Multi-Scale Conformal Prediction: A Theoretical Framework with Coverage Guarantees

TL;DR

This paper introduces a multi-scale conformal prediction framework that constructs prediction sets across different resolutions, providing coverage guarantees and often resulting in smaller, more precise prediction sets in applications like image analysis and time series.

Contribution

It extends conformal prediction to multiple scales, establishing theoretical coverage guarantees and demonstrating improved set efficiency through a novel multi-scale approach.

Findings

Achieves or exceeds nominal coverage levels in synthetic classification.

Produces smaller prediction sets compared to single-scale methods.

Theoretically guarantees coverage while refining set sizes across scales.

Abstract

We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of conformity, overlooking the multi-level structures that arise in applications such as image analysis, hierarchical data exploration, and multi-resolution time series modeling. In contrast, the proposed framework defines a distinct conformity function at each relevant scale or resolution, producing multiple conformal predictors whose prediction sets are then intersected to form the final multi-scale output. We establish theoretical results confirming that the multi-scale prediction set retains the marginal coverage guarantees of the original conformal framework and can, in fact, yield smaller or more precise sets in practice. By distributing the total miscoverage probability across scales in proportion to their informative power, the method further refines the set sizes. We also show that dependence between scales can lead to conservative coverage, ensuring that the actual coverage exceeds the nominal level. Numerical experiments in a synthetic classification setting demonstrate that multi-scale conformal prediction achieves or surpasses the nominal coverage level while generating smaller prediction sets compared to single-scale conformal methods.