# Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications

arXiv: https://arxiv.org/abs/1904.00176 · HTML: https://mlsanity.com/paper/1904.00176/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2019.

## Built on by (most cited first, 18 of 18)

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- [Anomaly Detection with Variance Stabilized Density Estimation](https://mlsanity.com/paper/2306.00582/) (2023)
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- [Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals](https://mlsanity.com/paper/2308.14945/) (2023)
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- [Conditional Kernel Imitation Learning for Continuous State Environments](https://mlsanity.com/paper/2308.12573/) (2023)
- [Discrete distributions are learnable from metastable samples](https://mlsanity.com/paper/2410.13800/) (2024)
- [MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design](https://mlsanity.com/paper/2406.08591/) (2024)
- [NeuroPMD: Neural Fields for Density Estimation on Product Manifolds](https://mlsanity.com/paper/2501.02994/) (2025)
- [Density Sketches for Sampling and Estimation](https://mlsanity.com/paper/2102.12301/) (2021)
- [Bona fide Riesz projections for density estimation](https://mlsanity.com/paper/2204.13606/) (2022)
- [Implicit Hypothesis Testing and Divergence Preservation in Neural Network Representations](https://mlsanity.com/paper/2601.20477/) (2026)

## Abstract (arXiv)

Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization, and machine learning. Density Estimation is widely adopted in the domain of unsupervised learning especially for the application of clustering. As big data become pervasive in almost every area of data sciences, analyzing high-dimensional data that have many features and variables appears to be a major focus in both academia and industry. High-dimensional data pose challenges not only from the theoretical aspects of statistical inference, but also from the algorithmic/computational considerations of machine learning and data analytics. This paper reviews a collection of selected nonparametric density estimation algorithms for high-dimensional data, some of them are recently published and provide interesting mathematical insights. The important application domain of nonparametric density estimation, such as { modal clustering}, are also included in this paper. Several research directions related to density estimation and high-dimensional data analysis are suggested by the authors.