A variational inference for the Lévy adaptive regression with multiple kernels

This paper presents a variational Bayes approach to a Lévy adaptive regression kernel (LARK) model that represents functions with an overcomplete system. In particular, we develop a variational inference method for a LARK model with multiple kernels (LARMuK) which estimates arbitrary functions that could have jump discontinuities. The algorithm is based on a variational Bayes approximation method with simulated annealing. We compare the proposed algorithm to a simulation-based reversible jump Markov chain Monte Carlo (RJMCMC) method using numerical experiments and discuss its potential and limitations.