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

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. Introduction In real-world applications, it is often required to estimate more than one response variable [1, 2, 3]. Consider, for example, estimating the effects and side effects of a drug given the patient's demographic information and medical measurements.