A0334
Title: Nonparametric reduced-rank estimation of multiple regression functions
Authors: Kwan-Young Bak - Sungshin Women's University (Korea, South) [presenting]
Ja Yong Koo - Korea University (Korea, South)
Abstract: A multi-task nonparametric regression problem in which the underlying functions possess a low-rank structure is examined. A nonparametric function estimation method based on the nuclear norm penalization (NNP) approach is proposed to incorporate the low-dimensional structure in the recovery of multiple functions. This leads to a nonparametric version of the reduced rank regression estimator under the multi-task learning framework. Numerical studies are provided to illustrate the efficiency of the proposed method. The results show that the information pooling across multiple experiments based on the low-rank structure can significantly outperform the separate estimation method. Regarding the theoretical aspect, a non-asymptotic oracle-type inequality is first obtained to study the properties of the reduced rank estimator. Using the inequality, the proposed method's minimaxity and rank identification consistency is proved.
