# Boosted Density Estimation Remastered

arXiv: https://arxiv.org/abs/1803.08178 · HTML: https://mlsanity.com/paper/1803.08178/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2018.

## Built on by (most cited first, 7 of 7)

- [Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows](https://mlsanity.com/paper/2305.18910/) (2023)
- [End-To-End Learning of Gaussian Mixture Priors for Diffusion Sampler](https://mlsanity.com/paper/2503.00524/) (2025)
- [NRGBoost: Energy-Based Generative Boosted Trees](https://mlsanity.com/paper/2410.03535/) (2024)
- [Boosting Variational Inference With Locally Adaptive Step-Sizes](https://mlsanity.com/paper/2105.09240/) (2021)
- [Tempered Calculus for ML: Application to Hyperbolic Model Embedding](https://mlsanity.com/paper/2402.04163/) (2024)
- [How to Boost Any Loss Function](https://mlsanity.com/paper/2407.02279/) (2024)
- [Seasoning Generative Models for a Generalization Aftertaste](https://mlsanity.com/paper/2603.18817/) (2026)

## Abstract (arXiv)

There has recently been a steady increase in the number iterative approaches to density estimation. However, an accompanying burst of formal convergence guarantees has not followed; all results pay the price of heavy assumptions which are often unrealistic or hard to check. The Generative Adversarial Network (GAN) literature --- seemingly orthogonal to the aforementioned pursuit --- has had the side effect of a renewed interest in variational divergence minimisation (notably f-GAN). We show that by introducing a weak learning assumption (in the sense of the classical boosting framework) we are able to import some recent results from the GAN literature to develop an iterative boosted density estimation algorithm, including formal convergence results with rates, that does not suffer the shortcomings other approaches. We show that the density fit is an exponential family, and as part of our analysis obtain an improved variational characterisation of f-GAN.