# Variational Polya Tree

arXiv: https://arxiv.org/abs/2510.22651 · HTML: https://mlsanity.com/paper/2510.22651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 26 Oct 2025.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Neural Architecture Search with Bayesian Optimisation and Optimal Transport](https://mlsanity.com/paper/1802.07191/) (2018)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [A Deep and Tractable Density Estimator](https://mlsanity.com/paper/1310.1757/) (2013)
- [Block Neural Autoregressive Flow](https://mlsanity.com/paper/1904.04676/) (2019)
- [All You Need is a Good Functional Prior for Bayesian Deep Learning](https://mlsanity.com/paper/2011.12829/) (2020)
- [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [Transformation Autoregressive Networks](https://mlsanity.com/paper/1801.09819/) (2018)
- [AMF: Aggregated Mondrian Forests for Online Learning](https://mlsanity.com/paper/1906.10529/) (2019)
- [Learning Generative Models using Denoising Density Estimators](https://mlsanity.com/paper/2001.02728/) (2020)
- [A Bayesian Approach to Recurrence in Neural Networks](https://mlsanity.com/paper/1910.11247/) (2019)
- [Hidden Markov P'olya trees for high-dimensional distributions](https://mlsanity.com/paper/2011.03121/) (2020)

## Abstract (arXiv)

Density estimation is essential for generative modeling, particularly with the rise of modern neural networks. While existing methods capture complex data distributions, they often lack interpretability and uncertainty quantification. Bayesian nonparametric methods, especially the polya tree, offer a robust framework that addresses these issues by accurately capturing function behavior over small intervals. Traditional techniques like Markov chain Monte Carlo (MCMC) face high computational complexity and scalability limitations, hindering the use of Bayesian nonparametric methods in deep learning. To tackle this, we introduce the variational polya tree (VPT) model, which employs stochastic variational inference to compute posterior distributions. This model provides a flexible, nonparametric Bayesian prior that captures latent densities and works well with stochastic gradient optimization. We also leverage the joint distribution likelihood for a more precise variational posterior approximation than traditional mean-field methods. We evaluate the model performance on both real data and images, and demonstrate its competitiveness with other state-of-the-art deep density estimation methods. We also explore its ability in enhancing interpretability and uncertainty quantification. Code is available at https://github.com/howardchanth/var-polya-tree.