Department of Epidemiology & Biostatistics Special Seminar presented by
Zhu Wang, PhD
Associate Professor, Biostatistics
Population Health Sciences Department
University of Texas Health San Antonio
Robust estimation is primarily concerned with how to provide reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. In modern penalized generalized linear model (GLM), however, there is limited research on robust estimation that can provide weights to determine outlier status of the observations. We propose a unified framework based on a large family of loss functions, a composite of concave and convex functions (CC-family) and propose the iteratively reweighted convex optimization (IRCO), a generalization of the iteratively reweighted least squares in robust linear regression. In the applications of robust GLM, the IRCO becomes iteratively reweighted GLM. The unified framework contains penalized estimation and robust support vector machine. Furthermore, the IRCO is applied to boosting, a popular machine learning algorithm with wide applications. The method fills a gap that there was a lack of weighted estimation in robust boosting to indicate outlier status of the observations. Data applications will be illustrated.
