# Learning Entangled Single-Sample Distributions via Iterative Trimming

arXiv: https://arxiv.org/abs/2004.09563 · HTML: https://mlsanity.com/paper/2004.09563/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Efficient Multivariate Robust Mean Estimation Under Mean-Shift Contamination](https://mlsanity.com/paper/2502.14772/) (2025)
- [Near-Optimal Mean Estimation with Unknown, Heteroskedastic Variances](https://mlsanity.com/paper/2312.02417/) (2023)
- [Entangled Mean Estimation in High-Dimensions](https://mlsanity.com/paper/2501.05425/) (2025)
- [Performance of the empirical median for location estimation in heteroscedastic settings](https://mlsanity.com/paper/2501.16956/) (2025)

## Abstract (arXiv)

In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one single sample from each distribution. We study mean estimation and linear regression under general conditions, and analyze a simple and computationally efficient method based on iteratively trimming samples and re-estimating the parameter on the trimmed sample set. We show that the method in logarithmic iterations outputs an estimation whose error only depends on the noise level of the lceil α n rceil-th noisiest data point where α is a constant and n is the sample size. This means it can tolerate a constant fraction of high-noise points. These are the first such results for the method under our general conditions. It also justifies the wide application and empirical success of iterative trimming in practice. Our theoretical results are complemented by experiments on synthetic data.