Dimensionality reduction in neural models: an information-theoretic generalization of spike-triggered average and covariance analysis.
We describe an information-theoretic framework for fitting neural spike responses with a Linear-Nonlinear-Poisson cascade model. This framework unifies the spike-triggered average (STA) and spike-triggered covariance (STC) approaches to neural characterization and recovers a set of linear filters that maximize mean and variance-dependent information between stimuli and spike responses. The resulting approach has several useful properties, namely, (1) it recovers a set of linear filters sorted according to their informativeness about the neural response; (2) it is both computationally efficient and robust, allowing recovery of multiple linear filters from a data set of relatively modest size; (3) it provides an explicit "default" model of the nonlinear stage mapping the filter responses to spike rate, in the form of a ratio of Gaussians; (4) it is equivalent to maximum likelihood estimation of this default model but also converges to the correct filter estimates whenever the conditions for the consistency of STA or STC analysis are met; and (5) it can be augmented with additional constraints on the filters, such as space-time separability. We demonstrate the effectiveness of the method by applying it to simulated responses of a Hodgkin-Huxley neuron and the recorded extracellular responses of macaque retinal ganglion cells and V1 cells.
Pillow
Jonathan W
JW
Gatsby Computational Neuroscience Unit, University College London, London, UK. pillow@gatsby.ucl.ac.uk
Simoncelli
Eero P
EP
D000200:Action Potentials; D000818:Animals; D003198:Computer Simulation; D007257:Information Theory; D016013:Likelihood Functions; D016014:Linear Models; D008253:Macaca mulatta; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D016012:Poisson Distribution; D012165:Retinal Ganglion Cells / Q000502:physiology; D014793:Visual Cortex / Q000502:physiology