Efficient Quantification of Time-Series Prediction Error: Optimal Selection Conformal Prediction

TL;DR

This paper introduces OSCP, a new conformal prediction method for time-series that optimizes score functions via MILP, achieving smaller uncertainty sets and faster computation.

Contribution

OSCP formulates score function optimization as a MILP, improving efficiency and validity guarantees over existing methods.

Findings

OSCP reduces the size of uncertainty sets in time-series prediction.

OSCP significantly lowers computational requirements compared to state-of-the-art methods.

Theoretical guarantees ensure OSCP's validity and efficiency.

Abstract

Designing effective score functions in Conformal Prediction (CP) for time-series data remains challenging due to conservativeness and/or computational inefficiency. We propose Optimal Selection Conformal Prediction (OSCP), which parameterizes the score function via offset terms. To determine these parameters, we formulate a mixed-integer linear program (MILP) that minimizes an empirical proxy of the region size. We further reformulate this optimization problem into a smaller form (fewer constraints) to improve computational efficiency. We provide theoretical guarantees on both validity and CP-efficiency of OSCP. Numerical experiments demonstrate that OSCP reduces uncertainty-set size and has much lower computational requirements compared to the state-of-the-art method.