We discussed state dependence of noise correlations in macaque primary visual cortex [1] today. Noise correlation quantifies the covariability in spike counts between neurons (it’s called noise correlation because the signal (stimulus) drive component has been subtracted out). In a 2010 science paper [2], noise correlation was shown to be much smaller than previously reported; in the range of 0.01 compared to the usual 0.10.2 range and stirred up the field (see [3] for a list of values). In this paper, they argue that this difference in noise correlation magnitude is due to population level covariations during anesthesia (they used sufentanil).
They showed that a factor model with 1dimensional latent process captures the excess noise correlations observed during anesthesia. They extended GPFA [4] to include a linear stimulus drive component, and fit the trials corresponding to the same stimulus. This model assumes that the squareroot transformed spike counts in 100 ms bins follows,
where is the stimulus, is the tuning curve drive, is the mean, represents the individual (diagonal) covariance, is the factor loadings vector, and is the 1dimensional population wide latent process with assumed smoothness given by the kernel . The squareroot transformation is for the variance stabilization, making Poissonlike spike count observations more like Gaussian distributed.
They show that the most of the extra noise correlation observed during anesthesia is explained by the 1D latent process, and the remaining noise correlation is in par with awake condition, while noise correlations in the awake data didn’t get explained away by it (figure below).
Note that this nonlinear relation between the mean rate and noise correlation is not a natural consequence of the generative model they assumed (equation above), since the noise is additive while firing rate is modulated by stimulus. That’s why they had to fit different factor loadings vector for different stimulus conditions. However, they show that a multiplicative LNP model where a 1D latent process multiplicatively interacts with the stimulus drive in the log firing rate does reproduce this quality (Fig. 6). (It’s a shame that they didn’t actually fit this more elegant generative model directly to their data.)
Furthermore, they showed that local field potentials (LFP) in 0.52Hz range is correlated with the inferred latent variable. Hence, lowpass filtered LFP averaged over electrodes is a good proxy for L4 population correlation under anesthesia.
1Dlatent process, LFP, and LNP results are all consistent with Matteo Carandini’s soloist vs chorister story except his preparations were awake rodent as far as I recall. This story also bears similarity with [58]. This is certainly an exciting type of model and there are many similar models being developed (e.g. [9, 10] and references therein). I hope to see more developments in these kinds of latent variable models; they have the advantage of scaling well in terms of number of parameters, but the disadvantage of being nonconvex optimization. Also, I would like to see similar analysis for awake but spontaneous (nontask performing) state.
Their data and code are all available online (awesome!).

Ecker, A. S., Berens, P., Cotton, R. J., Subramaniyan, M., Denfield, G. H., Cadwell, C. R., Smirnakis, S. M., Bethge, M., and Tolias, A. S. (2014). State dependence of noise correlations in macaque primary visual cortex. Neuron, 82(1):235248.

Ecker, A. S., Berens, P., Keliris, G. A., Bethge, M., Logothetis, N. K., and Tolias, A. S. (2010). Decorrelated neuronal firing in cortical microcircuits. Science, 327(5965):584587.

Cohen, M. R. and Kohn, A. (2011). Measuring and interpreting neuronal correlations. Nat Neurosci, 14(7):811819.

Yu, B. M., Cunningham, J. P., Santhanam, G., Ryu, S. I., Shenoy, K. V., and Sahani, M. (2009). GaussianProcess factor analysis for LowDimensional SingleTrial analysis of neural population activity. Journal of Neurophysiology, 102(1):614635.

Luczak, A., Bartho, P., and Harris, K. D. (2013). Gating of sensory input by spontaneous cortical activity. The Journal of Neuroscience, 33(4):16841695.

Goris, R. L. T., Movshon, J. A., and Simoncelli, E. P. (2014). Partitioning neuronal variability. Nat Neurosci, 17(6):858865. [last week’s blog post]

Tkačik, G., Marre, O., Mora, T., Amodei, D., Berry, M. J., and Bialek, W. (2013). The simplest maximum entropy model for collective behavior in a neural network. Journal of Statistical Mechanics: Theory and Experiment, 2013(03):P03011+.

Okun, M., Yger, P., Marguet, S. L., GerardMercier, F., Benucci, A., Katzner, S., Busse, L., Carandini, M., and Harris, K. D. (2012). Population rate dynamics and multineuron firing patterns in sensory cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience, 32(48):1710817119.

Buesing, L., Sahani, M., and Macke, J. H. (2012). Spectral learning of linear dynamics from generalisedlinear observations with application to neural population data. NIPS 25

Pfau, D., Pnevmatikakis, E. A., and Paninski, L. (2013). Robust learning of lowdimensional dynamics from large neural ensembles. NIPS 26