Jacobi Prior: An Alternative Bayesian Method for Supervised Learning

The `Jacobi prior' is an alternative Bayesian method for predictive models. It performs better than well-known methods such as Lasso, Ridge, Elastic Net, and MCMC-based Horse-Shoe Prior, particularly in terms of prediction accuracy and run-time. This method is implemented for Gaussian process classification, adeptly handling a nonlinear decision boundary. The Jacobi prior demonstrates its capability to manage partitioned data across global servers, making it highly useful in distributed computing environments. Additionally, we show that the Jacobi prior is more than a hundred times faster than these methods while maintaining similar predictive accuracy. As the method is both fast and accurate, it is advantageous for organisations looking to reduce their environmental impact and meet ESG standards. To demonstrate the effectiveness of the Jacobi prior, we conducted a detailed simulation study with four experiments focusing on statistical consistency, accuracy, and speed. We also present two empirical studies: the first evaluates credit risk by analysing default probability using data from the U.S. Small Business Administration (SBA), and the second uses the Jacobi prior for classifying stars, quasars, and galaxies in a three-class problem using multinomial logit regression on data from the Sloan Digital Sky Survey. Different filters were used as features in this study. All codes and datasets for this paper are available in the following GitHub repository : https://github.com/sourish-cmi/Jacobi-Prior/