Modeling statistical dependencies in multi-region spike train data.

Neural computations underlying cognition and behavior rely on the coordination of neural activity across multiple brain areas. Understanding how brain areas interact to process information or generate behavior is thus a central question in neuroscience. Here we provide an overview of statistical approaches for characterizing statistical dependencies in multi-region spike train recordings. We focus on two classes of models in particular: regression-based models and shared latent variable models. Regression-based models describe interactions in terms of a directed transformation of information from one region to another. Shared latent variable models, on the other hand, seek to describe interactions in terms of sources that capture common fluctuations in spiking activity across regions. We discuss the advantages and limitations of each of these approaches and future directions for the field. We intend this review to be an introduction to the statistical methods in multi-region models for computational neuroscientists and experimentalists alike.

Discrete Stepping and Nonlinear Ramping Dynamics Underlie Spiking Responses of LIP Neurons during Decision-Making.

Neurons in LIP exhibit ramping trial-averaged responses during decision-making. Recent work sparked debate over whether single-trial LIP spike trains are better described by discrete "stepping" or continuous "ramping" dynamics. We extended latent dynamical spike train models and used Bayesian model comparison to address this controversy. First, we incorporated non-Poisson spiking into both models and found that more neurons were better described by stepping than ramping, even when conditioned on evidence or choice. Second, we extended the ramping model to include a non-zero baseline and compressive output nonlinearity. This model accounted for roughly as many neurons as the stepping model. However, latent dynamics inferred under this model exhibited high diffusion variance for many neurons, softening the distinction between continuous and discrete dynamics. Results generalized to additional datasets, demonstrating that substantial fractions of neurons are well described by either stepping or nonlinear ramping, which may be less categorically distinct than the original labels implied.

Scaling the Poisson GLM to massive neural datasets through polynomial approximations.

Recent advances in recording technologies have allowed neuroscientists to record simultaneous spiking activity from hundreds to thousands of neurons in multiple brain regions. Such large-scale recordings pose a major challenge to existing statistical methods for neural data analysis. Here we develop highly scalable approximate inference methods for Poisson generalized linear models (GLMs) that require only a single pass over the data. Our approach relies on a recently proposed method for obtaining approximate sufficient statistics for GLMs using polynomial approximations [7], which we adapt to the Poisson GLM setting. We focus on inference using quadratic approximations to nonlinear terms in the Poisson GLM log-likelihood with Gaussian priors, for which we derive closed-form solutions to the approximate maximum likelihood and MAP estimates, posterior distribution, and marginal likelihood. We introduce an adaptive procedure to select the polynomial approximation interval and show that the resulting method allows for efficient and accurate inference and regularization of high-dimensional parameters. We use the quadratic estimator to fit a fully-coupled Poisson GLM to spike train data recorded from 831 neurons across five regions of the mouse brain for a duration of 41 minutes, binned at 1 ms resolution. Across all neurons, this model is fit to over 2 billion spike count bins and identifies fine-timescale statistical dependencies between neurons within and across cortical and subcortical areas.

A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG.

Functional connectivity (FC), defined as the statistical dependency between distinct brain regions, has been an important tool in understanding cognitive brain processes. Most of the current works in FC have focused on the assumption of temporally stationary networks. However, recent empirical work indicates that FC is dynamic due to cognitive functions. GOAL: The purpose of this paper is to understand the dynamics of FC for understanding the formation and dissolution of networks of the brain. METHOD: In this paper, we introduce a two-step approach to characterize the dynamics of functional connectivity networks (FCNs) by first identifying change points at which the network connectivity across subjects shows significant changes and then summarizing the FCNs between consecutive change points. The proposed approach is based on a tensor representation of FCNs across time and subjects yielding a four-mode tensor. The change points are identified using a subspace distance measure on low-rank approximations to the tensor at each time point. The network summarization is then obtained through tensor-matrix projections across the subject and time modes. RESULTS: The proposed framework is applied to electroencephalogram (EEG) data collected during a cognitive control task. The detected change-points are consistent with a priori known ERN interval. The results show significant connectivities in medial-frontal regions which are consistent with widely observed ERN amplitude measures. CONCLUSION: The tensor-based method outperforms conventional matrix-based methods such as singular value decomposition in terms of both change-point detection and state summarization. SIGNIFICANCE: The proposed tensor-based method captures the topological structure of FCNs which provides more accurate change-point-detection and state summarization.

A graph theoretic approach to dynamic functional connectivity tracking and network state identification.

With the advances in neuroimaging technology, it is now possible to measure human brain activity with increasing temporal and spatial resolution. This vast amount of spatio-temporal data requires the development of computational methods capable of building an integrated picture of the functional networks for a better understanding of the healthy and diseased brain [1]. Although the construction of these networks from neuroimaging data is well-established [2], current approaches are limited to the characterization of the global topology of static networks where the links between different brain regions represent average connectivity over a long time period [3], [2]. Recent studies suggest that human cognition arises from the rapid formation and dissociation of synchronized neural activity on short time scales in the order of milliseconds [4]. There is a strong need for new electroencephalogram (EEG)-based analytic frameworks for monitoring dynamic functional network activity. In this paper, we propose a graph theoretic approach for tracking the changing topology of functional connectivity networks across time. First, we introduce an event detection algorithm based on node level feature extraction and principal components analysis of time-dependent node correlation matrices. Then, we propose a k-means based clustering approach to characterize each time interval with the most common connectivity states. Finally, the proposed methodology is applied to the study of the dynamics of functional connectivity networks during error-related negativity (ERN).