  The standard approach to fitting an autoregressive spike train model is to
maximize the likelihood for one-step prediction. This maximum likelihood
estimation (MLE) often leads to models that perform poorly when generating
samples recursively for more than one time step. 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. Using different combinations of spike train kernels, we
show that we can control the trade-off between different features which is
critical for dealing with model-mismatch.
