Statistics Seminar: STA 290
Monday, April 9th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm prior to seminar in MSB 4110 (Statistics Lounge)
Speaker: Chunming Zhang (University of Wisconsin)
Title: Robust inference in regression and classification methods for large dimensional data
Abstract: In statistical data analysis and machine learning practice, Bregman divergence (BD) plays an important role in quantifying error measures for regression estimators, classification procedures and forecasting methods.
The quadratic loss function and the negative quasi-likelihood are two examples of widely used error measures which along with many others belong to the family of BD, but are not resistant to either outlying observations or high leverage points, more often encountered in large- and high-dimensional datasets. In this work, we introduce a class of robust forms of BD, called robust-BD, and develop robust inference for penalized robust-BD estimates of parameters in sparse large-dimensional regression models, which allow distributions of the response variables given covariates to be incompletely specified. It is shown that the new estimator, combined with appropriate penalties, achieves the oracle property of the ordinary penalized least-squares and penalized-likelihood estimators, but is robust to outliers, a very desirable property in many real-world applications. Numerical results are presented to compare the performance of the new estimators with that of the classical ones. A real dataset is analyzed for illustration.