# Recovery of Sparse Signals from a Mixture of Linear Samples

arXiv: https://arxiv.org/abs/2006.16406 · HTML: https://mlsanity.com/paper/2006.16406/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

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

- [Learning Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2201.11211/) (2022)
- [On Learning Mixture of Linear Regressions in the Non-Realizable Setting](https://mlsanity.com/paper/2205.13166/) (2022)
- [Support Recovery of Sparse Signals from a Mixture of Linear Measurements](https://mlsanity.com/paper/2106.05951/) (2021)
- [Support Recovery in Mixture Models with Sparse Parameters](https://mlsanity.com/paper/2202.11940/) (2022)
- [Learning and Generalization with Mixture Data](https://mlsanity.com/paper/2504.20651/) (2025)
- [Agnostic Learning of Mixed Linear Regressions with EM and AM Algorithms](https://mlsanity.com/paper/2406.01149/) (2024)

## Abstract (arXiv)

Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and mixed together. Recent works of Yin et al. and Krishnamurthy et al., 2019, focus on an experimental design setting of model recovery for this problem. It is assumed that the features can be designed and queried with to obtain their label. When queried, an oracle randomly selects one of the two different sparse linear models and generates a label accordingly. How many such oracle queries are needed to recover both of the models simultaneously? This question can also be thought of as a generalization of the well-known compressed sensing problem (Cand`es and Tao, 2005, Donoho, 2006). In this work, we address this query complexity problem and provide efficient algorithms that improves on the previously best known results.