Spectral methods for neural characterization using generalized quadratic models

Il Memming Park, Evan Archer, Nicholas Priebe, Jonathan William Pillow

Research output: Contribution to journalConference articlepeer-review

43 Scopus citations


We describe a set of fast, tractable methods for characterizing neural responses to high-dimensional sensory stimuli using a model we refer to as the generalized quadratic model (GQM). The GQM consists of a low-rank quadratic function followed by a point nonlinearity and exponential-family noise. The quadratic function characterizes the neuron's stimulus selectivity in terms of a set linear receptive fields followed by a quadratic combination rule, and the invertible nonlinearity maps this output to the desired response range. Special cases of the GQM include the 2nd-order Volterra model [1, 2] and the elliptical Linear-Nonlinear-Poisson model [3]. Here we show that for "canonical form" GQMs, spectral decomposition of the first two response-weighted moments yields approximate maximumlikelihood estimators via a quantity called the expected log-likelihood. The resulting theory generalizes moment-based estimators such as the spike-triggered covariance, and, in the Gaussian noise case, provides closed-form estimators under a large class of non-Gaussian stimulus distributions. We show that these estimators are fast and provide highly accurate estimates with far lower computational cost than full maximum likelihood. Moreover, the GQM provides a natural framework for combining multi-dimensional stimulus sensitivity and spike-history dependencies within a single model. We show applications to both analog and spiking data using intracellular recordings of V1 membrane potential and extracellular recordings of retinal spike trains.

Original languageEnglish (US)
JournalAdvances in Neural Information Processing Systems
StatePublished - 2013
Event27th Annual Conference on Neural Information Processing Systems, NIPS 2013 - Lake Tahoe, NV, United States
Duration: Dec 5 2013Dec 10 2013

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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