Statistical SVMs for detection and universal classification
 
The support vector machine (SVM) has emerged as one of the most popular approaches to classification and supervised learning.
It is a flexible approach for solving the problems posed in these areas, but the approach is not easily adapted to noisy data in which
absolute discrimination is not possible. We address this issue in this paper by returning to the statistical setting.  The main
contribution is the introduction of a statistical support vector machine (SSVM) that captures all of the desirable features
of the SVM, along with desirable statistical features of the classical likelihood ratio test. In particular, we establish the following: 

(i) The SSVM can be designed so that it forms a continuous function of the data, yet also approximates the potentially discontinuous log likelihood ratio test.

(ii) Extension to universal detection is developed, in which only  one hypothesis is labeled (a semi-supervised learning problem).

(iii)  The SSVM generalizes the robust hypothesis testing problem based on a moment class.

Motivation for the approach and analysis are each based on ideas from information theory.  A detailed performance analysis is provided in the special case of i.i.d. observations. 

Research supported by NSF under grant CCF 07-29031, by UTRC, Motorola, and by the DARPA ITMANET program.