Jacobi Prior: An Alternative Bayesian Method for Supervised Learning

The Jacobi prior offers an alternative Bayesian framework, designed to achieve superior computational efficiency without compromising predictive performance. Compared to widely used methods such as Lasso, Ridge, Elastic Net, uniLasso, the MCMC-based Horseshoe prior, and non-Bayesian machine learning methods including Support Vector Machines (SVM), Random Forests, and Extreme Gradient Boosting (XGBoost), the Jacobi prior achieves competitive or better accuracy with significantly reduced computational cost. The method is well suited to distributed computing environments, as it naturally accommodates partitioned data across multiple servers. We propose a parallelisable Monte Carlo algorithm to quantify the uncertainty in the estimated coefficients. We establish that the Jacobi estimator is asymptotically close to, and asymptotically equivalent to, the posterior mode under the Jacobi prior. To demonstrate its practical utility, we conduct a comprehensive simulation study comprising seven experiments focused on statistical consistency, prediction accuracy, scalability, sensitivity analysis and robustness study. We further present three real-data applications multi-class classification of stars, quasars, and galaxies using Sloan Digital Sky Survey data, and spinal degeneration classification using sagittal MRI scans from the RSNA 2024 Lumbar Spine Degenerative Classification Challenge. In the spine classification task, we extract last-layer features from a fine-tuned ResNet-50 model and evaluate multiple classifiers, including Jacobi-Multinomial logit regression, SVM, and Random Forest. All code and datasets used in this paper are available at: https://github.com/sourish-cmi/Jacobi-Prior/