# ANGLE: Angular Neural Generative Learning via Engression

arXiv: https://arxiv.org/abs/2607.12833 · HTML: https://mlsanity.com/paper/2607.12833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 98 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Deep Learning-Based Object Pose Estimation: A Comprehensive Survey](https://mlsanity.com/paper/2405.07801/) (2024)
- [Single Image Estimation of Cell Migration Direction by Deep Circular Regression](https://mlsanity.com/paper/2406.19162/) (2024)
- [Testing Equality of Conditional Distributions via Generative Models](https://mlsanity.com/paper/2606.06930/) (2026)
- [Regularized estimation of Monge-Kantorovich quantiles for spherical data](https://mlsanity.com/paper/2407.02085/) (2024)
- [Nonparametric estimation on the circle based on Fej'er polynomials](https://mlsanity.com/paper/2411.19138/) (2024)
- [A Conditional Distribution Equality Testing Framework using Deep Generative Learning](https://mlsanity.com/paper/2509.17729/) (2025)
- [Modeling Zero-Inflated Longitudinal Circular Data Using Bayesian Methods: Application to Ophthalmology](https://mlsanity.com/paper/2601.13998/) (2026)
- [A Bayesian regression framework for circular models with INLA](https://mlsanity.com/paper/2602.08413/) (2026)
- [Robust measures of dispersion for circular data with an anomaly detection rule](https://mlsanity.com/paper/2603.01237/) (2026)
- [Analyzing directional errors in spatial orientation using nonparametric circular regression with mixed covariates](https://mlsanity.com/paper/2604.21498/) (2026)

## Abstract (arXiv)

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.