# Rescuing neural spike train models from bad MLE

arXiv: https://arxiv.org/abs/2010.12362 · HTML: https://mlsanity.com/paper/2010.12362/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [Fully Spiking Variational Autoencoder](https://mlsanity.com/paper/2110.00375/) (2021)
- [Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics](https://mlsanity.com/paper/2212.07892/) (2022)
- [Spiking-Diffusion: Vector Quantized Discrete Diffusion Model with Spiking Neural Networks](https://mlsanity.com/paper/2308.10187/) (2023)
- [Fitting summary statistics of neural data with a differentiable spiking network simulator](https://mlsanity.com/paper/2106.10064/) (2021)
- [Temporal Conditioning Spiking Latent Variable Models of the Neural Response to Natural Visual Scenes](https://mlsanity.com/paper/2306.12045/) (2023)
- [Topology Optimization of Random Memristors for Input-Aware Dynamic SNN](https://mlsanity.com/paper/2407.18625/) (2024)

## Abstract (arXiv)

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.