  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.
