# Learning Mixtures of Gaussians with Censored Data

arXiv: https://arxiv.org/abs/2305.04127 · HTML: https://mlsanity.com/paper/2305.04127/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 6 May 2023.

## Builds on (most cited first, 15 of 15)

- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Agnostic Estimation of Mean and Covariance](https://mlsanity.com/paper/1604.06968/) (2016)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [Being Robust (in High Dimensions) Can Be Practical](https://mlsanity.com/paper/1703.00893/) (2017)
- [Robust and Differentially Private Mean Estimation](https://mlsanity.com/paper/2102.09159/) (2021)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Ten Steps of EM Suffice for Mixtures of Two Gaussians](https://mlsanity.com/paper/1609.00368/) (2016)
- [Robustly Learning a Gaussian: Getting Optimal Error, Efficiently](https://mlsanity.com/paper/1704.03866/) (2017)
- [Global analysis of Expectation Maximization for mixtures of two Gaussians](https://mlsanity.com/paper/1608.07630/) (2016)
- [On Learning Mixtures of Well-Separated Gaussians](https://mlsanity.com/paper/1710.11592/) (2017)
- [Tight bounds for learning a mixture of two gaussians](https://mlsanity.com/paper/1404.4997/) (2014)
- [Efficient Statistics, in High Dimensions, from Truncated Samples](https://mlsanity.com/paper/1809.03986/) (2018)
- [Computationally and Statistically Efficient Truncated Regression](https://mlsanity.com/paper/2010.12000/) (2020)
- [On the Analysis of EM for truncated mixtures of two Gaussians](https://mlsanity.com/paper/1902.06958/) (2019)
- [A Fourier Approach to Mixture Learning](https://mlsanity.com/paper/2210.02415/) (2022)

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

- [Efficient Statistics With Unknown Truncation, Polynomial Time Algorithms, Beyond Gaussians](https://mlsanity.com/paper/2410.01656/) (2024)
- [Efficient Learning of Truncated Boolean Product Distributions: Influence to the Rescue](https://mlsanity.com/paper/2607.22889/) (2026)

## Abstract (arXiv)

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent variable models such as Gaussian mixtures are missing. Formally, we are given censored data from a mixture of univariate Gaussians  sumi=1k wi N(μi,σ2),  i.e. the sample is observed only if it lies inside a set S. The goal is to learn the weights wi and the means μi. We propose an algorithm that takes only frac1varepsilonO(k) samples to estimate the weights wi and the means μi within varepsilon error.