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Spike Triggered Covariance in Strongly Correlated Gaussian Stimuli

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  • Johnatan Aljadeff
  • Ronen Segev
  • Michael J Berry II
  • Tatyana O Sharpee

Abstract

Many biological systems perform computations on inputs that have very large dimensionality. Determining the relevant input combinations for a particular computation is often key to understanding its function. A common way to find the relevant input dimensions is to examine the difference in variance between the input distribution and the distribution of inputs associated with certain outputs. In systems neuroscience, the corresponding method is known as spike-triggered covariance (STC). This method has been highly successful in characterizing relevant input dimensions for neurons in a variety of sensory systems. So far, most studies used the STC method with weakly correlated Gaussian inputs. However, it is also important to use this method with inputs that have long range correlations typical of the natural sensory environment. In such cases, the stimulus covariance matrix has one (or more) outstanding eigenvalues that cannot be easily equalized because of sampling variability. Such outstanding modes interfere with analyses of statistical significance of candidate input dimensions that modulate neuronal outputs. In many cases, these modes obscure the significant dimensions. We show that the sensitivity of the STC method in the regime of strongly correlated inputs can be improved by an order of magnitude or more. This can be done by evaluating the significance of dimensions in the subspace orthogonal to the outstanding mode(s). Analyzing the responses of retinal ganglion cells probed with Gaussian noise, we find that taking into account outstanding modes is crucial for recovering relevant input dimensions for these neurons.Author Summary: In many areas of computational biology, including the analyses of genetic mutations, protein stability and neural coding, as well as in economics, one of the most basic and important steps of data analysis is to find the relevant input dimensions for a particular task. In neural coding problems, the spike-triggered covariance (STC) method identifies relevant input dimensions by comparing the variance of the input distribution along different dimensions to the variance of inputs that elicited a neural response. While in theory the method can be applied to Gaussian stimuli with or without correlations, it has so far been used in studies with only weakly correlated stimuli. Here we show that to use STC with strongly correlated, -type inputs, one has to take into account that the covariance matrix of random samples from this distribution has a complex structure, with one or more outstanding modes. We use simulations on model neurons as well as an analysis of the responses of retinal neurons to demonstrate that taking the presence of these outstanding modes into account improves the sensitivity of the STC method by more than an order of magnitude.

Suggested Citation

  • Johnatan Aljadeff & Ronen Segev & Michael J Berry II & Tatyana O Sharpee, 2013. "Spike Triggered Covariance in Strongly Correlated Gaussian Stimuli," PLOS Computational Biology, Public Library of Science, vol. 9(9), pages 1-12, September.
    • Handle: RePEc:plo:pcbi00:1003206
    DOI: 10.1371/journal.pcbi.1003206
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    References listed on IDEAS

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    1. Niru Maheswaranathan & David B Kastner & Stephen A Baccus & Surya Ganguli, 2018. "Inferring hidden structure in multilayered neural circuits," PLOS Computational Biology, Public Library of Science, vol. 14(8), pages 1-30, August.

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