Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression

2025-03-04

AI Summary

This paper addresses the challenge in multi-output regression of simultaneously achieving statistical validity and geometric flexibility in uncertainty quantification. We propose a novel prediction set construction method based on volume ranking. Our approach models the high-density regions of the conditional joint target distribution using conditional normalizing flows, then integrates conformal calibration with Jacobian-determinant-based density estimation to produce non-convex, volume-optimal prediction sets that strictly satisfy the user-specified coverage probability. Unlike conventional methods relying on convex or axis-aligned rectangular assumptions, our framework overcomes representational limitations, significantly reducing prediction set volume—especially in high-dimensional, complex settings—thereby enhancing informativeness and practical utility. The key innovation lies in the first principled integration of volume-ranking paradigms with conditional density modeling, unifying statistical rigor with geometric adaptability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

We introduce Volume-Sorted Prediction Set (VSPS), a novel method for uncertainty quantification in multi-target regression that uses conditional normalizing flows with conformal calibration. This approach constructs flexible, non-convex predictive regions with guaranteed coverage probabilities, overcoming limitations of traditional methods. By learning a transformation where the conditional distribution of responses follows a known form, VSPS identifies dense regions in the original space using the Jacobian determinant. This enables the creation of prediction regions that adapt to the true underlying distribution, focusing on areas of high probability density. Experimental results demonstrate that VSPS produces smaller, more informative prediction regions while maintaining robust coverage guarantees, enhancing uncertainty modeling in complex, high-dimensional settings.

Problem

• Uncertainty quantification in multi-target regression
• Constructing flexible, non-convex predictive regions
• Enhancing uncertainty modeling in high-dimensional settings

Innovation

• Uses conditional normalizing flows for uncertainty quantification
• Constructs non-convex predictive regions with conformal calibration
• Adapts prediction regions to high probability density areas