題 目：Degrees of Freedom of the Reduced Rank Regression
主講人：王乃昕教授 (University of Michigan, USA)
時 間：101年12月28日(星期五)上午10:40-11:30
地 點：交大綜合一館427室
Abstract
We study the degrees of freedom of the reduced rank regression estimator in
the framework of Stein's unbiased risk estimation (SURE). We derive a
finite-sample exact unbiased estimator of the degrees of freedom for the
reduced rank regression. We show that it is significantly different from the
number of free parameters in the model, which is often taken as a heuristic
estimate of the degrees of freedom for the reduced rank regression. Using the
exact unbiased estimator of the degrees of freedom, one can easily employ
various model selection criteria such as Mallow's Cp or GCV to efficiently
choose an optimal rank for the reduced rank regression problem, which often
outperforms its heuristic counterpart in terms of prediction accuracy and
successfully avoids computationally expensive data perturbation or bootstrap
based methods. We have also extended the proposed approach to other related
estimation procedures, including the reduced rank ridge regression and a
weighted nuclear norm penalized multivariate regression.
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