[論文レビュー] Conformal Prediction for Time Series with Modern Hopfield Networks

Andreas Auer, Martin Gauch+2 more|arXiv (Cornell University)|Mar 22, 2023

Time Series Analysis and Forecasting被引用数 10

ひとこと要約

HopCPT は a Modern Hopfield Network を用いて past errors を regime similarity によって reweight し、非交換性の時間系列全体で coverage guarantees を伴うより効率的な prediction intervals を提供する time series の conformal prediction method。

ABSTRACT

To quantify uncertainty, conformal prediction methods are gaining continuously more interest and have already been successfully applied to various domains. However, they are difficult to apply to time series as the autocorrelative structure of time series violates basic assumptions required by conformal prediction. We propose HopCPT, a novel conformal prediction approach for time series that not only copes with temporal structures but leverages them. We show that our approach is theoretically well justified for time series where temporal dependencies are present. In experiments, we demonstrate that our new approach outperforms state-of-the-art conformal prediction methods on multiple real-world time series datasets from four different domains.

研究の動機と目的

• Motivate uncertainty quantification for time series predictions and address exchangeability violations.
• Introduce error regimes as a concept to improve CP efficiency in time series.
• Develop HopCPT to learn similarity-based sample reweighting from past observations.
• Provide theoretical motivation and empirical evidence that HopCPT yields tighter, valid prediction intervals across diverse domains.

提案手法

• Use a Modern Hopfield Network (MHN) to identify past regimes similar to the current time step.
• Compute a soft association vector a_{t+1} via a learned encoding m(Z) and memory Z_{1:t} with a softmax over similarities.
• Construct time-series CP intervals using conditional, regime-aware error quantiles.
• Employ upper and lower interval bounds calculated from resampled errors weighted by a_{t+1} (per Equation 7).
• Train MHN with an auxiliary regression objective on absolute errors to align regime-based retrieval with error distributions (loss in Equation 8).
• Incorporate temporal encoding z_{T,t}^{time} to capture time-dependent similarity.

実験結果

リサーチクエスチョン

• RQ1 Can a conformal prediction approach circumvent exchangeability violations in time series by leveraging regime-based similarities?
• RQ2 Does learning regime-based reweighting via MHN yield shorter, coverage-guaranteed prediction intervals across multiple real-world domains?
• RQ3 How does HopCPT compare to state-of-the-art CP methods in efficiency (PI-width, Winkler score) while maintaining coverage under non-exchangeable data?
• RQ4 What are the theoretical justifications linking MHN-based reweighting to conditional/marginal coverage guarantees in time series CP?

主な発見

• HopCPT achieves state-of-the-art efficiency for conformal prediction in multiple real-world time series datasets across four domains.
• The MHN-based retrieval assigns higher weights to past samples from similar regimes, improving interval tightness without sacrificing coverage.
• HopCPT demonstrates competitive or superior PI-width and Winkler scores compared to EnbPI, SPCI, NexCP, CopulaCPTS, and AdaptiveCI under non-exchangeability.
• The method provides conditional and marginal coverage bounds under regime-based assumptions, extending conformal prediction theory to non-exchangeable time series.
• Experiments show robust performance across solar radiation, air quality, sap flow, and streamflow datasets with various predictive models (RF, LightGBM, Ridge, LSTM).
• HopCPT is scalable to very long time series due to linear memory growth in inference and supports arbitrary coverage levels without retraining.