想处理角度或方向数据？ANGLE用深度生成模型做圆形回归，比传统方法更准，能搞定多模风向和物体姿态估计。
ANGLE是一种针对圆形响应数据的轻量级深度生成框架，通过广义圆形能量分数(GCES)损失优化生成映射，学习给定欧几里得和圆形协变量的全条件分布。理论性质包括损失严格性、估计量旋转等变性，支持加性噪声前后模型。在物体姿态估计和风向预测任务中，相比传统条件均值回归，ANGLE在处理多模、偏斜数据时展现出更优的预测性能和不确定性量化。实验覆盖模拟数据和真实应用，包括视频监控、自动驾驶和能源系统场景。
ANGLE: Angular Neural Generative Learning via Engression
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.