Bayesian curve fitting for discontinuous functions using overcomplete system with multiple kernels

Abstract

We propose a Bayesian model for estimating functions that may have jump discontinuities, and variational method for inference. The proposed model is an extension of the LARK model, which enables functions to be represented by the small number of elements from an overcomplete system composing of multiple kernels. The location of jumps, the number of elements, and even the smoothness of functions are automatically determined by the Levy random measure, there is no need for model selection. A simulation study and a real data analysis illustrate that the proposed model performs better than the standard nonparametric models for the estimation of discontinuous functions and show the suggested variational method significantly reduces the computation time than the conventional inference method, reversible jump Markov chain Monte Carlo. Finally, we prove prior positivity of the model and show that the prior has sufficiently large support including discontinuous functions with finite number of jumps.