Reza Hajargasht
arXiv 2 Mar 2019 · Statistics — Machine Learning
arXiv:1903.00617 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Karlsson, S (2013) Forecasting with Bayesian Vector Autoregression | 0.950 | 7 | 3 | 86% |
| 2 | Koop, G. and Korobilis, D (2018) Variational Bayes Inference in High-dimensional Time-varying Parameter Models | 0.737 | 3 | 2 | 100% |
| 3 | Blei, D. M., Kucukelbir, A., and McAuliffe, J. D (2017) Variational Inference: A Review for Statisticians | 0.644 | 2 | 2 | 100% |
| 4 | Giannone, D., Lenza, M., and Primiceri, G. E (2015) Prior Selection for Vector Autoregressions | 0.644 | 2 | 2 | 100% |
| 5 | Ormerod, J. T. and Wand, M. P (2010) Explaining Variational Approximations | 0.644 | 2 | 2 | 100% |
| 6 | Hajargasht, G. and Woźniak, T (2018) Accurate Computation of Marginal Data Densities Using Variational Bayes | 0.644 | 2 | 2 | 100% |
| 7 | Koop, G. and Korobilis, D (2010) Bayesian Multivariate Time Series Methods for Empirical Macroeconomics | 0.511 | 2 | 1 | 100% |
| 8 | Stock, J. H. and Watson, M. W (2008) Forecasting in Dynamic Factor Models Subject to Structural Instability | 0.405 | 1 | 1 | 100% |
| 9 | Attias, H (2000) A Variational Bayesian Framework for Graphical Models | 0.405 | 1 | 1 | 100% |
| 10 | Bickel, P., Choi, D., Chang, X., Zhang, H., et al (2013) Asymptotic Normality of Maximum Likelihood and its Variational Approximation for Stochastic Blockmodels | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 21 scored citations.