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JAPAN: Joint Adaptive Prediction Areas with Normalising Flow

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.5Download Report PDF
Uncertainty QuantificationNormalising FlowsJoint 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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces JAPAN, a framework that constructs conformal prediction regions using normalizing flow density estimates for regression tasks. It resides in the 'Single-Target Regression with Flow-Based Conformity' leaf, which contains only three papers total, including the original work. This leaf sits within the broader 'Conformal Prediction with Normalizing Flows for Regression' branch, indicating a relatively sparse research direction. The sibling papers in this leaf—CONTRA and Normalizing Flows Conformal—share the core approach of leveraging flow-based densities for conformity scoring, suggesting that while the general idea is established, the specific design space remains under-explored.

The taxonomy reveals neighboring research directions that contextualize JAPAN's positioning. The adjacent 'Multi-Target Regression with Joint Prediction Regions' leaf addresses joint distributions for multi-dimensional outcomes, while the 'Time Series' branch tackles temporal dependencies with specialized flow architectures. JAPAN's focus on single-target regression with density thresholding distinguishes it from multi-target volume-based calibration methods and from sequential forecasting approaches that incorporate Transformer encoders or explicit temporal modeling. The taxonomy's scope notes clarify that JAPAN excludes manifold learning and time series methods, concentrating instead on localized regression prediction intervals.

Among the three contributions analyzed, the core JAPAN framework examined ten candidates and found three potentially refutable, while the theoretical efficiency analysis examined five candidates with none clearly refuting. The multiple conformity scores contribution examined ten candidates with one refutable. Across all contributions, twenty-five total candidates were examined, yielding four refutable pairs. This limited search scope—top-K semantic matches plus citation expansion—suggests that while some prior work overlaps with the framework's general approach, the specific theoretical motivations and score flexibility may offer incremental distinctions. The theoretical analysis appears least contested among examined candidates.

Based on the limited literature search covering twenty-five candidates, JAPAN appears to occupy a moderately explored niche within flow-based conformal prediction. The sparse taxonomy leaf and modest refutation counts suggest incremental novelty rather than a fundamentally new direction. However, the analysis does not cover exhaustive prior work, and the theoretical contributions show no clear refutation among examined candidates, hinting at potential originality in specific technical aspects. The framework's emphasis on practical calibration and score flexibility may differentiate it from closely related sibling papers.

Taxonomy

Core-task Taxonomy Papers
10
3
Claimed Contributions
25
Contribution Candidate Papers Compared
4
Refutable Paper

Research Landscape Overview

Core task: Constructing prediction regions using density-based conformity scores with normalizing flows. The field centers on leveraging normalizing flows—flexible generative models that learn complex probability distributions—to build statistically valid prediction regions via conformal prediction. The taxonomy reveals three main branches: regression tasks where flows provide density estimates for single or multiple targets, time series forecasting where temporal dependencies require specialized flow architectures, and manifold learning where flows capture lower-dimensional structure in high-dimensional data. Works like Normalizing Flows Conformal[2] and CONTRA[1] exemplify the regression branch, using flow-based densities to score conformity and construct adaptive prediction sets. Meanwhile, the time series branch, represented by Flow Conformal Time Series[5] and Conformal Time Series Flows[9], addresses sequential dependencies and distribution shifts over time. The manifold learning branch, including Conformal Embedding Flows[7][8], focuses on learning intrinsic geometry to improve density estimation and uncertainty quantification. Recent developments highlight trade-offs between computational efficiency, coverage guarantees, and region shape. Some methods prioritize volume-minimizing regions through density sorting, as in Volume Sorted Prediction[4], while others emphasize robustness to distribution shift or out-of-distribution detection, exemplified by OOD Normalizing Flows[10]. JAPAN[0] sits within the single-target regression cluster, closely aligned with CONTRA[1] and Normalizing Flows Conformal[2], all employing flow-based conformity scores to achieve finite-sample coverage. However, JAPAN[0] appears to emphasize practical calibration and interpretability of density-based scores, contrasting with CONTRA[1]'s focus on conditional coverage and Normalizing Flows Conformal[2]'s exploration of alternative flow architectures. Open questions persist around scaling to high dimensions, handling model misspecification, and extending validity guarantees to complex temporal or manifold settings.

Claimed Contributions

JAPAN framework using flow-based density estimates for conformal prediction

The authors propose JAPAN, a method that leverages normalising flow models to estimate conditional densities and constructs prediction areas by thresholding on estimated density scores. This enables compact, potentially disjoint, and context-adaptive regions while retaining finite-sample coverage guarantees.

10 retrieved papers
Can Refute
Theoretical analysis of JAPAN efficiency under rank preservation

The authors provide theoretical results showing that prediction regions constructed by JAPAN closely approximate those formed by the true unconditional threshold under mild ranking errors, establishing optimality under rank preservation and approximate optimality under approximate rank preservation.

5 retrieved papers
Multiple density-based conformity scores demonstrating framework flexibility

The authors introduce and demonstrate several variants of density-based conformity scores including unconditional, conditional, posterior-based, latent-based, and adaptive threshold modelling setups, showcasing the versatility of the JAPAN framework across different application scenarios.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

JAPAN framework using flow-based density estimates for conformal prediction

The authors propose JAPAN, a method that leverages normalising flow models to estimate conditional densities and constructs prediction areas by thresholding on estimated density scores. This enables compact, potentially disjoint, and context-adaptive regions while retaining finite-sample coverage guarantees.

Contribution

Theoretical analysis of JAPAN efficiency under rank preservation

The authors provide theoretical results showing that prediction regions constructed by JAPAN closely approximate those formed by the true unconditional threshold under mild ranking errors, establishing optimality under rank preservation and approximate optimality under approximate rank preservation.

Contribution

Multiple density-based conformity scores demonstrating framework flexibility

The authors introduce and demonstrate several variants of density-based conformity scores including unconditional, conditional, posterior-based, latent-based, and adaptive threshold modelling setups, showcasing the versatility of the JAPAN framework across different application scenarios.

Table of Contents

JAPAN: Joint Adaptive Prediction Areas with Normalising Flow | Novelty Validation