title: Beyond GLMs: a generative mixture modeling approach to neural system identification.
abstract: 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.
authors.affiliation: Werner Reichardt Centre for Integrative Neuroscience, Tübingen, Germany ; Graduate School of Neural Information Processing, University of Tübingen, Tübingen, Germany.
authors.forename: Lucas
authors.initials: L
authors.lastname: Theis
authors.forename: Andrè Maia
authors.initials: AM
authors.lastname: Chagas
authors.forename: Daniel
authors.initials: D
authors.lastname: Arnstein
authors.forename: Cornelius
authors.initials: C
authors.lastname: Schwarz
authors.forename: Matthias
authors.initials: M
authors.lastname: Bethge
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D019295:Computational Biology / Q000379:methods*; D016014:Linear Models; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology; D051381:Rats; D014738:Vibrissae / Q000294:innervation