Conformal prediction for multi-dimensional time series by ellipsoidal sets

2024/03/06 by Chen Xu, Xu, Chen, Hanyang Jiang +3 · 14 citations
Computer Science · #Neural Networks and Applications #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2403.03850

Abstract

Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building prediction intervals for univariate responses. In this work, we develop a sequential CP method called MultiDimSPCI that builds prediction regions for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate finite-sample high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that MultiDimSPCI maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.

Cited by

• Learning Confidence Ellipsoids and Applications to Robust Subspace Recovery
• Efficient Quantification of Time-Series Prediction Error: Optimal Selection Conformal Prediction
• The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Markets
• Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization
• Foundation Model Forecasts: Form and Function
• Conformal Inference for Time Series over Graphs
• Calibrating Decision Robustness via Inverse Conformal Risk Control
• ResCP: Reservoir Conformal Prediction for Time Series Forecasting
• A Conformal Prediction-Based Chance-Constrained Programming Approach for 24/7 Carbon-Free Data Center Operation Scheduling
• SpeedCP: Fast Kernel-based Conditional Conformal Prediction
• Towards Trustworthy Vital Sign Forecasting: Leveraging Uncertainty for Prediction Intervals
• Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks
• Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces
• Directional Conformal Uncertainty Quantification from Learned Model Discrepancy

Related

• Conformal prediction for time series
• Sequential Predictive Conformal Inference for Time Series
• JANET: Joint Adaptive predictioN-region Estimation for Time-series
• Optimal Transport-based Conformal Prediction
• Multi-Scale Conformal Prediction: A Theoretical Framework with Coverage Guarantees