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Beyond GLMs: A Generative Mixture Modeling Approach to Neural System Identification

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83805

Bethge,  M
Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Theis, L., Chagas, A., Arnstein, D., Schwarz, C., & Bethge, M. (2013). Beyond GLMs: A Generative Mixture Modeling Approach to Neural System Identification. PLoS Computational Biology, 9(11), 1-9. doi:10.1371/journal.pcbi.1003356.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-001A-127D-5
Zusammenfassung
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.