# Support Recovery in Mixture Models with Sparse Parameters

arXiv: https://arxiv.org/abs/2202.11940 · HTML: https://mlsanity.com/paper/2202.11940/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 20 of 20)

- [Mixture Models, Robustness, and Sum of Squares Proofs](https://mlsanity.com/paper/1711.07454/) (2017)
- [List-Decodable Robust Mean Estimation and Learning Mixtures of Spherical Gaussians](https://mlsanity.com/paper/1711.07211/) (2017)
- [Learning Mixtures of Linear Regressions with Nearly Optimal Complexity](https://mlsanity.com/paper/1802.07895/) (2018)
- [Tight bounds for learning a mixture of two gaussians](https://mlsanity.com/paper/1404.4997/) (2014)
- [Solving a Mixture of Many Random Linear Equations by Tensor Decomposition and Alternating Minimization](https://mlsanity.com/paper/1608.05749/) (2016)
- [Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression](https://mlsanity.com/paper/1810.05752/) (2018)
- [Spectral Experts for Estimating Mixtures of Linear Regressions](https://mlsanity.com/paper/1306.3729/) (2013)
- [Sample-Optimal Density Estimation in Nearly-Linear Time](https://mlsanity.com/paper/1506.00671/) (2015)
- [Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation](https://mlsanity.com/paper/1306.2035/) (2013)
- [A Latent Source Model for Online Collaborative Filtering](https://mlsanity.com/paper/1411.6591/) (2014)
- [Learning Mixtures of Linear Classifiers](https://mlsanity.com/paper/1311.2547/) (2013)
- [Sample Complexity of Learning Mixtures of Sparse Linear Regressions](https://mlsanity.com/paper/1910.14106/) (2019)
- [Detection and Feature Selection in Sparse Mixture Models](https://mlsanity.com/paper/1405.1478/) (2014)
- [Uniform Convergence Rates for Maximum Likelihood Estimation under Two-Component Gaussian Mixture Models](https://mlsanity.com/paper/2006.00704/) (2020)
- [Recovery of Sparse Signals from a Mixture of Linear Samples](https://mlsanity.com/paper/2006.16406/) (2020)
- [Recovery of sparse linear classifiers from mixture of responses](https://mlsanity.com/paper/2010.12087/) (2020)
- [Support Recovery of Sparse Signals from a Mixture of Linear Measurements](https://mlsanity.com/paper/2106.05951/) (2021)
- [Matrix factorization with Binary Components](https://mlsanity.com/paper/1401.6024/) (2014)
- [Algebraic and Analytic Approaches for Parameter Learning in Mixture Models](https://mlsanity.com/paper/2001.06776/) (2020)
- [A Simple Approach to Sparse Clustering](https://mlsanity.com/paper/1602.07277/) (2016)

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

- [Personalized Prediction By Learning Halfspace Reference Classes Under Well-Behaved Distribution](https://mlsanity.com/paper/2509.15592/) (2025)
- [Efficient Support Recovery of Mixtures of Sparse Linear Classifiers with Fewer Measurements](https://mlsanity.com/paper/2609.32176/) (2026)

## Abstract (arXiv)

Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter learning in mixture models is well-studied, the sparsity constraint remains relatively unexplored. Sparsity of parameter vectors is a natural constraint in variety of settings, and support recovery is a major step towards parameter estimation. We provide efficient algorithms for support recovery that have a logarithmic sample complexity dependence on the dimensionality of the latent space. Our algorithms are quite general, namely they are applicable to 1) mixtures of many different canonical distributions including Uniform, Poisson, Laplace, Gaussians, etc. 2) Mixtures of linear regressions and linear classifiers with Gaussian covariates under different assumptions on the unknown parameters. In most of these settings, our results are the first guarantees on the problem while in the rest, our results provide improvements on existing works.