# Global Convergence of Online Identification for Mixed Linear Regression

arXiv: https://arxiv.org/abs/2311.18506 · HTML: https://mlsanity.com/paper/2311.18506/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 46 references that are in the map.
- First posted on arXiv 30 Nov 2023.

## Builds on (most cited first, 14 of 14)

- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Phase Retrieval using Alternating Minimization](https://mlsanity.com/paper/1306.0160/) (2013)
- [Ten Steps of EM Suffice for Mixtures of Two Gaussians](https://mlsanity.com/paper/1609.00368/) (2016)
- [Learning Mixtures of Linear Regressions with Nearly Optimal Complexity](https://mlsanity.com/paper/1802.07895/) (2018)
- [EM Converges for a Mixture of Many Linear Regressions](https://mlsanity.com/paper/1905.12106/) (2019)
- [Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression](https://mlsanity.com/paper/1810.05752/) (2018)
- [On the Minimax Optimality of the EM Algorithm for Learning Two-Component Mixed Linear Regression](https://mlsanity.com/paper/2006.02601/) (2020)
- [Spectral Experts for Estimating Mixtures of Linear Regressions](https://mlsanity.com/paper/1306.3729/) (2013)
- [Estimating the Coefficients of a Mixture of Two Linear Regressions by Expectation Maximization](https://mlsanity.com/paper/1704.08231/) (2017)
- [Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities](https://mlsanity.com/paper/1906.06776/) (2019)
- [Convergence of Parameter Estimates for Regularized Mixed Linear Regression Models](https://mlsanity.com/paper/1903.09235/) (2019)
- [Imbalanced Mixed Linear Regression](https://mlsanity.com/paper/2301.12559/) (2023)
- [Supervised clustering of high dimensional data using regularized mixture modeling](https://mlsanity.com/paper/2007.09720/) (2020)
- [Robust structured heterogeneity analysis approach for high-dimensional data](https://mlsanity.com/paper/2211.16475/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learning a Class of Mixed Linear Regressions: Global Convergence under General Data Conditions](https://mlsanity.com/paper/2503.18500/) (2025)

## Abstract (arXiv)

Mixed linear regression (MLR) is a powerful model for characterizing nonlinear relationships by utilizing a mixture of linear regression sub-models. The identification of MLR is a fundamental problem, where most of the existing results focus on offline algorithms, rely on independent and identically distributed (i.i.d) data assumptions, and provide local convergence results only. This paper investigates the online identification and data clustering problems for two basic classes of MLRs, by introducing two corresponding new online identification algorithms based on the expectation-maximization (EM) principle. It is shown that both algorithms will converge globally without resorting to the traditional i.i.d data assumptions. The main challenge in our investigation lies in the fact that the gradient of the maximum likelihood function does not have a unique zero, and a key step in our analysis is to establish the stability of the corresponding differential equation in order to apply the celebrated Ljung's ODE method. It is also shown that the within-cluster error and the probability that the new data is categorized into the correct cluster are asymptotically the same as those in the case of known parameters. Finally, numerical simulations are provided to verify the effectiveness of our online algorithms.