Sparse network estimation for dynamical spatio-temporal array models

Neural field models represent neuronal communication on a population level via synaptic weight functions. Using voltage sensitive dye (VSD) imaging it is possible to obtain measurements of neural fields with a relatively high spatial and temporal resolution. The synaptic weight functions represent functional connectivity in the brain and give rise to a spatio-temporal dependence structure. We present a stochastic functional differential equation for modeling neural fields, which leads to a vector autoregressive model of the data via basis expansions of the synaptic weight functions and time and space discretization. Fitting the model to data is a pratical challenge as this represents a large scale regression problem. By using a 1-norm penalty in combination with localized basis functions it is possible to learn a sparse network representation of the functional connectivity of the brain, but still, the explicit construction of a design matrix can be computationally prohibitive. We demonstrate that by using tensor product basis expansions, the computation of the penalized estimator via a proximal gradient algorithm becomes feasible. It is crucial for the computations that the data is organized in an array as is the case for the three dimensional VSD imaging data. This allows for the use of array arithmetic that is both memory and time efficient.The proposed method is implemented and showcased in the R package dynamo available from CRAN.

• Publication year

  2018

• Venue

  Journal of Multivariate Analysis

• Publication date

  2018-02-25

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/J.JMVA.2019.104532arXiv 1802.08982
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Penalized Estimation in Large-Scale Generalized Linear Array Models

  2015influential reference
• Stochastic neural field equations: a rigorous footing

  2013cited by this paper
• Dynamic causal modeling with neural fields

  2012cited by this paper
• Spatiotemporal dynamics of continuum neural fields

  2012cited by this paper
• Sparse Vector Autoregressive Modeling

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• Stochastic Differential Equations in Banach Spaces: Decoupling, Delay Equations, and Approximations in Space and Time

  2012influential reference
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  2012cited by this paper
• Front Propagation in Stochastic Neural Fields

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  2011cited by this paper
• Sparse High Dimensional Models in Economics.

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• Sparse Multivariate Regression With Covariance Estimation

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  2010cited by this paper
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  2009influential reference
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  2009cited by this paper
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• Inverse Problems in Neural Field Theory

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• Stochastic Equations in Infinite Dimensions

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  2006influential reference
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• Estimating brain functional connectivity with sparse multivariate autoregression

  2005cited by this paper
• Organization, development and function of complex brain networks.

  2004cited by this paper
• Weak approximation of stochastic differential delay equations

  2001influential reference
• Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

  2000cited by this paper
• Stochastic Differential Equations and Applications

  1998cited by this paper
• Stochastic evolution equations with a spatially homogeneous Wiener process

  1997cited by this paper
• Regression Shrinkage and Selection via the Lasso

  1996cited by this paper
• Efficient vector and parallel manipulation of tensor products

  1996influential reference
• Block-relaxation Algorithms in Statistics

  1994cited by this paper
• Efficient Computer Manipulation of Tensor Products

  1979cited by this paper

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