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Beyond GLMs: a generative mixture modeling approach to neural sys- tem identification


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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Theis, L., Arnstein, D., Chagas, A., Schwarz, C., & Bethge, M. (2013). Beyond GLMs: a generative mixture modeling approach to neural sys- tem identification. Poster presented at Computational and Systems Neuroscience Meeting (COSYNE 2013), Salt Lake City, UT, USA.

Cite as: https://hdl.handle.net/21.11116/0000-0001-18AF-0
One of the principle goals of sensory systems neuroscience is to characterize the relationship between external
stimuli and neuronal responses. A popular choice for modeling the responses of neurons is the generalized
linear model (GLM). However, due to its inherent linearity, choosing a set of nonlinear features is often crucial
but can be difficult in practice if the stimulus dimensionality is high or if the stimulus-response dependencies are complex. We derived a more flexible neuron model which is able to automatically extract highly nonlinear stimulus-response relationships from data. We start out by representing intuitive and well understood distributions such as the spike-triggered and inter-spike interval distributions using nonparametric models. For instance, we use mixtures of Gaussians to represent spike-triggered distributions which allows for complex stimulus dependencies such as those of cells with multiple preferred stimuli. A simple application of Bayes’ rule allows us to turn these distributions into a model of the neuron’s response, which we dub spike-triggered mixture model (STM). The superior representational power of the STM can be demonstrated by fitting it to data generated by a GLM and
vice versa. While the STM is able to reproduce the behavior of the GLM, the opposite is not the case. We also
apply our model to single-cell recordings of primary afferents of the rat’s whisker system and find quantitatively and qualitatively that it is able to better reproduce the cells’ behavior than the GLM. In particular, we obtain much higher estimates of the cells’ mutual information rates.