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Spike Triggered Covariance in Strongly Correlated Gaussian Stimuli
Figure 3
Spike triggered covariance analysis of a model neuron with two relevant features orthogonal to the coherent mode.
Spectra of 
for increasing dataset size in the case of strongly correlated Gaussian noise (A–C) and white noise (D). (A–D) The range of spikes covered is from 
to 
. Panel B shows the results using the pre-whitening (“one-centered”) method, and panel C shows the results after evaluating significance in the subspace orthogonal to the coherent mode. Each vertical line shows the result of a single simulation. Significant (insignificant) eigenvalues are shown in red (black), and the range of the null distribution (1000 evaluations of 
, 
confidence interval) is shown in gray. (E–H, left) Gray shaded area is the support of the null distribution, which itself is plotted in blue. The significant (insignificant) portion of the spectrum of 
is plotted in red (black). These example spectra, with the corresponding significant vectors, are for conditions with a small number of spikes (indicated by an orange star in A–D) for which both of the formulations find no significant dimensions. 
, 
for the correlated stimulus condition in panels E–G, 
, 
for the white stimulus condition in panel H. (E–H, right) Results of the nested significance testing. We note that the second ranked eigenvalue in panel E is outside of its confidence interval, but still cannot be found to be significant. This happens because of the noise along the coherent mode. (I) STC analysis using all pseudoinverse orders using the nested significance testing with 
confidence intervals (large box) compared to the analysis using our proposed correction scheme. Black means no significant features were found for that combination of 
and pseudoinverse order. Cold (hot) colors indicate that one (two) features were found to be significant. The corresponding color bars on the right indicate the geometric average of the feature projections on the two model dimensions (cold colors) or the subspace overlap with the model, cf. Eq. (36) (hot colors). (J) Results when STC is performed using the proposed correction scheme. The two relevant dimensions (black frame) and the decorrelated significant features (red frame) have subspace overlap of 0.82. The models were defined such that the mean firing rate remained unchanged between the two stimulus conditions.
doi: https://doi.org/10.1371/journal.pcbi.1003206.g003