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(Ed.)
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.
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