Imbalanced Mixed Linear Regression

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Mixture regression model, Mixture of linear models, Iteratively reweighted least squares
TL;DR: We solve imbalanced mixed linear regression using tools from robust regression
Abstract: We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. In practical applications, the mixture of the $K$ models may be imbalanced with a significantly different number of samples from each model. Unfortunately, most MLR methods do not perform well in such settings. Motivated by this practical challenge, in this work we propose Mix-IRLS, a novel, simple and fast algorithm for MLR with excellent performance on both balanced and imbalanced mixtures. In contrast to popular approaches that recover the $K$ models simultaneously, Mix-IRLS does it sequentially using tools from robust regression. Empirically, beyond imbalanced mixtures, Mix-IRLS succeeds in a broad range of additional settings where other methods fail, including small sample sizes, presence of outliers, and an unknown number of models $K$. Furthermore, Mix-IRLS outperforms competing methods on several real-world datasets, in some cases by a large margin. We complement our empirical results by deriving a recovery guarantee for Mix-IRLS, which highlights its advantage on imbalanced mixtures.
Supplementary Material: pdf
Submission Number: 1793