# Recent progress in log-concave density estimation

arXiv: https://arxiv.org/abs/1709.03154 · HTML: https://mlsanity.com/paper/1709.03154/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2017.

## Built on by (most cited first, 15 of 15)

- [Adaptive transfer learning](https://mlsanity.com/paper/2106.04455/) (2021)
- [On the Minimal Error of Empirical Risk Minimization](https://mlsanity.com/paper/2102.12066/) (2021)
- [Universal Inference Meets Random Projections: A Scalable Test for Log-concavity](https://mlsanity.com/paper/2111.09254/) (2021)
- [Boosting in Univariate Nonparametric Maximum Likelihood Estimation](https://mlsanity.com/paper/2101.08505/) (2021)
- [Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning](https://mlsanity.com/paper/2304.09154/) (2023)
- [On the quality of randomized approximations of Tukey's depth](https://mlsanity.com/paper/2309.05657/) (2023)
- [Truncated LinUCB for Stochastic Linear Bandits](https://mlsanity.com/paper/2202.11735/) (2022)
- [Active-set algorithms based statistical inference for shape-restricted generalized additive Cox regression models](https://mlsanity.com/paper/2106.15735/) (2021)
- [An Efficient Minimax Optimal Estimator For Multivariate Convex Regression](https://mlsanity.com/paper/2205.03368/) (2022)
- [Log-concave density estimation in undirected graphical models](https://mlsanity.com/paper/2206.05227/) (2022)
- [A statistical perspective on algorithm unrolling models for inverse problems](https://mlsanity.com/paper/2311.06395/) (2023)
- [Simultaneous estimation of multiple discrete unimodal distributions under stochastic order constraints](https://mlsanity.com/paper/2603.11532/) (2026)
- [Density estimation for Hellinger via minimum-distance estimators: mixtures of Gaussians, log-concave, and more](https://mlsanity.com/paper/2606.11469/) (2026)
- [Nonparametric Hypothesis Testing of High-dimensional Clustering With Application to Single-cell RNA Data](https://mlsanity.com/paper/2609.05683/) (2026)
- [Instance-Optimal Adaptive Location Estimation via Multiscale Mid-Summaries](https://mlsanity.com/paper/2609.20749/) (2026)

## Abstract (arXiv)

In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one or more bandwidths. The purpose of this article is to describe some of the properties of the class of log-concave densities on ℝd which make it so attractive from a statistical perspective, and to outline the latest methodological, theoretical and computational advances in the area.