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Bayesian Optimization of Hyperparameters from Noisy Marginal Likelihood Estimates

Oskar Gustafsson, Mattias Villani, Pär Stockhammar

arXiv 21 Apr 2020 · Statistics — Computation · publishedJournal of Applied Econometrics (2023) · 7 citations (OpenAlex)

arXiv:2004.10092 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. An acquisition strategy uses this posterior distribution to decide where to place the next function evaluation. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort, and therefore the precision of the function evaluations. This is a common situation in econometrics where the marginal likelihood is often computed by Markov chain Monte Carlo (MCMC) or importance sampling methods, with the precision of the marginal likelihood estimator determined by the number of samples. The new acquisition strategy gives the optimizer the option to explore the function with cheap noisy evaluations and therefore find the optimum faster. The method is applied to estimating the prior hyperparameters in two popular models on US macroeconomic time series data: the steady-state Bayesian vector autoregressive (BVAR) and the time-varying parameter BVAR with stochastic volatility. The proposed method is shown to find the optimum much quicker than traditional Bayesian optimization or grid search.

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27
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82
in-text mentions
27
distinct cited
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self-citations
11,565
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Chan, J. C. and Eisenstat, E (2018) Bayesian model comparison for time-varying parameter vars with stochastic volatility1.000153100%
2Giannone, D., Lenza, M., and Primiceri, G. E (2015) Prior selection for vector autoregressions1.00083100%
3Villani, M (2009) Steady-state priors for vector autoregressions self1.00073100%
4Chib, S (1995) Marginal likelihood from the Gibbs output1.00053100%
5Snoek, J., Larochelle, H., and Adams, R. P (2012) Practical bayesian optimization of machine learning algorithms0.87462100%
6Carriero, A., Kapetanios, G., and Marcellino, M (2012) Forecasting government bond yields with large Bayesian vector autoregressions0.87452100%
7Chib, S. and Jeliazkov, I (2001) Marginal likelihood from the Metropolis-Hastings output0.84333100%
8Geweke, J (1999) Using simulation methods for Bayesian econometric models: inference, development, and communication0.84333100%
9Williams, C. K. and Rasmussen, C. E (2006) Gaussian processes for machine learning, volume 20.69351100%
10Bańbura, M., Giannone, D., and Reichlin, L (2010) Large Bayesian vector auto regressions0.64422100%

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12512.020920.58531