Efficient Algorithms for Estimating the Parameters of Mixed Linear Regression Models

Mixed linear regression (MLR) models nonlinear data as a mixture of linear components. When noise is Gaussian, the Expectation-Maximization (EM) algorithm is commonly used for maximum likelihood estimation. However, with nonGaussian noise-such as Laplacian-EM loses its closed-form updates, making it computationally inefficient. In this work, we address MLR parameter estimation under Laplacian noise by proposing a new algorithm that combines EM's structure with the efficiency of the Alternating Direction Method of Multipliers (ADMM). Experiments show our method outperforms EM in both accuracy and runtime.