# Spectral Experts for Estimating Mixtures of Linear Regressions

arXiv: https://arxiv.org/abs/1306.3729 · HTML: https://mlsanity.com/paper/1306.3729/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2013.

## Built on by (most cited first, 22 of 22)

- [Towards Understanding Mixture of Experts in Deep Learning](https://mlsanity.com/paper/2208.02813/) (2022)
- [Breaking the gridlock in Mixture-of-Experts: Consistent and Efficient Algorithms](https://mlsanity.com/paper/1802.07417/) (2018)
- [On Learning Mixture of Linear Regressions in the Non-Realizable Setting](https://mlsanity.com/paper/2205.13166/) (2022)
- [A Wasserstein Minimax Framework for Mixed Linear Regression](https://mlsanity.com/paper/2106.07537/) (2021)
- [Statistical-Computational Tradeoffs in Mixed Sparse Linear Regression](https://mlsanity.com/paper/2303.02118/) (2023)
- [Support Recovery of Sparse Signals from a Mixture of Linear Measurements](https://mlsanity.com/paper/2106.05951/) (2021)
- [Efficient List-Decodable Regression using Batches](https://mlsanity.com/paper/2211.12743/) (2022)
- [Sparse Mixed Linear Regression with Guarantees: Taming an Intractable Problem with Invex Relaxation](https://mlsanity.com/paper/2206.01167/) (2022)
- [Tight Bounds on the Hardness of Learning Simple Nonparametric Mixtures](https://mlsanity.com/paper/2203.15150/) (2022)
- [Imbalanced Mixed Linear Regression](https://mlsanity.com/paper/2301.12559/) (2023)
- [Mixed Regression via Approximate Message Passing](https://mlsanity.com/paper/2304.02229/) (2023)
- [Linear Regression using Heterogeneous Data Batches](https://mlsanity.com/paper/2309.01973/) (2023)
- [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)
- [Efficient Algorithms for Estimating the Parameters of Mixed Linear Regression Models](https://mlsanity.com/paper/2105.05953/) (2021)
- [Sharp analysis of EM for learning mixtures of pairwise differences](https://mlsanity.com/paper/2302.10066/) (2023)
- [Global Convergence of Online Identification for Mixed Linear Regression](https://mlsanity.com/paper/2311.18506/) (2023)
- [Agnostic Learning of Mixed Linear Regressions with EM and AM Algorithms](https://mlsanity.com/paper/2406.01149/) (2024)
- [In-context Learning for Mixture of Linear Regressions: Existence, Generalization and Training Dynamics](https://mlsanity.com/paper/2410.14183/) (2024)
- [On the robust learning mixtures of linear regressions](https://mlsanity.com/paper/2305.15317/) (2023)
- [Expectation Maximization (EM) Converges for General Agnostic Mixtures](https://mlsanity.com/paper/2604.05842/) (2026)
- [Robust Subgroup Analysis for Heterogeneous Censored Data](https://mlsanity.com/paper/2607.11389/) (2026)

## Abstract (arXiv)

Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture of linear regressions, a simple instance of a discriminative latent-variable model. Our approach relies on a low-rank linear regression to recover a symmetric tensor, which can be factorized into the parameters using a tensor power method. We prove rates of convergence for our estimator and provide an empirical evaluation illustrating its strengths relative to local optimization (EM).