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A variational inference for the Lévy adaptive regression with multiple kernels

Author

Listed:
  • Youngseon Lee

    (Samsung SDS)

  • Seongil Jo

    (Inha University)

  • Jaeyong Lee

    (Seoul National University)

Abstract

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.

Suggested Citation

  • Youngseon Lee & Seongil Jo & Jaeyong Lee, 2022. "A variational inference for the Lévy adaptive regression with multiple kernels," Computational Statistics, Springer, vol. 37(5), pages 2493-2515, November.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01200-z
    DOI: 10.1007/s00180-022-01200-z
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    References listed on IDEAS

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    1. Kang, Kee-Hoon & Koo, Ja-Yong & Park, Cheol-Woo, 2000. "Kernel estimation of discontinuous regression functions," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 277-285, April.
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    3. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    4. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    5. Faes, C. & Ormerod, J. T. & Wand, M. P., 2011. "Variational Bayesian Inference for Parametric and Nonparametric Regression With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 959-971.
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