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

Abstract

A major challenge in contemporary neuroscience is to analyze data from large numbers of neurons recorded simultaneously across many experimental replications (trials), where the data are counts of neural firing events, and one of the basic problems is to characterize the dependence structure among such multivariate counts. Methods of estimating high-dimensional covariation based on ℓ1-regularization are most appropriate when there are a small number of relatively large partial correlations, but in neural data there are often large numbers of relatively small partial correlations. Furthermore, the variation across trials is often confounded by Poisson-like variation within trials. To overcome these problems we introduce a comprehensive methodology that imbeds a Gaussian graphical model into a hierarchical structure: the counts are assumed Poisson, conditionally on latent variables that follow a Gaussian graphical model, and the graphical model parameters, in turn, are assumed to depend on physiologically-motivated covariates, which can greatly improve correct detection of interactions (non-zero partial correlations). We develop a Bayesian approach to fitting this covariate-adjusted generalized graphical model and we demonstrate its success in simulation studies. We then apply it to data from an experiment on visual attention, where we assess functional interactions between neurons recorded from two brain areas.

A Computationally Efficient Method for Learning Exponential Family Distributions

“…In recent years, sparse-plus-low-rank matrix recovery has received considerable attention in machine learning and statistical inference, e.g., robust PCA [7], latent variable graphical models [8]. Latent variable graphical models has a variety of applications including assessing the functional interactions between neurons recorded from two brain areas [54,38]. In latent variable graphical models, there are variables not present in observations.…”

Latent Network Structure Learning from High Dimensional Multivariate Point Processes

“…We remark that there is another class of approaches that estimate the latent network structure from high dimensional multivariate point process data (Zhang et al, 2016;Vinci et al, 2016Vinci et al, , 2018. These methods divide the observation window into a number of bins, and model the number of events in each bin.…”

“…These methods divide the observation window into a number of bins, and model the number of events in each bin. The network structure is inferred using methods such as correlation of event counts (Vinci et al, 2016), regularized generalized linear models (Zhang et al, 2016), or Gaussian graphical models (Vinci et al, 2018). Such a type of approaches do not involve estimating the multivariate intensity function underlying the observed point patterns, and are potentially more computationally efficient.…”

Latent Network Estimation and Variable Selection for Compositional Data via Variational EM

“…Therefore, even though the latent Gaussian layer does not allow us to recover relationships directly among the observed counts, the inferred dependences do provide some insights into the relationships among the underlying processes. Latent graphical models for Poisson-distributed count data that use Gaussian layers were used by Vinci et al (2018), for spike-count data. See also Talhouk et al (2012) and Li et al (2020) for latent graphical model constructions for binary data.…”