Negative correlation in neural systems

In our attempt to understand neural systems, it is useful to identify statistical principles that may be beneficial in neural information processing, outline how these principles may work in theory, and demonstrate the benefits through computational modelling and simulation. Negative correlation is one such principle, and is the subject of this work. The main body of the work falls into three parts. The first part demonstrates the space filling and accelerated central limit convergence benefits of negative correlation, both generally and in the specific neural context of V1 receptive fields. I outline two new algorithms combining traditional ICA with a correlation objective function. Correlated component analysis seeks components with a given correlation matrix, while correlated basis analysis seeks basis functions with a given correlation matrix. The benefits of recovering components and basis functions with negative correlations are shown. The second part looks at the functional role of negative correlation for integrate- and-fire neurons in the context of suprathreshold stochastic resonance, for neurons receiving Poisson inputs modelled by a diffusion approximation. I show how the SSR effect can be seen in networks of spiking neurons, and further show how correlation can be used to control the noise level, and that optimal information transmission occurs for negatively correlated inputs when parameters take biophysically plausible values. The final part examines the question of how negative correlation may be implemented in the context of small networks of spiking neurons. Networks of integrate-and-fire neurons with and without lateral inhibitory connections are tested, and the networks with the inhibitory connections are found to perform better and show negatively correlated firing patterns. This result is extended to more biophysically detailed neuron and synapse models, highlighting the robust nature of the mechanism. Finally, the mechanism is explained as a threshold-unit approximation to non-threshold maximum likelihood signal/noise decomposition.