Component-wise Adaptive Trimming For Robust Mixture Regression

TL;DR

The paper introduces a fast, robust mixture regression algorithm called Component-wise Adaptive Trimming (CAT) that effectively detects outliers and estimates parameters simultaneously, improving performance in heterogeneous data like genomics.

Contribution

The paper presents the CAT algorithm, a novel robust mixture regression method that adaptively trims outliers without prior contamination level knowledge, outperforming existing methods.

Findings

CAT handles outliers and heavy-tailed noise effectively.

It outperforms existing algorithms in simulated and real genomic data.

Implemented in R package 'RobMixReg' available on CRAN.

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.