Thresholding based robust estimation for generalized mixture model

Music City Center 

Finite mixture regression models are versatile tools for analyzing mixed regression relationships within clustered and heterogeneous populations. However, the classical normal mixture model often falls short when dealing with nonlinear regression data, especially in the presence of severe outliers. To address this, we introduce a novel generalized robust mixture regression procedure within the finite mixture regression framework. This procedure features sparse, scale dependent mean shift parameters, facilitating outlier detection and ensuring robust parameter estimation. Our approach incorporates three key innovations. (1)A penalized likelihood approach using a combination of L0 and L2 regularization to induce sparsity among mean shift parameters.(2) A close connection to the method of trimming, including explicit outlyingness parameters for all samples, which simplifies computation, aids theoretical analysis, and reduces the need for parameter tuning.(3) High scalability, allowing the implementation to handle nonlinear regression data. A threshold-based generalized Expectation-Maximization algorithm has been developed to ensure stable and efficient computation.

Mixture regression models

EM algorithm

Thresholding

Outlier detection

Mean-shift

Robust procedures 

IMS