Title: Flow-based Conformal Prediction for Multi-dimensional Time Series
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Conformal Prediction, Time Series Prediction

Abstract: 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 reliable uncertainty quantification. While conformal prediction has gained attention as a reliable uncertainty quantification method, conformal prediction for time series faces two key challenges: (1) leveraging correlations in features and non-conformity scores, and (2) constructing prediction sets for multi-dimensional outcomes. To address these challenges jointly, we propose a novel conformal prediction method for time series using flow with classifier-free guidance. We use flow to model the distribution of prediction residuals and their transformations conditioned on historical context, which is encoded using Transformer. Non-conformity scores are defined as the Euclidean distance between transformed prediction residuals and the mean of a Gaussian source distribution, enabling direct construction of prediction sets at any desired confidence level. 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 while maintaining target coverage.

TL;DR: We propose a novel conformal prediction method for time series using flow with classifier-free guidance.