Jacobi Prior: An Alternate Bayesian Method for Supervised Learning

This paper introduces the `Jacobi prior,' an alternative Bayesian method, that aims to address the computational challenges inherent in traditional techniques. It demonstrates that the Jacobi prior performs better than well-known methods like Lasso, Ridge, Elastic Net, and MCMC-based Horse-Shoe Prior, especially in predicting accurately. Additionally, We also show that the Jacobi prior is more than a hundred times faster than these methods while maintaining similar predictive accuracy. The method is implemented for Generalised Linear Models, Gaussian process regression, and classification, making it suitable for longitudinal/panel data analysis. The Jacobi prior shows it can handle partitioned data across servers worldwide, making it useful for distributed computing environments. As the method runs faster while still predicting accurately, it's good for organizations wanting to reduce their environmental impact and meet ESG standards. To show how well the Jacobi prior works, we did a detailed simulation study with four experiments, looking at statistical consistency, accuracy, and speed. Additionally, we present two empirical studies. First, we thoroughly evaluate Credit Risk by studying default probability using data from the U.S. Small Business Administration (SBA). Also, we use the Jacobi prior to classifying stars, quasars, and galaxies in a 3-class problem using multinational logit regression on Sloan Digital Sky Survey data. We use different filters as features. All codes and datasets for this paper are available in the following GitHub repository: https://github.com/sourish-cmi/Jacobi-Prior/