Al-Qadisiyah Journal of Pure Science

Robust Quantile Horseshoe algorithm for sparse data

https://doi.org/10.29350/qjps.2026.170814.1070
Volume 31, Issue 1
Summer 2026
Pages 53-69
Al-Qadisiyah Journal of Pure Science

Document Type : Mathematics

Authors

Ahmed Alhamzawi 1
Gorgees Shaheed Mohammad 2
Daniele Ettore Otera 3

1 Department of Mathematics, College of Science, University of AL-Qadisiyah, Iraq

2 Department of Mathematics, College of Education, University of AL-Qadisiyah, Iraq

3 Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University, 08412 Vilnius, Lithuania

Abstract
Current Quantile approaches relay on the asymmetric laplace distribution, which usually requires the solving of large matrix equations at every step that beomes very complex as the data size grows. To fix this, a faster method for high-dimensional Bayesian quantile regression is introduced. This method works directly on the posterior distribution without extra latent variables. By using a Horseshoe prior as the proposal, this algorithm avoids costly matrix operations. This reduces the computational cost from cubic O(p^3 ) to linear O(np) complexity. Tests on real and simulation data show that this method is much faster and more efficient than existing techniques.

Keywords

Bayesian inference
Horseshoe prior
shrinkage priors
slice sampling
Crossmark
Subjects

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