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

• ¹ Centre for Integrative Neuroscience, Germany
• ² Graduate School of Neural Information Processing, Germany
• ³ Graduate School of Neural & Behavioral Sciences, Germany
• ⁴ Hertie Institute for Clinical Brain Research, Germany
• ⁵ Bernstein Center for Computational Neuroscience, Germany
• ⁶ Max Planck Institute for Biological Cybernetics, Germany

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.

Here, we derive a more flexible neuron model which is able to automatically extract highly nonlinear stimulus-response relationships from the 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).

We demonstrate the superior representational power of the STM by fitting it to data generated by a trained 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.