ANGLE: Angular Neural Generative Learning via Engression

2026-07-14

AI Summary

This work addresses the geometric misalignment inherent in traditional regression approaches when modeling multimodal, skewed, or asymmetric circular data, as they only predict the conditional mean. To overcome this limitation, the authors propose ANGLE, a lightweight, nonparametric framework for circular distributional regression. ANGLE leverages deep generative models to learn the full conditional distribution of angular responses, incorporating pre- and post-additive noise modeling and optimizing via a generalized circular energy score (GCES) loss. The method is theoretically grounded, ensuring strict propriety and rotational equivariance, and enables distributional extrapolation, effective dimensionality reduction, and equivalence testing of conditional distributions. Empirical evaluations on object pose estimation and wind direction forecasting demonstrate that ANGLE substantially outperforms existing methods, delivering both high predictive accuracy and reliable uncertainty quantification.

Abstract

Circular data, representing angles or directions, are frequently encountered in computer vision, biology, geology, and meteorology. Traditional regression targets the conditional mean, which is often geometrically misleading for circular responses under multimodal, skewed, or asymmetric data structures. To address these limitations, a lightweight deep generative framework, namely ANGLE, is introduced for non-parametric distributional regression on the circle. The full conditional distribution of an angular response, given Euclidean and circular covariates, is learned through a generative map optimized via a generalized circular energy score (GCES) loss. Desirable theoretical properties, including the strict propriety of the loss and the rotational equivariance of the estimators, are established. Furthermore, both pre- and post-additive noise models are accommodated. A unified toolbox is provided for advancing previously underexplored challenges in circular statistics: extrapolation, sufficient dimension reduction, and conditional distribution equality testing. The framework's efficacy is demonstrated through extensive simulations and real-world applications. Specifically, the proposal is utilized for object pose estimation from imagery and wind direction prediction, which are integral to surveillance, autonomous vehicles, and energy systems, respectively. Superior predictive performance and robust uncertainty quantification of the proposed method in these tasks are revealed.

Problem

• circular data
• conditional distribution
• angular regression
• distributional regression
• directional statistics

Innovation

• circular data
• generative learning
• distributional regression
• rotational equivariance
• energy score