Flow-based Conformal Prediction for Multi-dimensional Time Series

TL;DR

This paper introduces a flow-based conformal prediction method for multi-dimensional time series that provides reliable uncertainty quantification and constructs smaller, accurate prediction sets while addressing key challenges in the field.

Contribution

It proposes a novel flow-based conformal prediction approach that leverages correlations and handles multi-dimensional outcomes, with theoretical guarantees and improved prediction set efficiency.

Findings

Constructs smaller prediction sets than existing methods

Maintains target coverage with finite-sample guarantees

Addresses key challenges in conformal prediction for time series

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 uncertainty quantification. While conformal prediction has gained attention as a reliable uncertainty quantification method, conformal prediction for time series faces two key challenges: (1) \textbf{leveraging correlations in observations and non-conformity scores to overcome the exchangeability assumption}, and (2) \textbf{constructing prediction sets for multi-dimensional 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.