Semi-Analytic Nonparametric Bayesian Inference for Spike-Spike Neuronal Connectivity

Ambrogioni, Luca; Pwj, Ebel; Hinne, Max; Güçlü, Umut; Maj, van Gerven; Maris, Eric

doi:10.1101/340489

Cited by 6 publications

(9 citation statements)

References 16 publications

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“…Generally speaking, in Bayesian statistics, approximate inference under different divergences is a field of active research, although the primary focus is not on dynamic models. Some examples include α-divergence [15], χ-divergence [16], Wasserstein divergence [17], and Renyi divergence [18]. In particular, there are two papers that use an energy function related to ours.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Kalman Filtering With Divergence Minimization

Gultekin

Paisley

2017

IEEE Trans. Signal Process.

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Abstract-We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and α-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the α-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Kalman Filtering With Divergence Minimization

Gultekin

Paisley

2017

IEEE Trans. Signal Process.

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“…Only recently has a novel variant of BNMs been proposed in which brain dynamics during the "resting state" are described by an Ornstein-Uhlenbeck process and which provided maximum likelihood estimates of directed connection strengths in networks comprising up to 68 regions (Gilson et al, 2016(Gilson et al, , 2017Rolls et al, 2018;Senden et al, 2018). Additionally, other variants of connectivity analyses have been proposed that might potentially enable the investigation of larger networks (Ambrogioni et al, 2017;Prando et al, 2017).In contrast, dynamic causal modeling (DCM) uses a Bayesian framework to compute the posterior distribution over effective connectivity parameters. DCM was originally devised for fMRI and later extended to other modalities like M/EEG (David et al, 2006).…”

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confidence: 99%

A generative model of whole-brain effective connectivity

et al. 2018

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A B S T R A C TThe 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 wholebrain network structure. IntroductionThe human brain comprises multiple levels of organization, with cognitive functions arising from the interplay of functional specialization and integration (Sporns, 2013;Tononi et al., 1994). With the advent of non-invasive neuroimaging techniques, such as functional magnetic resonance imaging (fMRI), researchers have begun to systematically study these fundamental properties of human brain organization. While early neuroimaging studies focused on localizing cognitive processes to specific brain regions, contemporary studies are commonly concerned with functional integration of these regions; this requires analyzing brain connectivity (Smith, 2012). In addition to analyses of structural (anatomical) connections, assessments of functional connectivity (statistical dependencies between network nodes) play a major role. Particularly, functional connectivity has been used frequently for studying the functional organization of large (whole-brain) networks both in tasks and in the "resting state" (i.e., unconstrained cognition in the absence of external perturbations). Various methods have been proposed (for a comprehensive review, see Karahanoglu and Van De Ville, 2017), ranging from conventional correlation or coherence analyses which assume stationarity (Fox et al., 2005) to sliding-window correlation analyses that can capture dyna...

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“…Understanding effective connectivity has long been a central challenge in neuroscience [1,[50][51][52]. The identification of connectivity has garnered significant interest in recent years, primarily due to advancements enabling the simultaneous recording of a vast number of neurons [53][54][55][56]. Essentially, we now exploit the understanding that synaptic connections induce voltage fluctuations capable of triggering postsynaptic action potentials.…”

Section: Discussionmentioning

confidence: 99%

Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator

Izzi,

Ferreira,

Girardi

et al. 2024

Brain Sciences

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Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test—no causal influence—requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

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Semi-Analytic Nonparametric Bayesian Inference for Spike-Spike Neuronal Connectivity

Cited by 6 publications

References 16 publications

Nonlinear Kalman Filtering With Divergence Minimization

Nonlinear Kalman Filtering With Divergence Minimization

A generative model of whole-brain effective connectivity

Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator

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