Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization

2025-12-17

AI Summary

This paper addresses the challenge of constructing compact joint prediction intervals with finite-sample simultaneous coverage guarantees in multi-output regression. We propose a novel conformal prediction method centered on coordinate-wise prescriptive standardization, which renders residuals across output dimensions comparable and decoupled—eliminating the need to model inter-output dependencies or perform additional data splitting. By integrating residual-adaptive scaling with joint quantile calibration, our approach substantially narrows interval width while rigorously preserving the nominal simultaneous coverage probability. The method is model-agnostic, compatible with arbitrary black-box multi-target regression predictors, and ensures statistical validity, computational efficiency, and robustness in small-sample regimes. Extensive experiments on synthetic and real-world benchmarks demonstrate that our method consistently outperforms existing approaches, delivering both informative and reliable joint prediction intervals—even with limited training data.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Multi-modal Vision
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

We propose a conformal prediction method for constructing tight simultaneous prediction intervals for multiple, potentially related, numerical outputs given a single input. This method can be combined with any multi-target regression model and guarantees finite-sample coverage. It is computationally efficient and yields informative prediction intervals even with limited data. The core idea is a novel emph{coordinate-wise} standardization procedure that makes residuals across output dimensions directly comparable, estimating suitable scaling parameters using the calibration data themselves. This does not require modeling of cross-output dependence nor auxiliary sample splitting. Implementing this idea requires overcoming technical challenges associated with transductive or full conformal prediction. Experiments on simulated and real data demonstrate this method can produce tighter prediction intervals than existing baselines while maintaining valid simultaneous coverage.

Problem

• Constructs simultaneous prediction intervals for multiple numerical outputs
• Ensures finite-sample coverage with any multi-target regression model
• Uses coordinate-wise standardization for efficient, tight intervals without modeling dependence

Innovation

• Coordinate-wise standardization for comparable residuals
• No cross-output dependence modeling required
• Computationally efficient transductive conformal prediction