Relational Conformal Prediction for Correlated Time Series

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.

This paper introduces Conformal Relational Prediction (CoRel), a new framework for estimating the uncertainty of forecasts when dealing with multiple, correlated time series such as those produced by sensor networks. Indeed, besides maximizing prediction accuracy, understanding the potential range of outcomes (prediction intervals) is crucial for reliable decision-making. However, existing methods for uncertainty quantification often treat each time series independently of the others, disregarding dependencies among correlated series. CoRel addresses this by using graph deep learning, a class of deep learning methods that model relationships by relying on graph representations. CoRel accounts for dependencies between different time series, even if these connections are not known beforehand, by learning from prediction errors. This allows us to condition uncertainty estimates for one series on observations at related neighbors. A key advantage of CoRel is that it can be applied to any pre-existing forecasting model without needing any modification. Furthermore, it is "distribution-free", meaning it does not rely on strong assumptions about the data's underlying distribution. CoRel includes an adaptive component to adjust to changes in the time series data over time. Experiments on real-world datasets (traffic, air quality, energy consumption) demonstrate that our approach can achieve accurate uncertainty predictions and narrower, more informative prediction intervals compared to existing methods.