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 and spike-triggered covariance 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: (1) it recovers a set of linear filters sorted according to their

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... formativeness 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 spike-triggered average or covariance analysis are met; (5) it can be augmented with additional constraints, such as space-time separability, on the filters. 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.