面向相关时间序列的关系保形预测
Relational Conformal Prediction for Correlated Time Series
AI总结：
本文提出CoRel方法，利用图深度学习和保形预测框架对相关时间序列进行不确定性量化，无需预知图结构且能自适应处理不可交换数据，在基准上达到最先进水平。
摘要：
我们通过利用相关序列上的观测来解决时间序列预测中的不确定性量化问题。利用图表示的关系深度学习方法是从时空数据和相关时间序列中获得点估计的最有效工具之一。然而，在同一背景下，利用关系结构来估计此类预测的不确定性问题在很大程度上被忽视了。为此，我们提出了一种基于保形预测框架和分位数回归的新型无分布方法。尽管保形预测最近被应用于序列数据，但现有方法在每个目标时间序列上独立运行，在构建预测区间时并未考虑它们之间的关系。我们通过引入一种基于图深度学习算子的新型保形预测方法来填补这一空白。我们的方法名为Conformal Relational Prediction (CoRel)，不需要预先知道关系结构（图），并且可以应用于任何预训练预测器之上。此外，CoRel包含一个自适应组件，用于处理不可交换数据和输入时间序列的变化。我们的方法提供了准确的覆盖率，并在相关基准上实现了最先进的不确定性量化。
英文摘要：
We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.
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