A variational inference for the Lévy adaptive regression with multiple kernels

• Published in: Computational statistics Vol. 37; no. 5; pp. 2493 - 2515
• Main Authors: Lee, Youngseon, Jo, Seongil, Lee, Jaeyong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-11-2022; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computer simulation; Economic Theory/Quantitative Economics/Mathematical Methods; Inference; Kernels; Markov analysis; Markov chains; Mathematical analysis; Mathematics and Statistics; Methods; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Regression models; Simulated annealing; Simulation; Statistics; Lévy adaptive regression kernel model; Variational Bayes; Multiple kernels; Simulated annealing
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-022-01200-z

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.