Yu Fu, Michael Stanley Smith, Anastasios Panagiotelis
arXiv 3 Mar 2025 · Statistics — Machine Learning · publishedJournal of Computational and Graphical Statistics (2025)
arXiv:2503.01072 · PDF · DOI · OpenAlex · Extracted main text
The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a common choice is to assume independence between multivariate blocks in a partition of the parameter space. While this simplifies the problem it can reduce accuracy. This paper proposes using vector copulas to capture dependence between the blocks parsimoniously. Tailored multivariate marginals are constructed using learnable transport maps. We call the resulting joint distribution a “dependent block posterior” approximation. Vector copula models are suggested that make tractable and flexible variational approximations. They allow for differing marginals, numbers of blocks, block sizes and forms of between block dependence. They also allow for solution of the variational optimization using efficient stochastic gradient methods. The approach is demonstrated using four different statistical models and 16 datasets which have posteriors that are challenging to approximate. This includes models that use global-local shrinkage priors for regularization, and hierarchical models for smoothing and heteroscedastic time series. In all cases, our method produces more accurate posterior approximations than benchmark VI methods that either assume block independence or factor-based dependence, at limited additional computational cost. A python package implementing the method is available on GitHub at https://github.com/YuFuOliver/VCVI_Rep_PyPackage.
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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 | Fan, Y. and Henry, M (2023) Vector copulas | 1.000 | 9 | 4 | 100% |
| 2 | Ong, V. M.-H., Nott, D. J., and Smith, M. S (2018) Gaussian variational approximation with a factor covariance structure self | 1.000 | 7 | 3 | 100% |
| 3 | Smith, M. S., Loaiza-Maya, R., and Nott, D. J (2020) High-dimensional copula variational approximation through transformation self | 1.000 | 7 | 3 | 100% |
| 4 | Smith, M. S. and Loaiza-Maya, R (2023) Implicit copula variational inference self | 1.000 | 5 | 3 | 100% |
| 5 | Bryan, J. G., Niles-Weed, J., and Hoff, P. D (2025) The multirank likelihood for semiparametric canonical correlation analysis | 0.843 | 3 | 3 | 100% |
| 6 | Bernardi, M., Bianchi, D., and Bianco, N (2024) Variational inference for large Bayesian vector autoregressions | 0.737 | 3 | 2 | 100% |
| 7 | Brechmann, E. C (2014) Hierarchical Kendall copulas: Properties and inference | 0.737 | 3 | 2 | 100% |
| 8 | Chan, J. C (2017) The stochastic volatility in mean model with time-varying parameters: An application to inflation modeling | 0.737 | 3 | 2 | 100% |
| 9 | Han, S., Liao, X., Dunson, D., and Carin, L (2016) Variational Gaussian copula inference | 0.737 | 3 | 2 | 100% |
| 10 | Menictas, M., Di Credico, G., and Wand, M. P (2023) Streamlined variational inference for linear mixed models with crossed random effects | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 54 scored citations.