Learning quadratic receptive fields from neural responses to natural stimuli

TL;DR

This paper investigates methods to infer quadratic stimulus-response models of neurons, which depend on local covariance structures, using naturalistic stimuli and compares information-theoretic and likelihood-based inference approaches.

Contribution

It reviews and compares inference methods for quadratic neural response models, demonstrating their practical application with model neurons responding to naturalistic stimuli.

Findings

Likelihood and information-based methods yield consistent inference results.

Quadratic models can effectively capture neural responses to complex stimuli.

Practical inference procedures are feasible with naturalistic stimulus data.

Abstract

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.