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.
Highlights
To account for the stochasticity inherent to neural responses, single cells as well as populations of cells are often characterized in terms of a probabilistic model
An essential goal of sensory systems neuroscience is to characterize the functional relationship between neural responses and external stimuli
Of particular interest are the nonlinear response properties of single cells. Linear approaches such as generalized linear modeling can be used to fit nonlinear behavior by choosing an appropriate feature space for the stimulus. This requires, that one has already obtained a good understanding of a cells nonlinear properties, whereas more flexible approaches are necessary for the characterization of unexpected nonlinear behavior
Summary
To account for the stochasticity inherent to neural responses, single cells as well as populations of cells are often characterized in terms of a probabilistic model. A popular choice for this task are generalized linear models (GLMs) and related approaches [1,2,3,4,5,6]. These models can often be chosen such that the corresponding maximum likelihood problem is a convex optimization problem where a global optimum can be found. This guarantee comes at a price, as GLMs tightly constrain the computations which can be performed on the input. It is typically very challenging to select the appropriate feature space because it presupposes a deeper understanding of the cell’s nonlinear behavior or unfeasibly large amounts of data
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