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.

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.

Strengths: Updated Review: I'd like to thank the authors for answering my concerns re: the stochastic nature of the kernel optimization. I am now even more confident in my assessment that this is a good submission and an accept from me. In response to an under constrained general MLE framework for fitting autoregressive models, the authors introduce a method to balance multiple objectives (fidelity to outputs under data-constrained and free-running conditions). They achieve this with model-based MMD (sometimes with the addition of a likelihood objective), which requires matching of free-running and data-constrained model features, essentially maximizing likelihood under the constraint of requiring faithful behavior in both conditions. This leads to a model that is both faithful and stable in the free-running condition.

In this submission, the authors attack the problem of modeling spike trains in neural data using auto-regressive GLM models. The authors recognize a disparity in the set up for training a MLE estimate of the model parameters and a "free running" model used for inference as has been observed in training RNNs. This disparity may lead to unnaturally long sequences and consequently in spike trains, runaway excitation in the spike train history. To address this issue, the authors propose a new method for fitting GLM's based on maximum mean discrepancy, coupled with spike train kernels. The authors show favorable predictive performance with respect to MLE methods 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.