Density-sorted prediction set: Efficient conformal prediction for multi-target regression

We introduce Density-Sorted Prediction Set (DSPS), 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, DSPS identifies dense regions in the original space using the conditional probability density, which is computed via the Jacobian determinant and the latent density. 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 DSPS produces smaller, more informative prediction regions while maintaining robust coverage guarantees, enhancing uncertainty modeling in complex, high-dimensional settings. © 2025 The Author(s).