Title: JAPAN: Joint Adaptive Prediction Areas with Normalising Flow
Primary area: generative models
Keywords: Uncertainty Quantification, Normalising Flows, Joint Prediction Areas

Abstract: Conformal prediction provides a model-agnostic framework for uncertainty quantification with finite-sample validity guarantees, making it an attractive tool for constructing reliable prediction sets. However, existing approaches commonly rely on residual-based conformity scores, which impose geometric constraints and struggle when the underlying distribution is multimodal. In particular, they tend to produce overly conservative prediction areas centred around the mean, often failing to capture the true shape of complex predictive distributions. In this work, we introduce JAPAN (Joint Adaptive Prediction Areas with Normalising-Flows), a flow-based framework that uses density estimates for several conformal scores. By leveraging flow-based models, JAPAN estimates the (predictive) density and constructs prediction areas by thresholding on the estimated density scores, enabling compact, potentially disjoint, and context-adaptive regions that retain finite-sample coverage guarantees. We theoretically motivate the efficiency of JAPAN and empirically validate it across multivariate regression and forecasting tasks, demonstrating good calibration and tighter prediction areas compared to existing baselines. Furthermore, several density-based conformity scores showcase the flexibility of our proposed framework.

TL;DR: An application of Normalising Flows to obtain compact disjoint prediction regions without any geometrical assumption