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Hybrid unadjusted Langevin methods for high-dimensional latent variable models

Author

Listed:
  • Ruben Loaiza-Maya
  • Didier Nibbering
  • Dan Zhu
Abstract
The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a novel approximate Bayesian method based on the Langevin diffusion process. The method employs the Fisher identity to integrate out the latent variables, which makes it accurate and computationally feasible when applied to big data. In contrast to other approximate estimation methods, it does not require the choice of a parametric distribution for the unknowns, which often leads to inaccuracies. In an empirical discrete choice example with a million observations, the proposed method accurately estimates the posterior choice probabilities using only 2% of the computation time of exact MCMC.

Suggested Citation

  • Ruben Loaiza-Maya & Didier Nibbering & Dan Zhu, 2023. "Hybrid unadjusted Langevin methods for high-dimensional latent variable models," Papers 2306.14445, arXiv.org.
    • Handle: RePEc:arx:papers:2306.14445
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    References listed on IDEAS

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    1. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
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    3. G. O. Roberts & O. Stramer, 2002. "Langevin Diffusions and Metropolis-Hastings Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 337-357, December.
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    6. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.
    7. Rubén Loaiza-Maya & Didier Nibbering, 2022. "Scalable Bayesian Estimation in the Multinomial Probit Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1678-1690, October.
    8. George Poyiadjis & Arnaud Doucet & Sumeetpal S. Singh, 2011. "Particle approximations of the score and observed information matrix in state space models with application to parameter estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 65-80.
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