Conformal prediction for high-dimensional functional time series: Applications to subnational mortality

2026-03-11

AI Summary

This study addresses the challenge of unreliable uncertainty quantification in high-dimensional functional time series forecasting, which arises from model misspecification, selection bias, and limited sample sizes. To overcome these issues, the authors introduce a model-free, distribution-agnostic conformal prediction approach to construct statistically reliable prediction intervals. They innovatively propose both a split conformal framework and a validation-set-free sequential conformal framework, which dynamically update quantiles through an autoregressive process and calibrate prediction intervals based on empirical coverage probabilities. Empirical evaluations on age-specific log mortality data from Japan and Canada demonstrate that both methods achieve coverage probabilities close to the nominal level and yield low mean interval scores, even under finite-sample settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can potentially mitigate some of these concerns, it is often computationally demanding. Instead, we take a model-agnostic and distribution-free approach, namely conformal prediction, to construct prediction intervals in high-dimensional functional time series. Among a rich family of conformal prediction methods, we study split and sequential conformal prediction. In split conformal prediction, the data are divided into training, validation, and test sets, where the validation set is used to select optimal tuning parameters by calibrating empirical coverage probabilities to match nominal levels; after this, prediction intervals are constructed for the test set, and their accuracy is evaluated. In contrast, sequential conformal prediction removes the need for a validation set by updating predictive quantiles sequentially via an autoregressive process. Using subnational age-specific log-mortality data from Japan and Canada, we compare the finite-sample forecast performance of these two conformal methods using empirical coverage probability and the mean interval score.

Problem

• conformal prediction
• high-dimensional functional time series
• forecast uncertainty
• prediction intervals
• finite-sample validity

Innovation

• conformal prediction
• high-dimensional functional time series
• forecast uncertainty
• split conformal prediction
• sequential conformal prediction