Communications in Mathematical Sciences

Volume 16 (2018)

Number 5

Regularized semi-supervised least squares regression with dependent samples

Pages: 1347 – 1360



Hongzhi Tong (School of Statistics, University of International Business and Economics, Beijing, China)

Michael Ng (Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong)


In this paper, we study regularized semi-supervised least squares regression with dependent samples. We analyze the regularized algorithm based on reproducing kernel Hilbert spaces, and show, with the use of unlabelled data that the regularized least squares algorithm can achieve the nearly minimax optimal learning rate with a logarithmic term for dependent samples. Our new results are better than existing results in the literature.


semi-supervised learning, regularization, least squares regression, non-iid sampling

2010 Mathematics Subject Classification

62J02, 68T05

Received 25 December 2017

Received revised 28 April 2018

Accepted 28 April 2018

Published 19 December 2018