Flow-based Conformal Prediction for Multi-dimensional Time Series

Time series prediction underpins a broad range of downstream tasks across many scientific domains. Recent advances and increasing adoption of black-box machine learning models for time series prediction highlight the critical need for uncertainty quantification. While conformal prediction has gained attention as a reliable uncertainty quantification method, conformal prediction for time series faces two key challenges: (1) $\mathbf{\text{leveraging}}\mathbf{\text{correlations}}\mathbf{\text{in}}\mathbf{\text{observations}}\mathbf{\text{and}}\mathbf{\text{non-conformity}}\mathbf{\text{scores}}\mathbf{\text{to}}\mathbf{\text{overcome}}\mathbf{\text{the}}\mathbf{\text{exchangeability}}\mathbf{\text{assumption}}$, and (2) $\mathbf{\text{constructing}}\mathbf{\text{prediction}}\mathbf{\text{sets}}\mathbf{\text{for}}\mathbf{\text{multi-dimensional}}\mathbf{\text{outcomes}}$. To address these challenges, we propose a novel conformal prediction method for time series using flow with classifier-free guidance. We provide coverage guarantees by establishing exact non-asymptotic marginal coverage and a finite-sample bound on conditional coverage for the proposed method. Evaluations on real-world time series datasets demonstrate that our method constructs significantly smaller prediction sets than existing conformal prediction methods, maintaining target coverage.