Directional Statistics on Circles and Spheres: A New Angle on Data
Siddhesh Kulkarni
Oct 2026
Artificial IntelligenceData Science
Abstract
Two compass bearings near north can have an ordinary arithmetic mean pointing south: the difficulty is that angles live on a circle, not a straight line. Using real wind observations, diffusion-MRI orientations, and geometric examples from machine learning, this article introduces circular and axial averages, directional variability, and probability models on circles and spheres. The guiding principle is to identify the geometry and symmetries of the observations before choosing a statistical method.
This paper investigates developing real-world perception for active agents, proposes Gibson Environment for this purpose, and showcases a set of perceptual tasks learned therein.
F. Xia, Amir Zamir, Zhi-Yang He et al.· 2018 IEEE/CVF Conference on...· 1,069 citations· ⚡112
This publication proposes a definition and a classification of agile software development approaches and analyses ten software development methods that can be characterized as being "agile" against the defined criterion.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 727 citations· ⚡54
The study shows that agile practices improve both informal and formal communication, but indicates that, in larger development situations involving multiple external stakeholders, a mismatch of adequate communication mechanisms can sometimes even hinder the communication.
M. Pikkarainen, Jukka Haikara, O. Salo et al.· Empirical Software Engineeri...· 401 citations· ⚡48
The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
It is proved that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution, and empirically demonstrate the benefits of the trajectories balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequenc...
Esmeralda S. Whitammer, Moksh Jain, Emmanuel Bengio et al.· Neural Information Processin...· 302 citations· ⚡60
