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Approximation Properties of Variational Bayes for Vector Autoregressions

Reza Hajargasht

arXiv 2 Mar 2019 · Statistics — Machine Learning

arXiv:1903.00617 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive density and KL divergence for the linear Gaussian multi-equation regression. Our results indicate that VB approximates the posterior mean perfectly. Factors affecting the magnitude of underestimation in posterior variance and mode are revealed. Importantly, We demonstrate that VB estimates predictive densities accurately.

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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
1Karlsson, S (2013) Forecasting with Bayesian Vector Autoregression0.9507386%
2Koop, G. and Korobilis, D (2018) Variational Bayes Inference in High-dimensional Time-varying Parameter Models0.73732100%
3Blei, D. M., Kucukelbir, A., and McAuliffe, J. D (2017) Variational Inference: A Review for Statisticians0.64422100%
4Giannone, D., Lenza, M., and Primiceri, G. E (2015) Prior Selection for Vector Autoregressions0.64422100%
5Ormerod, J. T. and Wand, M. P (2010) Explaining Variational Approximations0.64422100%
6Hajargasht, G. and Woźniak, T (2018) Accurate Computation of Marginal Data Densities Using Variational Bayes0.64422100%
7Koop, G. and Korobilis, D (2010) Bayesian Multivariate Time Series Methods for Empirical Macroeconomics0.51121100%
8Stock, J. H. and Watson, M. W (2008) Forecasting in Dynamic Factor Models Subject to Structural Instability0.40511100%
9Attias, H (2000) A Variational Bayesian Framework for Graphical Models0.40511100%
10Bickel, P., Choi, D., Chang, X., Zhang, H., et al (2013) Asymptotic Normality of Maximum Likelihood and its Variational Approximation for Stochastic Blockmodels0.40511100%

Showing the top 10 of 21 scored citations.