# Data-driven deep density estimation

arXiv: https://arxiv.org/abs/2107.11085 · HTML: https://mlsanity.com/paper/2107.11085/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 23 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Fast On-Line Kernel Density Estimation for Active Object Localization](https://mlsanity.com/paper/1611.05369/) (2016)

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

- [A Simple Yet Effective Strategy to Robustify the Meta Learning Paradigm](https://mlsanity.com/paper/2310.00708/) (2023)
- [A Representation Learning Approach to Feature Drift Detection in Wireless Networks](https://mlsanity.com/paper/2505.10325/) (2025)
- [Adaptive Kernel Density Estimation with Pre-training](https://mlsanity.com/paper/2605.13092/) (2026)

## Abstract (arXiv)

Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in 2D sensor readings, or reconstructing scenes from 3D scans. In this paper, we introduce a learned, data-driven deep density estimation (DDE) to infer PDFs in an accurate and efficient manner, while being independent of domain dimensionality or sample size. Furthermore, we do not require access to the original PDF during estimation, neither in parametric form, nor as priors, or in the form of many samples. This is enabled by training an unstructured convolutional neural network on an infinite stream of synthetic PDFs, as unbound amounts of synthetic training data generalize better across a deck of natural PDFs than any natural finite training data will do. Thus, we hope that our publicly available DDE method will be beneficial in many areas of data analysis, where continuous models are to be estimated from discrete observations.