Statistical Learning of Neuronal Functional Connectivity (original) (raw)
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Journal of Computational Neuroscience, 2013
One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions.
A Novel Sparse Group Gaussian Graphical Model for Functional Connectivity Estimation
Lecture Notes in Computer Science, 2013
The estimation of intra-subject functional connectivity is greatly complicated by the small sample size and complex noise structure in functional magnetic resonance imaging (fMRI) data. Pooling samples across subjects improves the conditioning of the estimation, but loses subject-specific connectivity information. In this paper, we propose a new sparse group Gaussian graphical model (SGGGM) that facilitates joint estimation of intra-subject and group-level connectivity. This is achieved by casting functional connectivity estimation as a regularized consensus optimization problem, in which information across subjects is aggregated in learning group-level connectivity and group information is propagated back in estimating intra-subject connectivity. On synthetic data, we show that incorporating group information using SGGGM significantly enhances intra-subject connectivity estimation over existing techniques. More accurate group-level connectivity is also obtained. On real data from a cohort of 60 subjects, we show that integrating intra-subject connectivity estimated with SGGGM significantly improves brain activation detection over connectivity priors derived from other graphical modeling approaches.
Bayesian inference of functional connectivity and network structure from spikes
Neural Systems and …, 2009
Current multi-electrode techniques enable the simultaneous recording of spikes from hundreds of neurons. To study neural plasticity and network structure it is desirable to infer the underlying functional connectivity between the recorded neurons. Functional connectivity is defined by a large number of parameters, which characterize how each neuron influences the other neurons. A Bayesian approach that combines information from the recorded spikes (likelihood) with prior beliefs about functional connectivity (prior) can improve inference of these parameters and reduce overfitting. Recent studies have used likelihood functions based on the statistics of point-processes and a prior that captures the sparseness of neural connections. Here we include a prior that captures the empirical finding that interactions tend to vary smoothly in time. We show that this method can successfully infer connectivity patterns in simulated data and apply the algorithm to spike data recorded from primary motor (M1) and premotor (PMd) cortices of a monkey. Finally, we present a new approach to studying structure in inferred connections based on a Bayesian clustering algorithm. Groups of neurons in M1 and PMd show common patterns of input and output that may correspond to functional assemblies.
Frontiers in Neuroanatomy, 2014
Despite many structural and functional aspects of the brain organization have been extensively studied in neuroscience, we are still far from a clear understanding of the intricate structure-function interactions occurring in the multi-layered brain architecture, where billions of different neurons are involved. Although structure and function can individually convey a large amount of information, only a combined study of these two aspects can probably shade light on how brain circuits develop and operate at the cellular scale. Here, we propose a novel approach for refining functional connectivity estimates within neuronal networks using the structural connectivity as prior. This is done at the mesoscale, dealing with thousands of neurons while reaching, at the microscale, an unprecedented cellular resolution. The High-Density Micro Electrode Array (HD-MEA) technology, combined with fluorescence microscopy, offers the unique opportunity to acquire structural and functional data from large neuronal cultures approaching the granularity of the single cell. In this work, an advanced method based on probabilistic directional features and heat propagation is introduced to estimate the structural connectivity from the fluorescence image while functional connectivity graphs are obtained from the cross-correlation analysis of the spiking activity. Structural and functional information are then integrated by reweighting the functional connectivity graph based on the structural prior. Results show that the resulting functional connectivity estimates are more coherent with the network topology, as compared to standard measures purely based on cross-correlations and spatio-temporal filters. We finally use the obtained results to gain some insights on which features of the functional activity are more relevant to characterize actual neuronal interactions.
Ising Models for Inferring Network Structure From Spike Data
2011
Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of a simple model network to make its spike trains resemble the data as much as possible. The connections in the model network can then give us an idea of how the real neurons that generated the data are connected and how they influence each other. In this chapter we describe how to do this for the simplest kind of model: an Ising network. We derive algorithms for finding the best model connection strengths for fitting a given data set, as well as faster approximate algorithms based on mean field theory. We test the performance of these algorithms on data from model networks and experiments.
Sparse Predictive Structure of Deconvolved Functional Brain Networks
The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated highdimensional structures between experimental conditions or groups shuns typical mass univariate methods. Furthermore most network estimation methods cannot distinguish between real and spurious correlation arising from the convolution due to nodes' interaction, which thus introduces additional noise in the data. We propose a machine learning pipeline aimed at identifying multivariate differences between brain networks associated to different experimental conditions. The pipeline (1) leverages the deconvolved individual contribution of each edge and (2) maps the task into a sparse classification problem in order to construct the associated "sparse deconvolved predictive network", i.e. a graph with the same nodes of those compared but whose edge weights are defined by their relevance for out of sample predictions in classification. We present an application of the proposed method by decoding the covert attention direction (left or right) based on the single-trial functional connectivity matrix extracted from high-frequency magnetoencephalography (MEG) data. Our results demonstrate how network deconvolution matched with sparse classification methods outperforms typical approaches for MEG decoding.
A generative model of whole-brain effective connectivity
NeuroImage, 2018
The development of whole-brain models that can infer effective (directed) connection strengths from fMRI data represents a central challenge for computational neuroimaging. A recently introduced generative model of fMRI data, regression dynamic causal modeling (rDCM), moves towards this goal as it scales gracefully to very large networks. However, large-scale networks with thousands of connections are difficult to interpret; additionally, one typically lacks information (data points per free parameter) for precise estimation of all model parameters. This paper introduces sparsity constraints to the variational Bayesian framework of rDCM as a solution to these problems in the domain of task-based fMRI. This sparse rDCM approach enables highly efficient effective connectivity analyses in whole-brain networks and does not require a priori assumptions about the network's connectivity structure but prunes fully (all-to-all) connected networks as part of model inversion. Following the derivation of the variational Bayesian update equations for sparse rDCM, we use both simulated and empirical data to assess the face validity of the model. In particular, we show that it is feasible to infer effective connection strengths from fMRI data using a network with more than 100 regions and 10,000 connections. This demonstrates the feasibility of whole-brain inference on effective connectivity from fMRI data-in single subjects and with a run-time below 1 min when using parallelized code. We anticipate that sparse rDCM may find useful application in connectomics and clinical neuromodeling-for example, for phenotyping individual patients in terms of whole-brain network structure.
Connectivity-informed fMRI activation detection,” Lecture notes in computer science
2011
A growing interest has emerged in studying the correlation structure of spontaneous and task-induced brain activity to elucidate the functional architecture of the brain. In particular, functional networks estimated from resting state (RS) data were shown to exhibit high resemblance to those evoked by stimuli. Motivated by these findings, we propose a novel generative model that integrates RS-connectivity and stimulus-evoked responses under a unified analytical framework. Our model permits exact closed-form solutions for both the posterior activation effect estimates and the model evidence. To learn RS networks, graphical LASSO and the oracle approximating shrinkage technique are deployed. On a cohort of 65 subjects, we demonstrate increased sensitivity in fMRI activation detection using our connectivity-informed model over the standard univariate approach. Our results thus provide further evidence for the presence of an intrinsic relationship between brain activity during rest and task, the exploitation of which enables higher detection power in task-driven studies.
Multivariate Brain Functional Connectivity Through Regularized Estimators
Frontiers in Neuroscience, 2020
Functional connectivity analyses are typically based on matrices containing bivariate measures of covariability, such as correlations. Although this has been a fruitful approach, it may not be the optimal strategy to fully explore the complex associations underlying brain activity. Here, we propose extending connectivity to multivariate functions relating to the temporal dynamics of a region with the rest of the brain. The main technical challenges of such an approach are multidimensionality and its associated risk of overfitting or even the non-uniqueness of model solutions. To minimize these risks, and as an alternative to the more common dimensionality reduction methods, we propose using two regularized multivariate connectivity models. On the one hand, simple linear functions of all brain nodes were fitted with ridge regression. On the other hand, a more flexible approach to avoid linearity and additivity assumptions was implemented through random forest regression. Similarities...