  We apply information-based complexity analysis to support vector machine
(SVM) algorithms, with the goal of a comprehensive continuous algorithmic
analysis of such algorithms. This involves complexity measures in which some
higher order operations (e.g., certain optimizations) are considered primitive
for the purposes of measuring complexity. We consider classes of information
operators and algorithms made up of scaled families, and investigate the
utility of scaling the complexities to minimize error. We look at the division
of statistical learning into information and algorithmic components, at the
complexities of each, and at applications to support vector machine (SVM) and
more general machine learning algorithms. We give applications to SVM
algorithms graded into linear and higher order components, and give an example
in biomedical informatics.
