  This paper presents a general framework for obtaining interpretable
multivariate discriminative models that allow efficient statistical inference
for neuroimage analysis. The framework, termed generative discriminative
machine (GDM), augments discriminative models with a generative regularization
term. We demonstrate that the proposed formulation can be optimized in closed
form and in dual space, allowing efficient computation for high dimensional
neuroimaging datasets. Furthermore, we provide an analytic estimation of the
null distribution of the model parameters, which enables efficient statistical
inference and p-value computation without the need for permutation testing. We
compared the proposed method with both purely generative and discriminative
learning methods in two large structural magnetic resonance imaging (sMRI)
datasets of Alzheimer's disease (AD) (n=415) and Schizophrenia (n=853). Using
the AD dataset, we demonstrated the ability of GDM to robustly handle
confounding variations. Using Schizophrenia dataset, we demonstrated the
ability of GDM to handle multi-site studies. Taken together, the results
underline the potential of the proposed approach for neuroimaging analyses.
