Extensions to copula based modeling of spike counts

Recently, it has been shown that copula based models can be used to model a rich set of dependence structures together with appropriate distributions for single neuron variability [1, 2].
In this study, we extend the copula approach in three ways: Firstly, we present a novel copula transformation with interpretations for the underlying neural connectivity. The so-called Flashlight transformation is a generalization of the copula survival transformation and makes it possible to move the tail dependence of a copula into arbitrary corners of the distribution. We discuss several interpretations with respect to inhibitory and excitatory connections of projecting populations and demonstrate their validity on integrate and fire population models.

Secondly, we present a mixture approach that enables us to combine different dependence structures and thereby it allows us to test for different driving processes simultaneously. For example, we combine the advantages of the Flashlight transformation with the Farlie-Gumbel-Morgenstern family. Furthermore, we derive an expectation maximization inference method for the mixture model.

Thirdly, we address problems associated with the current approach: 1) The computational complexity restricts the number of neurons that can be analyzed. 2) Typically, not many samples are available for model inference - hence overfitting is an issue. We consider a second class of probability models: the exponential families of distributions which allow efficient inference in terms of computation time and sample size. Furthermore, it has been shown that a subfamily of the exponential families allows Bayes-optimal cue integration in easy manner [3]. Combining both approaches allows to make efficient inference, while maintaining the interpretability of the spike count distributions. The tool we use for combining the approaches is the Kullback-Leibler divergence between both families of distributions.