## Inferring input nonlinearities in neural encoding models

Network: Computation in Neural Systems, Volume 19, 2008,
pages 35-67.

We describe a class of models that predict how the instantaneous
firing rate of a neuron depends on a dynamic stimulus. The models
utilize a learnt pointwise nonlinear transform of the stimulus,
followed by a linear filter that acts on the sequence of transformed
inputs. In one case, the nonlinear transform is the same at all filter
lag-times. Thus, this and present techniques to regularise and
quantify uncertainty in the estimates. In a second approach, the model
is generalized to allow a different nonlinear transform of the
stimulus value at each lag-time. Although more general, this model is
algorithmically more straightforward to fit. However, it has many more
degrees of freedom than the first approach, thus requiring more data
for accurate estimation. We test the feasibility of these methods on
synthetic data, and on responses from a neuron in rodent barrel
cortex. The models are shown to predict responses to novel data
accurately, and to recover several important neuronal response
properties.

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