# Boosting in Univariate Nonparametric Maximum Likelihood Estimation

arXiv: https://arxiv.org/abs/2101.08505 · HTML: https://mlsanity.com/paper/2101.08505/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [Recent progress in log-concave density estimation](https://mlsanity.com/paper/1709.03154/) (2017)
- [On recursive Bayesian predictive distributions](https://mlsanity.com/paper/1508.07448/) (2015)
- [Simple Local Polynomial Density Estimators](https://mlsanity.com/paper/1811.11512/) (2018)

## Built on by (most cited first, 2 of 2)

- [Boosting Independent Component Analysis](https://mlsanity.com/paper/2112.06920/) (2021)
- [Neural-g: A Deep Learning Framework for Mixing Density Estimation](https://mlsanity.com/paper/2406.05986/) (2024)

## Abstract (arXiv)

Nonparametric maximum likelihood estimation is intended to infer the unknown density distribution while making as few assumptions as possible. To alleviate the over parameterization in nonparametric data fitting, smoothing assumptions are usually merged into the estimation. In this paper a novel boosting-based method is introduced to the nonparametric estimation in univariate cases. We deduce the boosting algorithm by the second-order approximation of nonparametric log-likelihood. Gaussian kernel and smooth spline are chosen as weak learners in boosting to satisfy the smoothing assumptions. Simulations and real data experiments demonstrate the efficacy of the proposed approach.