|
Abstract:
|
Cross validation is one of the most popular techniques for selecting tuning parameters in penalized M-estimation. To lessen the computational cost of cross validation, approximation schemes such as generalized approximate cross validation (GACV) are often employed. However, such approximations may not work well when non-smooth loss functions are involved. In this paper, we propose a new algorithm which computes the cross validation scores exactly through a case-weight adjusted solution path. The main idea is to add a weight for each individual case and adjust the weight continuously to link the estimators based on the full data and those with some cases deleted. This allows us to design a solution path algorithm to compute all leave-one-out estimators very efficiently from the full-data solution. We demonstrate our proposed method for quantile regression with ridge penalty. We show that the case-weight adjusted solution path is piecewise linear, and using the solution path, we observe that different modes of case influences emerge, depending on the data dimensions and penalty parameter. Extensive numerical experiments further illustrate the superior performance of our approach.
|
