An efficient and flexible spike train model via empirical Bayes

Qi She, Xiaoli Wu, Beth Jelfs, Adam S. Charles, Rosa H.M. Chan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neurons demonstrate over-dispersed spiking behaviour. Although the Negative Binomial Generalized Linear Model (NB-GLM) provides a powerful tool for modeling over-dispersed spike counts, the maximum likelihood-based standard NB-GLM leads to highly variable and inaccurate parameter estimates. Thus, we propose a hierarchical parametric empirical Bayes method to estimate the neural spike responses among neuronal population. Our method integrates both Generalized Linear Models (GLMs) and empirical Bayes theory, which aims to (1) improve the accuracy and reliability of parameter estimation, compared to the maximum likelihood-based method for NB-GLM and Poisson-GLM; (2) effectively capture the over-dispersion nature of spike counts from both simulated data and experimental data; and (3) provide insight into both neural interactions and spiking behaviours of the neuronal populations. We apply our approach to study both simulated data and experimental neural data. The estimation of simulation data indicates that the new framework can accurately predict mean spike counts simulated from different models and recover the connectivity weights among neural populations. The estimation based on retinal neurons demonstrate the proposed method outperforms both NB-GLM and Poisson-GLM in terms of the predictive log-likelihood of held-out data.1

Original languageEnglish
Pages (from-to)3236-3251
Number of pages16
JournalIEEE Transactions on Signal Processing
Publication statusPublished - 30 Apr 2021
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received July 13, 2020; revised January 20, 2021 and April 4, 2021; accepted April 12, 2021. Date of publication April 30, 2021; date of current version June 11, 2021. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Alexander Bertrand. This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China under Project CityU 11214020 and CityU C1020-19E. (Qi She and Xiaoli Wu contributed equally to this work.) (Corresponding author: Rosa Chan.) Qi She was with the Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong, and now he is with Bytedance AI Lab, Beijing 100086, China (e-mail:

Publisher Copyright:
© 2021 IEEE.


  • Empirical bayes
  • generalized linear model
  • hierarchical model
  • maximum marginal likelihood
  • negative binomial distribution
  • spike train model

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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