Deriving statistical significance maps for support vector regression using medical imaging data

Regression analysis involves predicting a continuous variable using imaging data. The Support Vector Regression (SVR) algorithm has previously been used in addressing regression analysis in neuroimaging. However, identifying the regions of the image that the SVR uses to model the dependence of a target variable remains an open problem. It is an important issue when one wants to biologically interpret the meaning of a pattern that predicts the variable(s) of interest, and therefore to understand normal or pathological process. One possible approach to the identification of these regions is the use of permutation testing. Permutation testing involves 1) generation of a large set of 'null SVR models' using randomly permuted sets of target variables, and 2) comparison of the SVR model trained using the original labels to the set of null models. These permutation tests often require prohibitively long computational time. Recent work in support vector classification shows that it is possible to analytically approximate the results of permutation testing in medical image analysis. We propose an analogous approach to approximate permutation testing based analysis for support vector regression with medical imaging data. In this paper we present 1) the theory behind our approximation, and 2) experimental results using two real datasets.