Stability of point process spiking neuron models

  • Yu ChenEmail author
  • Qi Xin
  • Valérie Ventura
  • Robert E. Kass


Point process regression models, based on generalized linear model (GLM) technology, have been widely used for spike train analysis, but a recent paper by Gerhard et al. described a kind of instability, in which fitted models can generate simulated spike trains with explosive firing rates. We analyze the problem by extending the methods of Gerhard et al. First, we improve their instability diagnostic and extend it to a wider class of models. Next, we point out some common situations in which instability can be traced to model lack of fit. Finally, we investigate distinctions between models that use a single filter to represent the effects of all spikes prior to any particular time t, as in a 2008 paper by Pillow et al., and those that allow different filters for each spike prior to time t, as in a 2001 paper by Kass and Ventura. We re-analyze the data sets used by Gerhard et al., introduce an additional data set that exhibits bursting, and use a well-known model described by Izhikevich to simulate spike trains from various ground truth scenarios. We conclude that models with multiple filters tend to avoid instability, but there are unlikely to be universal rules. Instead, care in data fitting is required and models need to be assessed for each unique set of data.


Generalized linear model Outlier trials Point process regression Spike train 



Yu Chen and Robert E. Kass were supported by NIH grant OT2OD023859.

Robert E. Kass and Valérie Ventura were supported by NIH grant R01 MH064537.

Robert E. Kass was also supported, in part, by NSF grant IIS-1430208.

Compliance with Ethical Standards

Conflict of interest

No potential conflict of interest was reported by the authors.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.University of Science and Technology of ChinaHefeiChina

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