Beyond GLMs: a generative mixture modeling approach to neural system identification

PLoS Comput Biol. 2013;9(11):e1003356. doi: 10.1371/journal.pcbi.1003356. Epub 2013 Nov 21.


Generalized linear models (GLMs) represent a popular choice for the probabilistic characterization of neural spike responses. While GLMs are attractive for their computational tractability, they also impose strong assumptions and thus only allow for a limited range of stimulus-response relationships to be discovered. Alternative approaches exist that make only very weak assumptions but scale poorly to high-dimensional stimulus spaces. Here we seek an approach which can gracefully interpolate between the two extremes. We extend two frequently used special cases of the GLM-a linear and a quadratic model-by assuming that the spike-triggered and non-spike-triggered distributions can be adequately represented using Gaussian mixtures. Because we derive the model from a generative perspective, its components are easy to interpret as they correspond to, for example, the spike-triggered distribution and the interspike interval distribution. The model is able to capture complex dependencies on high-dimensional stimuli with far fewer parameters than other approaches such as histogram-based methods. The added flexibility comes at the cost of a non-concave log-likelihood. We show that in practice this does not have to be an issue and the mixture-based model is able to outperform generalized linear and quadratic models.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials / physiology
  • Animals
  • Computational Biology / methods*
  • Linear Models*
  • Models, Neurological*
  • Neurons / physiology
  • Rats
  • Vibrissae / innervation

Grant support

This work was partially supported by the German Ministry of Education, Science, Research and Technology through the Bernstein Center for Computational Neuroscience (FKZ 01GQ1002), the German Excellency Initiative through the Centre for Integrative Neuroscience Tübingen (EXC307) and the German Research Foundation (SCHW 577/10-2). We also acknowledge support by the Open Access Publishing Fund of the University of Tübingen. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.