Rescuing neural spike train models from bad MLE

TL;DR

This paper introduces a kernel-based divergence minimization method to improve autoregressive neural spike train models, addressing issues of poor recursive sampling and feature capture caused by traditional MLE.

Contribution

It proposes a novel approach that directly minimizes divergence between recorded and generated spike trains using spike train kernels, enhancing model robustness and feature fidelity.

Findings

Models trained with the proposed method generate more realistic spike trains.

The approach effectively controls feature trade-offs through different kernel combinations.

Experiments on real and synthetic data validate the improved performance.

Abstract

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.