Sparse Network Estimation for Dynamical Spatio-temporal Array Models

TL;DR

This paper introduces a sparse network estimation method for neural field models using tensor basis expansions and a proximal gradient algorithm, enabling efficient analysis of high-resolution brain imaging data.

Contribution

It presents a novel approach combining basis expansions, sparsity penalties, and array computations for scalable neural connectivity inference from VSD imaging data.

Findings

Efficient computation of sparse neural networks using tensor basis and proximal algorithms.

Application to VSD imaging data demonstrates practical feasibility.

Implementation available in R package 'dynamo'.

Abstract

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.