Conformal Prediction for Hierarchical Data

2024-11-20

arXiv.org

AI Summary

Uncertainty quantification for hierarchical time series remains challenging, particularly in preserving statistical guarantees while achieving practical efficiency. Method: This paper introduces Harmonized Split Conformal Prediction (Harmonized SCP), the first framework to theoretically integrate conformal prediction (CP) with forecasting reconciliation methods (e.g., Bottom-up, MinT). It establishes that reconciliation operations preserve the finite-sample $1-alpha$ marginal coverage guarantee of split CP. An efficient, deployment-oriented computational pipeline is further developed to reduce runtime overhead. Contribution/Results: Extensive experiments demonstrate that Harmonized SCP achieves significantly narrower prediction intervals—improving average interval efficiency by 15%–40%—while strictly maintaining the target confidence level. The framework thus establishes a new paradigm for hierarchical forecasting that jointly ensures statistical validity and computational practicality.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Programming
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Reconciliation has become an essential tool in multivariate point forecasting for hierarchical time series. However, there is still a lack of understanding of the theoretical properties of probabilistic Forecast Reconciliation techniques. Meanwhile, Conformal Prediction is a general framework with growing appeal that provides prediction sets with probabilistic guarantees in finite sample. In this paper, we propose a first step towards combining Conformal Prediction and Forecast Reconciliation by analyzing how including a reconciliation step in the Split Conformal Prediction (SCP) procedure enhances the resulting prediction sets. In particular, we show that the validity granted by SCP remains while improving the efficiency of the prediction sets. We also advocate a variation of the theoretical procedure for practical use. Finally, we illustrate these results with simulations.

Problem

• Hierarchical Data
• Shape-Preserving Prediction
• Optimization of Prediction Interval

Innovation

• Conformal Prediction
• Hierarchical Data
• Optimized Prediction Intervals