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.
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