# Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updates

arXiv: https://arxiv.org/abs/2206.06462 · HTML: https://mlsanity.com/paper/2206.06462/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 64 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 20 of 20)

- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Convolutional Gaussian Processes](https://mlsanity.com/paper/1709.01894/) (2017)
- [Few-shot Autoregressive Density Estimation: Towards Learning to Learn Distributions](https://mlsanity.com/paper/1710.10304/) (2017)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Copula & Marginal Flows: Disentangling the Marginal from its Joint](https://mlsanity.com/paper/1907.03361/) (2019)
- [On recursive Bayesian predictive distributions](https://mlsanity.com/paper/1508.07448/) (2015)
- [Quasi-Bayes properties of a recursive procedure for mixtures](https://mlsanity.com/paper/1902.10708/) (2019)
- [Subsampling Sequential Monte Carlo for Static Bayesian Models](https://mlsanity.com/paper/1805.03317/) (2018)
- [On nonparametric estimation of a mixing density via the predictive recursion algorithm](https://mlsanity.com/paper/1812.02149/) (2018)
- [Bayesian predictive inference without a prior](https://mlsanity.com/paper/2104.11643/) (2021)
- [A Predictive Approach to Bayesian Nonparametric Survival Analysis](https://mlsanity.com/paper/2202.10361/) (2022)
- [A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions](https://mlsanity.com/paper/2204.01646/) (2022)

## Built on by (most cited first, 3 of 3)

- [TabMGP: Martingale Posterior with TabPFN](https://mlsanity.com/paper/2510.25154/) (2025)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [On Uncertainty Quantification for Near-Bayes Optimal Algorithms](https://mlsanity.com/paper/2403.19381/) (2024)

## Abstract (arXiv)

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the posterior predictive of the Dirichlet process mixture model. In general, direct estimation of the posterior predictive is intractable and so methods typically resort to approximating the posterior distribution as an intermediate step. The recent development of quasi-Bayesian predictive copula updates, however, has made it possible to perform tractable predictive density estimation without the need for posterior approximation. Although these estimators are computationally appealing, they tend to struggle on non-smooth data distributions. This is due to the comparatively restrictive form of the likelihood models from which the proposed copula updates were derived. To address this shortcoming, we consider a Bayesian nonparametric model with an autoregressive likelihood decomposition and a Gaussian process prior. While the predictive update of such a model is typically intractable, we derive a quasi-Bayesian predictive update that achieves state-of-the-art results in small-data regimes.