Adjusted regularization of cortical covariance

Latent Dynamic Factor Analysis of High-Dimensional Neural Recordings

High-dimensional neural recordings across multiple brain regions can be used to establish functional connectivity with good spatial and temporal resolution. We designed and implemented a novel method, Latent Dynamic Factor Analysis of High-dimensional time series (LDFA-H), which combines (a) a new approach to estimating the covariance structure among high-dimensional time series (for the observed variables) and (b) a new extension of probabilistic CCA to dynamic time series (for the latent variables). Our interest is in the cross-correlations among the latent variables which, in neural recordings, may capture the flow of information from one brain region to another. Simulations show that LDFA-H outperforms existing methods in the sense that it captures target factors even when within-region correlation due to noise dominates cross-region correlation. We applied our method to local field potential (LFP) recordings from 192 electrodes in Prefrontal Cortex (PFC) and visual area V4 during a memory-guided saccade task. The results capture time-varying lead-lag dependencies between PFC and V4, and display the associated spatial distribution of the signals.

Inference of synaptic connectivity and external variability in neural microcircuits

A major goal in neuroscience is to estimate neural connectivity from large scale extracellular recordings of neural activity in vivo. This is challenging in part because any such activity is modulated by the unmeasured external synaptic input to the network, known as the common input problem. Many different measures of functional connectivity have been proposed in the literature, but their direct relationship to synaptic connectivity is often assumed or ignored. For in vivo data, measurements of this relationship would require a knowledge of ground truth connectivity, which is nearly always unavailable. Instead, many studies use in silico simulations as benchmarks for investigation, but such approaches necessarily rely upon a variety of simplifying assumptions about the simulated network and can depend on numerous simulation parameters. We combine neuronal network simulations, mathematical analysis, and calcium imaging data to address the question of when and how functional connectivity, synaptic connectivity, and latent external input variability can be untangled. We show numerically and analytically that, even though the precision matrix of recorded spiking activity does not uniquely determine synaptic connectivity, it is in practice often closely related to synaptic connectivity. This relation becomes more pronounced when the spatial structure of neuronal variability is jointly considered.

ADJUSTED REGULARIZATION IN LATENT GRAPHICAL MODELS: APPLICATION TO MULTIPLE-NEURON SPIKE COUNT DATA

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 ℓ 1-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.