AUTHOR=Rastogi Abhishake , Sampath Sivananthan 

TITLE=Optimal Rates for the Regularized Learning Algorithms under General Source Condition

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=3

YEAR=2017

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2017.00003

DOI=10.3389/fams.2017.00003

ISSN=2297-4687

ABSTRACT=<p>We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discuss the upper convergence rates of Tikhonov regularizer under general source condition corresponding to increasing monotone index function. The convergence issues are studied for general regularization schemes by using the concept of operator monotone index functions in minimax setting. Further we also address the minimum possible error for any learning algorithm.</p>