Flow-based Conformal Prediction for Multi-dimensional Time Series
This work addresses a problem significant for time series forecasting applications, particularly those requiring reliable uncertainty estimates, such as finance or weather forecasting, offering an incremental improvement over existing methods.
The authors tackled the problem of conformal prediction for multi-dimensional time series, achieving smaller prediction regions while satisfying the desired coverage, with results demonstrated through experiments on simulated and real-world datasets. Their method outperformed baselines in terms of prediction region size.
Conformal prediction for time series presents two key challenges: (1) leveraging sequential correlations in features and non-conformity scores and (2) handling multi-dimensional outcomes. We propose a novel conformal prediction method to address these two key challenges by integrating Transformer and Normalizing Flow. Specifically, the Transformer encodes the historical context of time series, and normalizing flow learns the transformation from the base distribution to the distribution of non-conformity scores conditioned on the encoded historical context. This enables the construction of prediction regions by transforming samples from the base distribution using the learned conditional flow. We ensure the marginal coverage by defining the prediction regions as sets in the transformed space that correspond to a predefined probability mass in the base distribution. The model is trained end-to-end by Flow Matching, avoiding the need for computationally intensive numerical solutions of ordinary differential equations. We demonstrate that our proposed method achieves smaller prediction regions compared to the baselines while satisfying the desired coverage through comprehensive experiments using simulated and real-world time series datasets.