Analyzing brain networks from neuroimages is becoming a promising approach in identifying novel connectivity-based biomarkers for the Alzheimer's disease (AD). In this regard, brain ``effective connectivity" analysis, which studies the causal relationship among brain regions, is highly challenging and of many research opportunities. Most of the existing works in this field use generative methods. Despite their success in data representation and other important merits, generative methods are not necessarily discriminative, which may cause the ignorance of subtle but critical disease-induced changes. In this paper, we propose a learning-based approach that integrates the benefits of generative and discriminative methods to recover effective connectivity. In particular, we employ Fisher kernel to bridge the generative models of sparse Bayesian networks (SBN) and the discriminative classifiers of SVMs, and convert the SBN parameter learning to Fisher kernel learning via minimizing a generalization error bound of SVMs. Our method is able to simultaneously boost the discriminative power of both the generative SBN models and the SBN-induced SVM classifiers via Fisher kernel. The proposed method is tested on analyzing brain effective connectivity for AD from ADNI data, and demonstrates significant improvements over the state-of-the-art work.