# Log-concave Density Estimation with Independent Components

arXiv: https://arxiv.org/abs/2401.01500 · HTML: https://mlsanity.com/paper/2401.01500/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2024.

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

- [Statistical Properties of Rectified Flow](https://mlsanity.com/paper/2511.03193/) (2025)
- [Nonparametric inference under shape constraints: past, present and future](https://mlsanity.com/paper/2509.26040/) (2025)
- [Distributional sentiment modeling and anomaly detection for consumer complaint assessment](https://mlsanity.com/paper/2609.31653/) (2026)

## Abstract (arXiv)

We propose a method for estimating a log-concave density on mathbb Rd from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave density estimation is hard both computationally and statistically, the independent components assumption alleviates both issues, while still maintaining a large non-parametric class. We prove that under mild conditions, at most tildeO(ε-4) samples (suppressing constants and log factors) suffice for our proposed estimator to be within ε of the original density in squared Hellinger distance. On the computational front, while the usual log-concave maximum likelihood estimate can be obtained via a finite-dimensional convex program, it is slow to compute -- especially in higher dimensions. We demonstrate through numerical experiments that our estimator can be computed efficiently, making it more practical to use.