ambiguous ground truth in classification tasks. The work focuses on improving the reliability of prediction sets when label uncertainty is high, particularly in the presence of ambiguous or multiple interpretations of label data.

Key Contributions

1. Problem Context and Motivation: The authors highlight a gap in the classical CP approach, which assumes that calibration data represents a one-hot distribution reflecting the true posterior label distribution. This assumption often falls short in practical applications where labels are derived via expert opinion aggregation, leading to potential underestimation of uncertainty. Ambiguities in datasets, including renowned benchmarks like ImageNet and CIFAR10, motivate the need for a more robust system capable of dealing with uncertainty more effectively.
2. Monte Carlo Conformal Prediction: The paper proposes a novel approach, Monte Carlo CP, capable of providing more representative uncertainty bounds by leveraging expert opinions to approximate the true distribution of labels. Monte Carlo CP utilizes non-degenerate distributions for labels, obtained through processes such as expert voting, to better approximate the real distribution of possible labels. This is achieved via sampling synthetic pseudo-labels from an estimated distribution for each calibration example.
3. Empirical and Theoretical Validation: The proposed methodology is verified through a case paper on skin condition classification, where expert annotations often disagree. Techniques such as Monte Carlo CP filled a substantial coverage gap, achieving closer alignment between expected and actual coverage, thereby enhancing prediction reliability. The authors also extend their method to multi-label classification and scenarios enhanced by data augmentation, illustrating its adaptability and practicality.
4. Improved Coverage Guarantees: Two variants of the Monte Carlo CP procedure are proposed. The first guarantees coverage of $1-2\alpha$, whereas a second, more computationally intensive method, ensures coverage of $(1-\alpha)(1-\delta)$ by relying on empirical cumulative distribution function (ECDF) corrections. This consideration introduces a new dimension of accuracy, allowing finer control over prediction set reach and correctness in highly ambiguous conditions.

Implications and Future Directions

The implications of this work are extensive, particularly for fields requiring high assurance of accurate uncertainty quantification, such as medical diagnostics and safety-critical decision-making systems. By enhancing CP's ability to handle ambiguous ground truth, this research opens new pathways for deploying machine learning models in environments where label ambiguity is significant and impactful. Furthermore, the methodology's adaptability to robustify models against data augmentation perturbations signifies its utility beyond traditional CP applications.

Future developments may focus on further refining aggregation techniques for $P^{Y|X}$, integrating real-time feedback loops from expert annotations as additional data becomes available. This would entail dynamic adaptation in models trained to handle incoming high-variability data streams. Practical implementations could also explore hybrid methods combining Monte Carlo CP with other robust statistical techniques to address data scarcity and enhance computational efficiency, particularly in large-scale or resource-constrained environments.

By addressing the challenges associated with ambiguous label distributions, this paper paves the way for broader applications of CP in contexts that necessitate nuanced handling of label uncertainty. Its principles and results stand as pivotal for expanding the reliable implementation of machine learning solutions where conventional assumptions of label determinism are inadequate or misrepresentative.