Three-Toed Sloth

"Effect of Influential Observations on Penalized Linear Regression Estimators" (This Week at the Statistics Seminar)

It is only appropriate that a talk about influential outliers be held at on an unusual day, at an unusual time and place:

Karen Kafadar, "Effect of Influential Observations on Penalized Linear Regression Estimators"

Abstract: In current problems (e.g. microarrays, financial data) where the number of variables can greatly exceed the number of observations ("big p, small n"), penalized regression has been advocated as a way to identify informative variables by setting to zero a large subset of the regression coefficients. This approach to "model selection" aims for good fits to the data, but often attempts are made to interpret the resulting nonzero coefficients. With squared error loss and an L1 penalty (sum of the magnitudes of the regression coefficients, or "LASSO"), the resulting model can be highly sensitive to potential outliers, in either the response variable or the design space. In this study, we examine the effect of influential points (outliers and leverage points) on L1-penalized regression estimators, when the loss function is the usual L2 squared error loss, the biweight loss function, or the MM loss function, and show the advantages of a robust loss function to reduce the effect of influential points in the simple case of linear regression when the proportion of non-zero coefficients is less than 20 percent.

Joint work with Guilherme V. Rocha.

Time and place: 12:30--1:30 on Friday, 1 April 2011 in Rangos 2, University Center

As always, the talk is free and open to the public.

Enigmas of Chance