Linear-nonlinear-Poisson cascade model

[1][2][3] It has been successfully used to describe the response characteristics of neurons in early sensory pathways, especially the visual system.

The LNP model is generally implicit when using reverse correlation or the spike-triggered average to characterize neural responses with white-noise stimuli.

The first stage consists of a linear filter, or linear receptive field, which describes how the neuron integrates stimulus intensity over space and time.

The linear filtering stage performs dimensionality reduction, reducing the high-dimensional spatio-temporal stimulus space to a low-dimensional feature space, within which the neuron computes its response.

The nonlinearity converts the filter output to a (non-negative) spike rate, and accounts for nonlinear phenomena such as spike threshold (or rectification) and response saturation.

The model offers a useful approximation of neural activity, allowing scientists to derive reliable estimates from a mathematically simple formula.

denote the nonlinearity, a scalar function with non-negative output.

Then the LNP model specifies that, in the limit of small time bins, For finite-sized time bins, this can be stated precisely as the probability of observing y spikes in a single bin: For neurons sensitive to multiple dimensions of the stimulus space, the linear stage of the LNP model can be generalized to a bank of linear filters, and the nonlinearity becomes a function of multiple inputs.

denote the set of linear filters that capture a neuron's stimulus dependence.

The parameters of the LNP model consist of the linear filters

Techniques for estimating the LNP model parameters include: