Beyond EM: A faster Bayesian linear regression algorithm without matrix inversions

The Bayesian linear regression is a useful tool for many scientific communities. This paper presents a novel algorithm for solving the Bayesian linear regression problem with Gaussian priors, which shares the same spirit as the gradient based methods. In addition, the standard scheme for this task, the Expectation Maximization (EM) algorithm, involves matrix inversions but our proposed algorithm is free of. Numerical experiments demonstrate that the proposed algorithm performs as well as the gradient based and EM algorithms in term of precision, but runs significantly faster than the gradient based and EM algorithms. Due to its matrix-inversion-free nature, the algorithm of this paper is a viable alternative to the competing methods available in the literature.