ANGLE：通过回归进行角度神经生成学习

中文摘要 AI 辅助

圆形数据在计算机视觉、生物学、地质学和气象学中经常遇到。传统回归针对条件均值，在多模态、倾斜或不对称数据结构下对圆形响应通常存在几何误导。为此引入轻量级深度生成框架ANGLE进行圆上的非参数分布回归。通过广义圆能量得分损失优化生成映射来学习角度响应的全条件分布，建立了理想理论性质，还提供统一工具箱应对圆形统计中未充分探索的挑战。通过模拟和实际应用证明了该框架的有效性。

英文摘要

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.

发表机构

• LPSM, Sorbonne Université（索邦大学LPSM）
• SAFIR, Sorbonne University Abu Dhabi（索邦大学阿布扎赫德分校）
• Indian Institute of Management, Kozhikode（印度管理学院科钦分校）

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