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Variational inferences for partially linear additive models with variable selection

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  • Zhao, Kaifeng
  • Lian, Heng

Abstract

This article develops a mean field variational Bayes approximation algorithm for posterior inferences of the recently proposed partially linear additive models with simultaneous and automatic variable selection and linear/nonlinear component identification abilities. To solve the problem induced by some complicated expectation evaluations, we proposed two approximations based on Monte Carlo method and Laplace approximation respectively. With high accuracy, the algorithm we derived is much more computationally efficient than the existing Markov Chain Monte Carlo (MCMC) method. The simulation examples are used to demonstrate the performance of our new algorithm versus MCMC. The proposed approach is further illustrated on a real dataset.

Suggested Citation

  • Zhao, Kaifeng & Lian, Heng, 2014. "Variational inferences for partially linear additive models with variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 223-239.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:223-239
    DOI: 10.1016/j.csda.2014.07.003
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    References listed on IDEAS

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    1. Heng Lian & Xin Chen & Jian-Yi Yang, 2012. "Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences," Biometrics, The International Biometric Society, vol. 68(2), pages 437-445, June.
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    3. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
    4. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    5. Chib, Siddhartha & Jeliazkov, Ivan, 2006. "Inference in Semiparametric Dynamic Models for Binary Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 685-700, June.
    6. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    7. Cornwell, Christopher & Trumbull, William N, 1994. "Estimating the Economic Model of Crime with Panel Data," The Review of Economics and Statistics, MIT Press, vol. 76(2), pages 360-366, May.
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    Cited by:

    1. Kaifeng Zhao & Seyed Hanif Mahboobi & Saeed Bagheri, 2017. "Revenue-based Attribution Modeling for Online Advertising," Papers 1710.06561, arXiv.org.
    2. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2017. "A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 693-716, September.
    3. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.

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