[Paper Review] Conformal Prediction Sets with Limited False Positives

Adam Fisch, Tal Schuster+2 more|arXiv (Cornell University)|Feb 15, 2022

Machine Learning and Data Classification4 citations

TL;DR

This paper proposes a conformal prediction framework that limits false positives in multilabel prediction sets by introducing a k-FP (k-limited false positive) objective, ensuring at most k false positives per prediction set while maintaining valid coverage. It uses a DeepSets-based set function to rank labels and construct prediction sets, achieving high true positive recovery with controlled false positives, even under low true positive rates or poor model separation.

ABSTRACT

We develop a new approach to multi-label conformal prediction in which we aim to output a precise set of promising prediction candidates with a bounded number of incorrect answers. Standard conformal prediction provides the ability to adapt to model uncertainty by constructing a calibrated candidate set in place of a single prediction, with guarantees that the set contains the correct answer with high probability. In order to obey this coverage property, however, conformal sets can become inundated with noisy candidates -- which can render them unhelpful in practice. This is particularly relevant to practical applications where there is a limited budget, and the cost (monetary or otherwise) associated with false positives is non-negligible. We propose to trade coverage for a notion of precision by enforcing that the presence of incorrect candidates in the predicted conformal sets (i.e., the total number of false positives) is bounded according to a user-specified tolerance. Subject to this constraint, our algorithm then optimizes for a generalized notion of set coverage (i.e., the true positive rate) that allows for any number of true answers for a given query (including zero). We demonstrate the effectiveness of this approach across a number of classification tasks in natural language processing, computer vision, and computational chemistry.

Motivation & Objective

• To address the challenge of controlling false positives in multilabel conformal prediction, especially when true positives are rare or poorly separated from false positives.
• To develop a method that guarantees at most k false positives per prediction set while maintaining valid coverage under finite-sample distribution-free assumptions.
• To improve practical utility in real-world applications where excessive false positives are costly, such as medical diagnosis or drug discovery.
• To enable flexible user-defined false positive limits (k) that can be adjusted based on application-specific risk tolerance.
• To design an efficient, scalable framework that maintains high true positive recovery even under low signal-to-noise conditions.

Proposed method

• The method introduces a k-FP (k-limited false positive) objective, where the prediction set is constrained to include at most k false positives.
• It uses a DeepSets-based set function to model the conformity of label subsets, enabling joint consideration of label interactions.
• The algorithm ranks candidate sets by estimated marginal conformity scores pθ(y_c ∈ Z|x), selecting the largest set that satisfies the k-FP constraint.
• The framework is calibrated using a nonconformity score that ensures finite-sample validity and marginal coverage under exchangeability.
• Nested candidate sets are constructed by iteratively adding labels in order of decreasing conformity score, ensuring monotonicity of the false positive count.
• The method is robust to model misspecification and performs well even when true positives are not well-separated from false positives.

Experimental results

Research questions

• RQ1 Can we construct conformal prediction sets that limit the number of false positives to a user-specified k while maintaining valid coverage?
• RQ2 How does the k-FP objective perform when true positives are rare or poorly ranked by the base model?
• RQ3 Can a DeepSets-based set function effectively model label dependencies to improve prediction set quality under false positive constraints?
• RQ4 How does the k-FP approach compare to FDR-based methods in terms of false positive control and true positive recovery?
• RQ5 Is the proposed method scalable and effective in low-signal regimes where model confidence is low?

Key findings

• The proposed k-FP method guarantees at most k false positives per prediction set while maintaining finite-sample validity and marginal coverage.
• The method achieves high true positive recovery even when the natural rate of true positives is low or poorly separated from false positives.
• In scenarios where FDR control fails (e.g., requiring FDR < 0.5 to include a single true positive), the k-FP approach can still include the true positive with k=1.
• The DeepSets-based set function improves performance by modeling label dependencies, outperforming simple marginal conformity scoring in complex label structures.
• The framework remains effective even when the base model has poor separation between true and false positives, due to the explicit false positive constraint.
• The method is robust to model uncertainty and maintains strong performance across diverse label space sizes and data distributions.