  We give sublinear-time approximation algorithms for some optimization
problems arising in machine learning, such as training linear classifiers and
finding minimum enclosing balls. Our algorithms can be extended to some
kernelized versions of these problems, such as SVDD, hard margin SVM, and
L2-SVM, for which sublinear-time algorithms were not known before. These new
algorithms use a combination of a novel sampling techniques and a new
multiplicative update algorithm. We give lower bounds which show the running
times of many of our algorithms to be nearly best possible in the unit-cost RAM
model. We also give implementations of our algorithms in the semi-streaming
setting, obtaining the first low pass polylogarithmic space and sublinear time
algorithms achieving arbitrary approximation factor.
