Adjusted regularization of cortical covariance

Abstract

It is now common to record dozens to hundreds or more neurons simultaneously, and to ask how the network activity changes across experimental conditions. A natural framework for addressing questions of functional connectivity is to apply Gaussian graphical modeling to neural data, where each edge in the graph corresponds to a non-zero partial correlation between neurons. Because the number of possible edges is large, one strategy for estimating the graph has been to apply methods that aim to identify large sparse effects using an [Formula: see text] penalty. However, the partial correlations found in neural spike count data are neither large nor sparse, so techniques that perform well in sparse settings will typically perform poorly in the context of neural spike count data. Fortunately, the correlated firing for any pair of cortical neurons depends strongly on both their distance apart and the features for which they are tuned. We introduce a method that takes advantage of these known, strong effects by allowing the penalty to depend on them: thus, for example, the connection between pairs of neurons that are close together will be penalized less than pairs that are far apart. We show through simulations that this physiologically-motivated procedure performs substantially better than off-the-shelf generic tools, and we illustrate by applying the methodology to populations of neurons recorded with multielectrode arrays implanted in macaque visual cortex areas V1 and V4.

Inference of Synaptic Connectivity and External Variability in Neural Microcircuits

“…which is a common mask used on in vivo data (Vinci et al, 2018;Yatsenko et al, 2015) as well as in silico experiments following Dale's Law (Chambers et al, 2017;Lin et al, 2017;Lütcke et al, 2013;Pernice and Rotter, 2013;Poli et al, 2016). Like mask M 2 , it only distinguishes null and positive connections, but now it does so without knowledge of sub-population membership.…”

Adjusted regularization in latent graphical models: Application to multiple-neuron spike count data

“…In previous work we handled the first problem for pairs of neurons using bivariate hierarchical models (Vinci et al, 2016), where pairs of spike counts were assumed to be Poisson with bivariate log-normally distributed latent means; correlation between the latent means can then be thought of as a Poisson de-noised version of spike count correlation. We also handled the second problem, while ignoring the first, by allowing the LASSO penalty to vary with the pair of neurons based on informative covariates (Vinci et al, 2018a), which improved the detection of correct edges and the accuracy of partial correlation estimates. In this paper we combine those two previous strategies to provide a more comprehensive solution.…”

“…These covariates are available, but their effects may vary across brain areas, neuron types, and recording techniques. In Vinci et al (2018a) we introduced informative covariate vectors W ij composed of inter-neuron distances and tuning curve correlations to estimate a GGM using a Bayesian λ 1 regularization framework (the graphical LASSO with adjusted regularization, or GAR), where partial correlations between neurons i and j can be penalized differently according to a data driven function of W ij . Through an extensive simulation study we showed that this physiologically-motivated procedure performs substantially better (in terms of correct edge detection and accuracy of partial correlation estimates) than off-the-shelf generic tools, including not only graphical LASSO but also several of its variants that have appeared in the literature, the adaptive graphical LASSO (Fan et al, 2009), the latent variable graphical model (Chandrasekaran et al, 2012), and Bayesian graphical LASSO (Wang, 2012).…”

“…Improvements in functional connectivity estimation provided by auxiliary variables had previously been observed in analyses of other kinds of neural data by either using a weighted λ 1 penalty on the precision matrix, with weights taken to be inverse functions of metrics of the strength of anatomical connections (MEG data, Pineda-Pardo et al (2014); fMRI and dMRI data, Ng et al (2012); where the strength of anatomical connections were taken to be the fiber density and fiber count between regions, respectively), or by constraining the support of the precision matrix to reflect structural connections (fMRI data, Hinne et al (2014); the zeros were imposed in the precision matrix where structural connections were not found). However, those studies differ from Vinci et al (2018a) in that the dependence of the regularization on the covariates W ij was pre-specified rather than learned from the data. In Vinci et al (2018a), GAR used thresholding of estimated partial correlations to set edges to zero.…”

“…However, those studies differ from Vinci et al (2018a) in that the dependence of the regularization on the covariates W ij was pre-specified rather than learned from the data. In Vinci et al (2018a), GAR used thresholding of estimated partial correlations to set edges to zero. Here, we instead use spike-and-slab priors where the probability of zero for the ( i, j ) partial correlation depends on W ij , and we let the dependence on W ij be data driven.…”