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Neural field models represent neuronal communication on a population levelvia synaptic weight functions. Using voltage sensitive dye (VSD) imaging it ispossible to obtain measurements of neural fields with a relatively high spatialand temporal resolution. The synaptic weight functions represent functionalconnectivity in the brain and give rise to a spatio-temporal dependencestructure. We present a stochastic functional differential equation formodeling neural fields, which leads to a vector autoregressive model of thedata via basis expansions of the synaptic weight functions and time and spacediscretization. Fitting the model to data is a pratical challenge as thisrepresents a large scale regression problem. By using a 1-norm penalty incombination with localized basis functions it is possible to learn a sparsenetwork representation of the functional connectivity of the brain, but still,the explicit construction of a design matrix can be computationallyprohibitive. We demonstrate that by using tensor product basis expansions, thecomputation of the penalized estimator via a proximal gradient algorithmbecomes feasible. It is crucial for the computations that the data is organizedin an array as is the case for the three dimensional VSD imaging data. Thisallows for the use of array arithmetic that is both memory and timeefficient.The proposed method is implemented and showcased in the R packagedynamo available from CRAN.

Sparse Network Estimation for Dynamical Spatio-temporal Array Models