Multivariate Analysis from a Statistical Point of View

Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, most of the common approaches were borrowed from other fields. Each of these algorithms were developed for their own particular task, thus they look quite different at their core. It is not obvious that what these different algorithms do internally is optimal for the the tasks which they perform within high energy physics. It is also quite difficult to compare these different algorithms due to the differences in the formalisms that were used to derive and/or document them. In Section 2 we introduce a formalism for a Learning Machine, which is general enough to encompass all of the techniques used within high energy physics. In Sections 3 & 4 we review the statistical statements relevant to new particle searches and translate them into the formalism of statistical learning theory. In the remainder of the note, we look at the main results of statistical learning theory and their relevance to some of the common algorithms used within high energy physics.