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Moreover, the generated spike trains can fail to capture important features of the data and even show diverging firing rates. To alleviate this, we propose to directly minimize the divergence between neural recorded and model generated spike trains using spike train kernels. We develop a method that stochastically optimizes the maximum mean discrepancy induced by the kernel. Experiments performed on both real and synthetic neural data validate the proposed approach, showing that it leads to well-behaving models. 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