Efficient Algorithms for Estimating the Parameters of Mixed Linear Regression Models
This work addresses a specific bottleneck in statistical modeling for researchers dealing with non-Gaussian noise, offering an incremental improvement over existing methods.
The paper tackles the problem of estimating parameters in mixed linear regression models with non-Gaussian noise, specifically Laplacian noise, where EM algorithms fail due to lack of closed-form updates. It proposes a new algorithm combining ADMM with EM, showing improved statistical accuracy and computational time in numerical experiments.
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM) algorithm is a widely-used algorithm for maximum likelihood estimation of MLR parameters. However, when noise is non-Gaussian, the steps of EM algorithm may not have closed-form update rules, which makes EM algorithm impractical. In this work, we study the maximum likelihood estimation of the parameters of MLR model when the additive noise has non-Gaussian distribution. In particular, we consider the case that noise has Laplacian distribution and we first show that unlike the the Gaussian case, the resulting sub-problems of EM algorithm in this case does not have closed-form update rule, thus preventing us from using EM in this case. To overcome this issue, we propose a new algorithm based on combining the alternating direction method of multipliers (ADMM) with EM algorithm idea. Our numerical experiments show that our method outperforms the EM algorithm in statistical accuracy and computational time in non-Gaussian noise case.