STATISTICS SEMINAR
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.
