Distribution-Free, Risk-Controlling Prediction Sets (2101.02703v3)

Abstract: While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning.

• The paper proposes risk-controlling prediction sets that deliver finite-sample guarantees of expected loss control via a calibrated holdout method.
• It applies the novel methodology to tasks such as class-varying classification, image segmentation, and protein structure prediction to ensure robust performance.
• The study validates calibration techniques using UCBs and bounds like Waudby-Smith–Ramdas and Pinelis–Utev, offering reliable, distribution-free uncertainty quantification.

Distribution-Free, Risk-Controlling Prediction Sets: A Comprehensive Assessment

The paper "Distribution-Free, Risk-Controlling Prediction Sets" addresses a significant challenge in machine learning—providing reliable uncertainty quantification alongside predictive accuracy. Through a novel method, the authors propose generating set-valued predictions that offer explicit, finite-sample guarantees of expected loss control on future test points at user-defined levels.

Methodology and Scope

Recognizing the limitations of black-box predictors in conveying uncertainty, the authors introduce risk-controlling prediction sets (RCPS). These sets are designed to control the frequency of costly errors below a chosen threshold, effectively providing distribution-free, rigorous error control. The paper details the algorithm for constructing these sets, relying on a calibrated holdout method.

The authors demonstrate the applicability of RCPS in various large-scale machine learning tasks such as:

• Classification with Class-Varying Loss: Handling scenarios where misclassification penalties vary for different classes.
• Multi-Label Classification: Addressing predictions involving multiple correct labels per observation.
• Hierarchical Classification: Incorporating label hierarchies, ensuring that predictions respect structured label relationships.
• Image Segmentation: Facilitating predictive sets for identifying object boundaries within images.
• Protein Structure Prediction: Ensuring reliable predictions in complex biological datasets.

Numerical Results and Calibration Techniques

The paper highlights numerical techniques for calibrating RCPS using upper confidence bounds (UCBs). UCB calibration provides the statistical foundation to ensure prediction sets meet user-defined risk thresholds. The proposed method is validated through experiments across the aforementioned tasks, consistently demonstrating its ability to control risk while maintaining efficient set sizes.

The numerical studies emphasize the performance of various UCB calibration techniques in bounded and unbounded loss scenarios. They reveal that the Waudby-Smith–Ramdas bound effectively adapts to variable unknowns, providing robust finite-sample guarantees. The paper further explores unbounded losses using the Pinelis–Utev inequality, indicating robust applicability across diverse sample distributions.

Implications and Future Directions

The proposed RCPS framework holds substantial potential for practical and theoretical advancements in machine learning. This approach allows practitioners to effectively incorporate risk management into high-stakes decision-making processes without the constraints of traditional methods. The guarantee of finite-sample risk control underpins its appeal across multiple domains, including healthcare and environmental science, where predictive uncertainty can impact critical decisions.

Looking forward, areas of exploration include:

• Extension to Robust Learning: Exploring RCPS in adversarial settings where input data might be perturbed maliciously.
• Complex Loss Functions: Applying the RCPS framework to intricate loss landscapes, broadening its applicability in interdisciplinary machine learning challenges.
• Automation of Set Construction: Developing automated methods for the composition of nested set hierarchies to enhance computational efficiency in real-time applications.

Conclusion

The authors present a compelling advancement in uncertainty quantification, fostering reliable decision-making across various AI applications. By offering rigorous error control through set-valued predictions, the paper establishes a foundation for integrating risk management practices into machine learning models without reliance on distribution-specific assumptions. The insights and methodologies outlined pave the way for future developments in AI, championing robust, transparent, and accountable predictive systems.