Neural Conformal Control for Time Series Forecasting

TL;DR

The paper introduces NCC, a neural conformal control framework for time series forecasting that learns predictive controllers to adapt CP-based prediction intervals in non-stationary environments. By combining neural encoders for multi-view data, control-inspired losses, and a differentiable conformalization step, NCC maintains long-run coverage guarantees while achieving improved calibration and distributional consistency. It demonstrates superior calibration and competitive interval efficiency across diverse real-world datasets and base forecasters, with strong few-shot and transfer learning performance. The work highlights a pragmatic path to integrating deep learning with conformal prediction for reliable, adaptable uncertainty quantification in time series.

Abstract

We introduce a neural network conformal prediction method for time series that enhances adaptivity in non-stationary environments. Our approach acts as a neural controller designed to achieve desired target coverage, leveraging auxiliary multi-view data with neural network encoders in an end-to-end manner to further enhance adaptivity. Additionally, our model is designed to enhance the consistency of prediction intervals in different quantiles by integrating monotonicity constraints and leverages data from related tasks to boost few-shot learning performance. Using real-world datasets from epidemics, electric demand, weather, and others, we empirically demonstrate significant improvements in coverage and probabilistic accuracy, and find that our method is the only one that combines good calibration with consistency in prediction intervals.

Figures (6)

• Figure 1: Model architecture of NCC. The shaded area is the conformal control loop of our method. MLP, GRU and GNN are used to encode multi-view data. Additionally, GRUs are employed to encode past errors, predictions, and scores. These embeddings are integrated using multi-head cross-attention mechanisms and subsequently passed through an MLP to predict the quantiles of scores. Finally, the predicted quantiles are refined through a conformalization step.
• Figure 2: Comparison of CS and WIS across five datasets for four different steps ahead predictions. Our method (NCC) is highlighted with a red line, with the pink-shaded area around it indicating the error margin. NCC has the best CS across all datasets. Except for the smd dataset, NCC consistently achieves the best or near-best performance in WIS.
• Figure 3: (a) DCS versus CS, using the unsorted results. The top left corner represents the optimal performance region. (b) The number of datasets where our method achieves the best CS. The methods that do not achieve the best CS are not shown in this plot. (c) Cumulative average CS on covid-19 in a few-shot learning setup. (d) Ablation study on TTA and monotonicity loss. Comparison of NCC, NCC without TTA (NCC-T) and NCC without TTA and monotonicity loss (NCC-M).
• Figure 4: TTA procedure used at inference time to further enhance prediction interval consistency.
• Figure 5: Calibration curve of unsorted and sorted results on smd. (a) shows results from C-PID. (b) shows results from NCC.

Theorems & Definitions (2)

• Theorem 1
• Definition C.1: Distributional Consistency--DC