Component-wise Adaptive Trimming For Robust Mixture Regression

• URL: http://arxiv.org/abs/2005.11599v3
• Date: Mon, 19 Apr 2021 15:54:18 GMT
• Title: Component-wise Adaptive Trimming For Robust Mixture Regression
• Authors: Wennan Chang, Xinyu Zhou, Yong Zang, Chi Zhang, Sha Cao
• Abstract summary: Existing robust mixture regression methods suffer from outliers as they either conduct outlier estimation in presence of outliers, or rely on prior knowledge of the level of contamination. Here we propose a fast and efficient robust mixture regression algorithm called adaptive-wise Adaptive Component (CAT) method.
• Score: 15.633993488010292
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Parameter estimation of mixture regression model using the expectation maximization (EM) algorithm is highly sensitive to outliers. Here we propose a fast and efficient robust mixture regression algorithm, called Component-wise Adaptive Trimming (CAT) method. We consider simultaneous outlier detection and robust parameter estimation to minimize the effect of outlier contamination. Robust mixture regression has many important applications including in human cancer genomics data, where the population often displays strong heterogeneity added by unwanted technological perturbations. Existing robust mixture regression methods suffer from outliers as they either conduct parameter estimation in the presence of outliers, or rely on prior knowledge of the level of outlier contamination. CAT was implemented in the framework of classification expectation maximization, under which a natural definition of outliers could be derived. It implements a least trimmed squares (LTS) approach within each exclusive mixing component, where the robustness issue could be transformed from the mixture case to simple linear regression case. The high breakdown point of the LTS approach allows us to avoid the pre-specification of trimming parameter. Compared with multiple existing algorithms, CAT is the most competitive one that can handle and adaptively trim off outliers as well as heavy tailed noise, in different scenarios of simulated data and real genomic data. CAT has been implemented in an R package `RobMixReg' available in CRAN.

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