---
_id: '2818'
abstract:
- lang: eng
  text: Models of neural responses to stimuli with complex spatiotemporal correlation
    structure often assume that neurons are selective for only a small number of linear
    projections of a potentially high-dimensional input. In this review, 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, focusing in particular
    on two information theory–based approaches (maximization of stimulus energy and
    of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered
    covariance and extensions of generalized linear models). We analyze the formal
    relationship between the likelihood-based and information-based approaches to
    demonstrate how they lead to consistent inference. We demonstrate the practical
    feasibility of these procedures by using model neurons responding to a flickering
    variance stimulus.
article_processing_charge: No
arxiv: 1
author:
- first_name: Kanaka
  full_name: Rajan, Kanaka
  last_name: Rajan
- first_name: Olivier
  full_name: Marre, Olivier
  last_name: Marre
- first_name: Gasper
  full_name: Tkacik, Gasper
  id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
  last_name: Tkacik
  orcid: 0000-0002-6699-1455
citation:
  ama: Rajan K, Marre O, Tkačik G. Learning quadratic receptive fields from neural
    responses to natural stimuli. <i>Neural Computation</i>. 2013;25(7):1661-1692.
    doi:<a href="https://doi.org/10.1162/NECO_a_00463">10.1162/NECO_a_00463</a>
  apa: Rajan, K., Marre, O., &#38; Tkačik, G. (2013). Learning quadratic receptive
    fields from neural responses to natural stimuli. <i>Neural Computation</i>. MIT
    Press. <a href="https://doi.org/10.1162/NECO_a_00463">https://doi.org/10.1162/NECO_a_00463</a>
  chicago: Rajan, Kanaka, Olivier Marre, and Gašper Tkačik. “Learning Quadratic Receptive
    Fields from Neural Responses to Natural Stimuli.” <i>Neural Computation</i>. MIT
    Press, 2013. <a href="https://doi.org/10.1162/NECO_a_00463">https://doi.org/10.1162/NECO_a_00463</a>.
  ieee: K. Rajan, O. Marre, and G. Tkačik, “Learning quadratic receptive fields from
    neural responses to natural stimuli,” <i>Neural Computation</i>, vol. 25, no.
    7. MIT Press, pp. 1661–1692, 2013.
  ista: Rajan K, Marre O, Tkačik G. 2013. Learning quadratic receptive fields from
    neural responses to natural stimuli. Neural Computation. 25(7), 1661–1692.
  mla: Rajan, Kanaka, et al. “Learning Quadratic Receptive Fields from Neural Responses
    to Natural Stimuli.” <i>Neural Computation</i>, vol. 25, no. 7, MIT Press, 2013,
    pp. 1661–92, doi:<a href="https://doi.org/10.1162/NECO_a_00463">10.1162/NECO_a_00463</a>.
  short: K. Rajan, O. Marre, G. Tkačik, Neural Computation 25 (2013) 1661–1692.
das_tickbox: '1'
date_created: 2018-12-11T11:59:45Z
date_published: 2013-07-01T00:00:00Z
date_updated: 2026-07-06T13:45:52Z
day: '01'
department:
- _id: GaTk
doi: 10.1162/NECO_a_00463
external_id:
  arxiv:
  - '1209.0121'
  isi:
  - '000319903700001'
intvolume: '        25'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1209.0121
month: '07'
oa: 1
oa_version: Preprint
page: 1661 - 1692
publication: Neural Computation
publication_status: published
publisher: MIT Press
publist_id: '3983'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Learning quadratic receptive fields from neural responses to natural stimuli
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2013'
...