JAPAN: Joint Adaptive Prediction Areas with Normalising-Flows

TL;DR

JAPAN introduces a novel conformal prediction framework using normalising-flows to create adaptive, compact, and accurate prediction regions with finite-sample guarantees, especially effective for complex, multimodal distributions.

Contribution

The paper proposes JAPAN, a density-based conformal prediction method leveraging normalising-flows for improved, flexible prediction regions with theoretical guarantees.

Findings

JAPAN achieves tighter prediction areas than existing methods.

It maintains finite-sample coverage guarantees.

Empirical results show good calibration across tasks.

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 conformal prediction framework that uses density-based conformity 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. We also provide several \emph{extensions} adding flexibility to our proposed framework.