Trustworthy Predictive Distributions for Tail Events with Semiparametric Diagnostic Transport Maps

arXiv:2603.11229 · stat.ML, cs.LG · Submitted 2026-03-11 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-03-11

Updated: 2026-09-21

Comments: 33 pages, 6 figures, 3 tables

License: http://creativecommons.org/licenses/by/4.0/

The gist: Machine learning forecast systems are moving beyond point predictions to full predictive distributions for future outcomes y conditional on complex inputs x.

Terminology

Abstract

Machine learning forecast systems are moving beyond point predictions to full predictive distributions for future outcomes y conditional on complex inputs x. However, these distributions are often locally miscalibrated, especially for high-stakes tail events where accurate uncertainty quantification is most needed to establish trust in models. Local miscalibration occurs because training data often lack examples of low-frequency events. The goal of this paper is to describe a simple, yet flexible framework that, at deployment, produces interpretable diagnostics and a robust correction mechanism of predictive distributions when train examples are limited. With this goal in mind, we introduce a semiparametric version of the Local Amortized Diagnostic and Reshaping (LADaR) framework that posits a covariate-dependent parametric model for a diagnostic transport map regressed nonparametrically on inputs to describe how to correct tail probabilities across the feature space to match calibration data. These maps provide the user with local, real-time diagnostics and a reshaped predictive distribution that can be related back to physical processes in the input space. We apply these semiparametric diagnostic transport maps to short-term tropical cyclone intensity forecasting to detect evolutionary modes linked to local miscalibration in the National Hurricane Center's forecasts and improve predictions for severe weather hazards.

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