A stimulus-dependent connectivity analysis of neuronal networks

We present an analysis of interactions among neurons in stimulus-driven networks that is designed to control for effects from unmeasured neurons. This work builds on previous connectivity analyses that assumed connectivity strength to be constant with respect to the stimulus. Since unmeasured neuron activity can modulate with the stimulus, the effective strength of common input connections from such hidden neurons can also modulate with the stimulus. By explicitly accounting for the resulting stimulus-dependence of effective interactions among measured neurons, we are able to remove ambiguity in the classification of causal interactions that resulted from classification errors in the previous analyses. In this way, we can more reliably distinguish causal connections among measured neurons from common input connections that arise from hidden network nodes. The approach is derived in a general mathematical framework that can be applied to other types of networks. We illustrate the effects of stimulus-dependent connectivity estimates with simulations of neurons responding to a visual stimulus. This research was supported by the National Science Foundation grants DMS-0415409 and DMS-0748417.