Rescuing neural spike train models from bad MLE
This addresses model-mismatch issues in neural spike train modeling for neuroscience applications, but it is incremental as it builds on existing kernel-based divergence methods.
The paper tackled the problem of autoregressive spike train models performing poorly in multi-step generation due to maximum likelihood estimation, proposing a method that minimizes divergence between recorded and generated spike trains using kernels, which led to well-behaving models validated on real and synthetic neural data.
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.