用储层计算动态调整误差分布，实现高效时间序列预测区间
ResCP: Reservoir Conformal Prediction for Time Series Forecasting
- 用储层计算捕捉时序动态，自适应重加权残差
- 小样本下仍保持准确覆盖，无需重新训练
- 适合需要快速响应分布变化的实时预测场景
置信预测为可交换数据提供了无分布假设的预测区间。现有扩展到序列数据的方法依赖复杂模型捕捉时间依赖性，但小样本下表现不佳，且数据分布改变时需昂贵重训练。为此，我们提出无需训练的储层置信预测（ResCP）方法。该方法利用储层计算的高效性与表征能力，动态重加权符合度分数。具体地，计算储层状态间的相似度，并据此自适应调整每一步的观测残差。此方法在建模误差分布时考虑局部时序动态，同时保持计算可扩展性。我们在合理假设下证明了ResCP的渐近条件覆盖率，并在多种预测任务中实证其有效性。
原文摘要 · Abstract (English)
Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.
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