# Quasi-Bayes meets Vines

arXiv: https://arxiv.org/abs/2406.12764 · HTML: https://mlsanity.com/paper/2406.12764/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 100 references that are in the map.
- First posted on arXiv 18 Jun 2024.

## Builds on (most cited first, 30 of 41)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [The Cramer Distance as a Solution to Biased Wasserstein Gradients](https://mlsanity.com/paper/1705.10743/) (2017)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts](https://mlsanity.com/paper/2204.02028/) (2022)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [A-NICE-MC: Adversarial Training for MCMC](https://mlsanity.com/paper/1706.07561/) (2017)
- [Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization](https://mlsanity.com/paper/2112.08217/) (2021)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [Neural Adaptive Sequential Monte Carlo](https://mlsanity.com/paper/1506.03338/) (2015)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Score Matched Neural Exponential Families for Likelihood-Free Inference](https://mlsanity.com/paper/2012.10903/) (2020)
- [Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas](https://mlsanity.com/paper/1503.03305/) (2015)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Martingale Posterior Neural Processes](https://mlsanity.com/paper/2304.09431/) (2023)
- [Nonparametric estimation of simplified vine copula models: comparison of methods](https://mlsanity.com/paper/1701.00845/) (2017)
- [Generalized Bayesian Likelihood-Free Inference](https://mlsanity.com/paper/2104.03889/) (2021)
- [Probit transformation for nonparametric kernel estimation of the copula density](https://mlsanity.com/paper/1404.4414/) (2014)
- [Semi-Autoregressive Energy Flows: Exploring Likelihood-Free Training of Normalizing Flows](https://mlsanity.com/paper/2206.06672/) (2022)
- [Posterior Uncertainty Quantification in Neural Networks using Data Augmentation](https://mlsanity.com/paper/2403.12729/) (2024)
- [Estimation of copulas via Maximum Mean Discrepancy](https://mlsanity.com/paper/2010.00408/) (2020)
- [On recursive Bayesian predictive distributions](https://mlsanity.com/paper/1508.07448/) (2015)
- [Model selection in sparse high-dimensional vine copula models with application to portfolio risk](https://mlsanity.com/paper/1801.09739/) (2018)
- [Quasi-Bayes properties of a recursive procedure for mixtures](https://mlsanity.com/paper/1902.10708/) (2019)

## Built on by (most cited first, 5 of 5)

- [TabMGP: Martingale Posterior with TabPFN](https://mlsanity.com/paper/2510.25154/) (2025)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors](https://mlsanity.com/paper/2505.11325/) (2025)
- [Stepwise Variational Inference with Vine Copulas](https://mlsanity.com/paper/2603.22959/) (2026)

## Abstract (arXiv)

Recently proposed quasi-Bayesian (QB) methods initiated a new era in Bayesian computation by directly constructing the Bayesian predictive distribution through recursion, removing the need for expensive computations involved in sampling the Bayesian posterior distribution. This has proved to be data-efficient for univariate predictions, but extensions to multiple dimensions rely on a conditional decomposition resulting from predefined assumptions on the kernel of the Dirichlet Process Mixture Model, which is the implicit nonparametric model used. Here, we propose a different way to extend Quasi-Bayesian prediction to high dimensions through the use of Sklar's theorem by decomposing the predictive distribution into one-dimensional predictive marginals and a high-dimensional copula. Thus, we use the efficient recursive QB construction for the one-dimensional marginals and model the dependence using highly expressive vine copulas. Further, we tune hyperparameters using robust divergences (eg. energy score) and show that our proposed Quasi-Bayesian Vine (QB-Vine) is a fully non-parametric density estimator with an analytical form and convergence rate independent of the dimension of data in some situations. Our experiments illustrate that the QB-Vine is appropriate for high dimensional distributions (~64), needs very few samples to train (~200) and outperforms state-of-the-art methods with analytical forms for density estimation and supervised tasks by a considerable margin.