  Models of neural responses to stimuli with complex spatiotemporal correlation
structure often assume that neurons are only selective for a small number of
linear projections of a potentially high-dimensional input. Here we explore
recent modeling approaches where the neural response depends on the quadratic
form of the input rather than on its linear projection, that is, the neuron is
sensitive to the local covariance structure of the signal preceding the spike.
To infer this quadratic dependence in the presence of arbitrary (e.g.
naturalistic) stimulus distribution, we review several inference methods,
focussing in particular on two information-theory-based approaches
(maximization of stimulus energy or of noise entropy) and a likelihood-based
approach (Bayesian spike-triggered covariance, extensions of generalized linear
models). We analyze the formal connection between the likelihood-based and
information-based approaches to show how they lead to consistent inference. We
demonstrate the practical feasibility of these procedures by using model
neurons responding to a flickering variance stimulus.
