Stochastic Analysis of Neural Spike Count Dependencies

The question of how populations of neurons process information is not fully understood yet. With the advent of new experimental techniques, however, it becomes possible to measure a great number of neurons simultaneously. As a result, models of co-variation of neurons are becoming increasingly important. In this thesis new methods are introduced for analyzing the importance of stochastic dependencies for neural coding. The methods are verified on artificial data and applied to data that were recorded from animals. It is demonstrated that the novel features of the models can be material for investigating the neural code. First, a novel framework for modeling multivariate spike counts is introduced. The framework is based on copulas, which make it possible to couple arbitrary single neuron distributions and place a wide range of dependency structures at the disposal. Methods for parameter inference and for estimation of information measures are provided. Moreover, a relation between network architectures and copula properties is established. The copula-based models are then applied to data that were recorded from the prefrontal cortex of macaque monkey during a visual working memory task. We demonstrate that copula-based models are better suited for the data than common standard models and we identify possible underlying network structures of the recorded neurons. We then extend the copula approach by introducing a copula family that can be used to model strong higher-order correlations. The family is constructed as a mixture family with copula components of different order. In order to demonstrate the usefulness of the model we construct a network of leaky integrate-and-fire neurons. The network is connected in such a way that higher-order correlations are present in the resulting spike counts. The new copula family is then compared to other copulas and to the Ising model. We show, that compared to the other models the new copula family provides a better fit to the artificial data. In a third study, we investigate the sufficiency of the linear correlation coefficient for describing the dependencies of spike counts generated from a small network of leaky integrate-and-fire neurons. It is shown that estimated entropies can deviate by more than 25% of the true entropy if the model relies on the linear correlation coefficient only. We therefore propose a copula-based goodness-of-fit test which makes it easy to check whether a given copula-based model is appropriate for the data at hand. The test is then verified on several artificial data sets. Finally, we study the importance of higher-order correlations of spike counts for information-theoretic measures. For that purpose we introduce a goodness-of-fit test that has a second-order maximum entropy distribution as a reference distribution. The test quantifies the fit in terms of a selectable divergence measure such as the mutual information difference and is applicable even when the number of available data samples is very small. We verify the method on artificial data and apply it to data that were recorded from the primary visual cortex of an anesthetized cat during an adaptation experiment. We can show that higher-order correlations have a significant condition dependent impact on the entropy and on the mutual information of the recorded spike counts.