Calibrated Regression-as-Classification for Probabilistic Forecasting

Jef Jonkers, Glenn Van Wallendael, Duchateau Luc, Sofie Van Hoecke

Keywords: Distributional regression, Probabilistic forecasting, Calibration, Conformal predictive systems, Regression-as-classification

TL;DR: We predict a discrete CDF by turning regression into classification on bins, then apply conformal calibration to produce finite-sample calibrated predictive CDF bands that trade off reliability and sharpness.

Abstract: Regression-as-classification (R2C) is a pragmatic approach to distributional regression in which the response space is discretized, bin membership probabilities are estimated, and a monotone discrete cumulative distribution function (CDF) is subsequently reconstructed. The remaining challenge is calibration, ensuring predicted probabilities align with empirical frequencies in finite samples. We propose post-hoc calibration procedures for R2C predictors that are conformal predictive systems (CPS). These systems produce predictive CDF bands that, under the assumption of exchangeability, are guaranteed to enclose the out-of-sample calibrated distribution. Specifically, we propose four calibration methods that respectively target probabilistic calibration, grid calibration (a notion we introduce), isotonic calibration, and auto-calibration, all of which are compatible with discrete CDF outputs.

Submission Number: 11