# Detection and Feature Selection in Sparse Mixture Models

arXiv: https://arxiv.org/abs/1405.1478 · HTML: https://mlsanity.com/paper/1405.1478/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2014.

## Built on by (most cited first, 6 of 6)

- [Semi-Supervised Sparse Gaussian Classification: Provable Benefits of Unlabeled Data](https://mlsanity.com/paper/2409.03335/) (2024)
- [Support Recovery in Mixture Models with Sparse Parameters](https://mlsanity.com/paper/2202.11940/) (2022)
- [Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning](https://mlsanity.com/paper/2304.09154/) (2023)
- [On Parameter Estimation in Deviated Gaussian Mixture of Experts](https://mlsanity.com/paper/2402.05220/) (2024)
- [Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap](https://mlsanity.com/paper/2205.13527/) (2022)
- [Subject clustering by IF-PCA and several recent methods](https://mlsanity.com/paper/2306.05363/) (2023)

## Abstract (arXiv)

We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance of various procedures, including the top sparse eigenvalue of the sample covariance matrix and other projection tests based on moments, such as the skewness and kurtosis tests of Malkovich and Afifi (1973), and other variants which we were better able to control under the null.